Doc: Define authoritative design document hygiene rules

Feat: Add post-tone-map mesh diagnostics with RGBA overlays
Color antialiased half-edges by ray outcome with configurable Catppuccin colors and default opacity 0.5. Rasterize premultiplied RGBA8 overlays on the producer and composite in place after writing the clean image. Keep single-frame, movie, and replay output consistent. Add overlay, CLI, and queue ownership regressions and document the final output architecture.
2026-10-10 01:50:42 -04:00 · 2026-10-10 01:46:32 -04:00 · 2026-10-09 00:17:39 -04:00 · 2026-10-09 00:15:02 -04:00 · 2026-10-09 00:14:54 -04:00 · 2026-10-08 05:07:34 -04:00
600 changed files with 397275 additions and 1080 deletions
@@ -1,5 +1,6 @@
 /build
 /output
+/local
 /scripts/__pycache__
 assets/2mass/processed/all_sky/*.csv
 assets/2mass/processed/all_sky/.done/
@@ -0,0 +1,70 @@
+---
+description: 审查本项目代码变更，核实功能、修复与性能进展；复用已完成的完整测试，仅做受限专项验证，按实际影响报告可操作问题。
+mode: subagent
+model: openai/gpt-6.1-sol
+variant: high
+options:
+  reasoningEffort: high
+permission:
+  edit: deny
+  task: deny
+  bash:
+    "*": allow
+    "make test*": deny
+    "make * test*": deny
+    "git add*": deny
+    "git commit*": deny
+    "git push*": deny
+    "git reset*": deny
+    "git checkout*": deny
+    "git restore*": deny
+    "git clean*": deny
+---
+
+# 角色与目标
+
+你是本项目专属的 `code-reviewer`。进行独立、基于证据、与实际风险相称的 code review。你的职责是核实实现与宣称是否一致，发现值得修复的具体缺陷，并提出低复杂度、低开销的修正方向。
+
+默认只审查，不修改源码、测试、文档或配置，不暂存、提交或重置 Git，不启动其他 subagent。Shell 同样受只读审查约束，不得借助脚本、重定向或其他命令绕过编辑权限。仅允许必要的专项编译/测试产生构建产物；临时探针与日志放在 `/tmp/opencode/`，遵守项目的路径与仓库卫生规则。
+
+回复使用用户最新消息的语言；面向父 agent 的结论必须自包含，不能假定父 agent 已看到你的工具输出。
+
+# 审查范围与进展核实
+
+1. 先读项目 `AGENTS.md`，再读 `nr_spacetime_movie_renderer_design.md` 中与变更相关的章节。遵循当前权威设计，不把自己的偏好当作项目要求；文档与代码冲突时说明冲突及依据。
+2. 确认要求审查的范围：工作区变更、指定 commit/range 或相对指定 base 的分支变更。父 agent 给出的总结只作为待核实的线索，不作为实现证据。
+3. 用 `git status --short`、相关 `git diff`（包括 staged 与 unstaged）及必要的提交历史确认真实状态。新文件未必出现在普通 diff 中，必须检查审查范围内的 untracked 文件；已提交实现也不能因工作区 diff 为空而忽略。不得把无关的既有用户改动归因于本次实现。
+4. 阅读变更的完整上下文，沿实际调用链检查入口、配置、数据流、错误处理和输出。新增函数、字段、CLI 选项或测试文件的存在不等于功能已接通；排查未调用实现、stub、TODO、错误的默认路径、遗漏的 build/test 注册以及仅覆盖理想路径的测试。
+5. 对父 agent/用户明确描述的关键进展逐项核实，给出“代码支持”“部分支持”“与代码不符”或“证据不足”。区分已实现、已接入、已验证与性能已测量，避免把其中一项等同于全部完成。提供具体文件位置、调用链或日志证据；无法验证时如实说明，不推断其一定失败。
+6. bug 修复要检查原触发条件是否真的被阻断、相关分支是否仍有相同问题；性能提升要检查热点路径确实使用优化、工作量和结果语义是否可比，以及是否存在 fallback 或开销转移。未经测量只能确认优化实现，不能确认速度提升；已有有效 benchmark 足以支撑其测量范围内的结论，不强求扩展到所有平台与输入。
+7. 若审查期间代码继续变化，在结束前确认相关 diff 状态。结论限定于实际检查的版本；发现关键变化时仅复查受影响部分，不重启整轮审查或完整测试。
+
+# 测试复用与受限验证（硬性约束）
+
+- 父 agent 或用户明确声明已完成的 `make test` 类完整测试，必须复用该信息，绝不得重新完整运行。该约束覆盖带不同 flags 的同一 suite、其他完整测试入口、clean/rebuild 后重跑，以及拆成多个专项命令累计重跑整个 suite 等等价方式。不能为了“更放心”“独立确认”或补齐自己的测试记录而重跑。
+- 明确区分“父 agent/用户报告完成”“已查看原始日志”和“本 reviewer 亲自执行”。“完成”不自动等于“通过”；没有明确结果就注明结果未提供。缺少日志不构成不信任声明或重新完整测试的理由，可以读取已有日志或指出有限的证据缺口。
+- 即使没有完整测试声明，本 reviewer 也只运行受限规模的专项验证。需要完整 suite 时，将必要性与具体缺口交回父 agent/用户，不自行运行。配置中的命令拦截仅是辅助，不能利用命令包装、别名、脚本或其他工具绕过本节规则。
+- 优先静态检查和既有测试/benchmark 结果。仅当某个具体疑点不能由这些证据解决时，才选择直接针对疑点的最小测试、现有测试的单例/过滤子集或小型复现。不要为样式、注释或与生产逻辑无关的低影响变更运行测试。
+- 运行前先阅读 Makefile/测试入口，确认目标的依赖、默认数据规模和实际执行范围，防止“单个目标”隐式触发完整 suite、昂贵渲染或完整 benchmark。构建仅限必要目标，不做 `make clean` 或无关的全量重建。
+- 每次先明确要验证的假设、命令和规模上限。默认整轮审查最多 3 次专项执行，每次超时不超过 60 秒，累计运行预算不超过 120 秒；使用小 fixture、低分辨率、少量 ray/样本、有限线程。父 agent/用户可以指定更合适的专项预算，但这不解除完整测试禁令。
+- 超时、资源不足或无法在预算内复现时停止，报告验证限制，不将其直接判为产品失败。一次验证解决疑点后停止；只有新证据或失败需要解释时才继续使用剩余预算，不无限追加专项测试。
+- 性能审查优先读取已有原始输出，核对命令、输入、build/cache、线程、工作量、fallback 和数值结果。确有必要时仅做小规模、同条件的对照，不将微基准结论泛化到完整 4K 视频工作负载。
+
+# 风险校准与建议原则
+
+- 正式 finding 必须有具体触发条件、可达路径和实际影响。先检查调用方保证、现有 guard、输入约束、数值容差、fallback 与测试，再下结论。不能仅凭“理论上可能”声称崩溃、数据损坏、物理失真或严重性能退化。
+- 严重性根据实际影响、适用范围与触发可能性评估：P0 为已证实且广泛阻断的紧急问题；P1 为主要功能/物理正确性严重受损；P2 为明确可达、局部但值得修复的问题；P3 为低影响改进。P0/P1 必须有强证据，不因措辞耸动提高级别。
+- 对实际上不会造成问题、已经由不变量保证安全或仅属个人风格偏好的点，不报缺陷。低严重性点不得夸大为 blocker；可选建议与正式缺陷分开，默认不堆积 nitpick，也不为了凑数制造问题。可以明确给出“未发现值得报告的缺陷”。
+- 尚未证实的疑点作为待确认问题，写明缺少什么证据，不包装成已证实 bug。缺少某项测试本身不自动构成缺陷；说明它是否留下了与本次变更直接相关的、实质性的验证缺口。
+- 优先最小局部修正和适用的专项 regression，不要求为低风险假设增加复杂状态机、全局防御性扫描、细粒度锁、重复热路径检查或大规模架构重写。建议成本必须与风险相称。
+- 若确实存在严重正确性问题，而解决它必然涉及复杂度或性能代价，应如实说明证据与权衡；不隐藏问题，也不未经论证地指定最昂贵的方案。性能影响要有复杂度分析或测量支持，不使用无依据的倍数/百分比。
+- 聚焦本次变更引入或影响的问题。既有问题仅在直接阻碍本次目标时提出，并明确注明它并非本次新增。
+
+# 输出格式
+
+1. **结论与范围**：简述检查的版本/变更范围，是否发现需要修复的问题，以及重要限制。测试通过不是“没有 bug”的证明；审查未发现问题也不等于全系统认证。
+2. **Findings**：按严重性排序。每项包含 `[P1/P2/…] 简洁标题`、最小且相关的 `文件:行号`、触发条件、代码证据、实际影响与最小修正方向。合并同一根因，避免重复计数。不确定问题单列，不放入已证实 findings。
+3. **进展核实**：对关键宣称列出“宣称 → 核实状态 → 证据/缺口”，特别区分实现、集成、测试和性能测量；用实际状态修正过于乐观的描述，也承认已经充分完成的部分。
+4. **验证记录**：列出复用的完整测试声明/日志、自己实际执行的专项命令及规模/结果、未执行验证的具体限制。绝不声称自己运行了只由他人报告的测试。
+
+保持报告精炼、可操作；没有某类内容时直接省略或用一句话说明，不输出冗长模板或泛化风险清单。
@@ -0,0 +1,32 @@
+---
+description: 搭配 GPT 父 agent 执行技术路线已初步敲定的明确任务。委派前，父 agent 必须提供明确、完整、详细、可执行的计划，包含目标、范围、已确定的技术方案、步骤、约束及验收方法；尚需探索、路线选择或关键决策的任务不得交给本 agent。有疑问时暂停并询问父 agent，否则按计划完整推进。
+mode: subagent
+model: deepseek/deepseek-flash
+---
+
+# 角色与分工
+
+你是 `deepseek-coder`，作为 GPT 父 agent 的执行搭档，负责落实已经初步确定技术路线的明确任务。父 agent 负责探索、技术决策与计划制定，你负责按计划完成实现和验证，不自行承担未明确的路线选择或扩大任务范围。
+
+# 开始前
+
+1. 阅读当前适用的 `AGENTS.md`（包括相关目录的局部指引），以及它们和任务计划引用的设计文档、规范及必要的代码上下文，从这些文件获取实时要求。不要假定项目架构、模块边界或技术约定固定不变。
+2. 检查父 agent 提供的计划是否明确、完整、详细且可执行：应包含目标与交付物、修改范围、已确定的技术方案、实施步骤、约束、依赖和验收方法。简单任务无需冗长模板，但不能缺少执行所需的信息。
+3. 检查相关工作区状态，识别已有用户或其他 agent 的改动；不得覆盖、撤销或清理非你产生的修改。
+
+# 疑问与阻塞
+
+- 只要出现影响执行的疑问，就暂停并向父 agent 询问，包括需求含糊、计划缺漏、关键参数未定、存在需要取舍的多个方案、计划与实时指引或代码冲突，以及验证失败后需要改变技术路线。
+- 说明疑问或阻塞、相关证据、需要父 agent 决定的具体事项，以及已经完成和尚未完成的部分。向父 agent 返回澄清请求，等待其明确答复后再继续；不要以猜测代替确认，也不要直接要求最终用户决策。
+- 不擅自重新设计、替换已确定方案、降低验收标准或开展计划外重构。计划内不改变语义和路线的普通实现细节可依照现有代码惯例处理，无需逐项请示。
+
+# 执行与验证
+
+1. 没有疑问或阻塞时，按照计划持续推进全部步骤，完成实现、必要的接入、测试与要求的文档更新；不要只给出建议、留下占位实现，或在部分完成后无故停止。
+2. 遵守实时项目指引及现有代码风格，保持修改聚焦，只实施计划授权的内容。不得擅自委派其他 agent、提交或推送代码，除非父 agent 明确授权。
+3. 按计划执行验证并记录实际结果。失败时先做计划范围内的定位；若修复需要新决策，按上述规则暂停询问。不能通过跳过失败、修改预期或弱化测试来宣称完成。
+4. 如遇工具、权限、环境或资源限制，明确报告限制及其对交付的影响，不把未执行或未通过的验证描述为成功。
+
+# 向父 agent 交付
+
+使用父 agent 要求的语言，默认跟随用户最新消息的语言。报告应自包含，简明列出完成内容、涉及文件、实际运行的验证命令与结果，以及剩余问题或阻塞。明确区分已完成、未完成和未经验证的事项；不能假定父 agent 已看过你的工具输出。
@@ -59,9 +59,18 @@ catalog 内部数据保留 `(direction, temperature, amplitude)`，而非 RGB。

 优先从 3+1 identities、已知 gauge RHS 或 temporal interpolant 的解析导数获得时间导数；不要为已有插值量另行做低阶 finite difference，也不要在 geodesic RHS 中计算不会使用的量。

-## 黑洞终止
+## 黑洞终止与暗终态

-对 moving-puncture 数据，生产渲染使用经 AH calibration 得到、保守地位于 apparent horizon 内部的 puncture-centered cutoff 判定捕获。不要假定每次生产演化都会运行昂贵的 AH finder。可在未来加入 common-horizon 终止优化，但不得改变物理分类。
+过去向光线不使用 horizon 内位置 cutoff、AH-calibrated puncture 小球或 armed/re-entry
+状态机判定正常物理捕获。正常 dark 终态来自相机相对局域能量增长
+`L - L0 = ln(alpha p^0) - ln(alpha p^0)|_start` 达到可配置阈值（默认 8，可用
+`--dark-threshold` 覆盖），对所有 spacetime backend 统一生效；这是已确定需求，
+不重置光子能量或频移。不同 dark reason 不制造 mesh seam。无法可靠推进的
+积分必须报告具体数值失败，不得改写成 capture。轨迹仍可信但计算配额耗尽时返回可重试的
+`UNRESOLVED/BUDGET_EXHAUSTED`；有限分辨率下的 triangle 决策中 `UUU` 必须追加计算，
+`UUD/UDD` 达到几何停止尺度后可近似标黑并保留 triangle provenance 与面积统计。
+不假定每次生产演化都会运行昂贵的 AH finder，也不依赖 capture sidecar。跨 chart、
+跨 region 或穿越视界本身不是暗终态。

 ## 开发与验证顺序

@@ -76,6 +85,23 @@ catalog 内部数据保留 `(direction, temperature, amplitude)`，而非 RGB。

 性能 benchmark 记录必须保留完整、可复制的命令及原始终端输出，不能只记录汇总耗时或吞吐量；输出中的 build/cache、输入加载、工作线程、处理数量与 fallback 等统计是后续正确归因性能变化的证据。

+## 权威设计文档卫生
+
+- 仓库级文档规则应具有跨任务适用性，不夹带单次任务的细节或案例。
+- `nr_spacetime_movie_renderer_design.md` 应简明描述当前确定的架构、物理与数值约定、模块边界、数据流及 ownership；尚未确定的问题须明确标为待验证。
+- 写最终设计，不写 agent 工作过程、对话经过、实现日记或备选方案淘汰史。已排除的临时设想不要改写成长期禁止条款；必要的物理与架构约束仍须保留。
+- 决策依据只保留理解设计所必需的简要理由。实验过程、性能数据及详细对照放到符合仓库卫生要求的独立记录中，设计文档按需引用。
+- 使用说明集中到 `usage.md`；README 保留面向使用者的简介与示例，避免在权威设计文档中重复罗列。
+- 设计变更应改写并整合原有相关章节，删除过时或重复表述，检查跨章节一致性；不要通过不断追加补充段落堆积历史。
+
+## 仓库卫生与短期产物
+
+只有对本项目有长期记录价值、且值得进入 public repo 的测试与 benchmark 才纳入 git。
+
+- 短期性能对照、一次性 A/B 原始日志、临时测量脚本、ad-hoc probe 与中间数据放到仓库根目录的 `local/`；该目录已被 `.gitignore` 排除，不进入版本库。
+- 追踪文件必须可复现：命令把输出、原始日志写到 `/tmp` 或 `local/` 是正常的，这些仓库外/被忽略的数据无需跟踪；但复现所需的输入、脚本、fixture 必须一并纳入 git（放在 `scripts/` 或 `benchmarks/<name>/`），不得依赖未跟踪的脚本或数据。
+- `benchmarks/` 只保留自包含、可复现的长期记录；`tests/` 只保留针对生产代码的回归测试，不保留为单次实验服务的一次性探针。
+
 ## 修改原则

 - 改动应保持 backend、observer、geodesic、movie mesh 与 optics 的职责分离。
@@ -85,6 +111,7 @@ catalog 内部数据保留 `(direction, temperature, amplitude)`，而非 RGB。

 ## Git 提交消息

+- Git 提交消息必须使用英文，包括标题和正文。
 - 提交消息必须以 category 开头，格式为 `Category: 简洁说明`。
 - 常用 category 包括 `Doc:`、`Fix:`、`Feat:`、`Makefile:` 等。
 - 对不属于修复或功能的普通小更新，使用所涉及的模块作为 category，例如 `Catalog:`、`Geodesic:`、`Spacetime:` 或 `Output:`。
@@ -29,20 +29,14 @@ else
 IMAGE_EXT := ppm
 endif

-COMMON_SOURCES := $(filter-out src/main.c src/spacetime_minkowski.c src/spacetime_schwarzschild.c,$(wildcard src/*.c))
+COMMON_SOURCES := $(filter-out src/main.c src/dummy_psf.c src/fast_psf_fftw.c src/spacetime_minkowski.c src/spacetime_schwarzschild.c src/spacetime_alcubierre.c,$(wildcard src/*.c))
 PROVIDER_SOURCE := src/spacetime_$(SPACETIME).c
 BUILD_DIR := build/$(BUILD_TYPE)
 TARGET_BASENAME := $(SPACETIME)_sky
 OBJECT_DIR := $(BUILD_DIR)/obj/$(SPACETIME)
 CORE_MINKOWSKI_SOURCES := $(COMMON_SOURCES) src/spacetime_minkowski.c
-TEST_TARGET := $(BUILD_DIR)/test_geodesic
-FRAME_TEST_TARGET := $(BUILD_DIR)/test_frame
-SCHWARZSCHILD_TEST_TARGET := $(BUILD_DIR)/test_schwarzschild
-OBSERVER_TRACK_TEST_TARGET := $(BUILD_DIR)/test_observer_track
-CATALOG_PREFETCH_TEST_TARGET := $(BUILD_DIR)/test_catalog_prefetch
-HIP_PSF_TEST_TARGET := $(BUILD_DIR)/test_hip_psf

-.PHONY: all backend clean run test hip-psf-test minkowski schwarzschild FORCE
+.PHONY: all backend clean run test tone-map-test sensor-bloom-test sensor-bloom-bench mesh-overlay-test hip-psf-test hip-psf-bench fast-psf-fftw-bench minkowski schwarzschild alcubierre FORCE

 ifneq ($(filter 0 1,$(PSF_EVENT_SINK)),$(PSF_EVENT_SINK))
 $(error Unknown PSF_EVENT_SINK '$(PSF_EVENT_SINK)'; choose 0 or 1)
@@ -51,19 +45,50 @@ BUILD_CPPFLAGS += -DFRAME_PSF_EVENT_SINK=$(PSF_EVENT_SINK)

 ifeq ($(PSF_BACKEND),cpu)
 RENDER_LINKER := $(CC)
+ifeq ($(shell pkg-config --exists fftw3_omp && echo yes),yes)
+CPU_FFTW_CPPFLAGS := -DFAST_PSF_FFTW $(shell pkg-config --cflags fftw3_omp)
+CPU_FFTW_LDLIBS := $(shell pkg-config --libs fftw3_omp)
+CPU_FFTW_SOURCES := src/fast_psf_fftw.c
+BUILD_CPPFLAGS += $(CPU_FFTW_CPPFLAGS)
+LDLIBS += $(CPU_FFTW_LDLIBS)
+else
+$(error PSF_BACKEND=cpu requires the FFTW OpenMP package 'fftw3_omp' (pkg-config --exists fftw3_omp). On Gentoo enable sci-libs/fftw[openmp].)
+endif
 else ifeq ($(PSF_BACKEND),hip)
 RENDER_LINKER := $(HIPCC)
 BUILD_CPPFLAGS += -DPSF_BACKEND_HIP
+else ifeq ($(PSF_BACKEND),dummy)
+RENDER_LINKER := $(CC)
+BUILD_CPPFLAGS += -DPSF_BACKEND_DUMMY
 else
-$(error Unknown PSF_BACKEND '$(PSF_BACKEND)'; choose cpu or hip)
+$(error Unknown PSF_BACKEND '$(PSF_BACKEND)'; choose cpu, hip, or dummy)
+endif
+
+# `make test` builds and runs the CPU regression suite.  The dummy and hip
+# backends do not build those binaries, so reject the goal explicitly instead of
+# silently reusing a stale test binary left by an earlier CPU build.
+ifneq ($(filter test test-reference-images,$(MAKECMDGOALS)),)
+ifneq ($(PSF_BACKEND),cpu)
+$(error make test requires PSF_BACKEND=cpu)
+endif
+endif
+
+# psf-capture is a CPU producer diagnostic; the dummy and hip backends do not
+# provide the producer/frame symbols it links.
+ifneq ($(filter psf-capture,$(MAKECMDGOALS)),)
+ifneq ($(PSF_BACKEND),cpu)
+$(error psf-capture requires PSF_BACKEND=cpu)
+endif
 endif

 ifeq ($(SPACETIME),minkowski)
 BACKEND_CPPFLAGS := -DSPACETIME_MINKOWSKI
 else ifeq ($(SPACETIME),schwarzschild)
 BACKEND_CPPFLAGS := -DSPACETIME_SCHWARZSCHILD
+else ifeq ($(SPACETIME),alcubierre)
+BACKEND_CPPFLAGS := -DSPACETIME_ALCUBIERRE
 else
-$(error Unknown SPACETIME '$(SPACETIME)'; choose minkowski or schwarzschild)
+$(error Unknown SPACETIME '$(SPACETIME)'; choose minkowski, schwarzschild, or alcubierre)
 endif

 ifeq ($(ENABLE_HDR),1)
@@ -76,12 +101,45 @@ else
 $(error Unknown ENABLE_HDR '$(ENABLE_HDR)'; choose 0 or 1)
 endif

+# Test binaries are namespaced by spacetime and build tag so that switching
+# PSF_BACKEND/ENABLE_HDR/PSF_EVENT_SINK cannot silently reuse a stale binary
+# built for a different backend.
+TEST_OUT_DIR := $(OBJECT_DIR)/$(HDR_BUILD_TAG)
+TEST_TARGET := $(TEST_OUT_DIR)/test_geodesic
+ADAPTIVE_GEODESIC_TEST_TARGET := $(TEST_OUT_DIR)/test_geodesic_adaptive
+ASYMPTOTIC_TEST_TARGET := $(TEST_OUT_DIR)/test_asymptotic
+ASYMPTOTIC_ENTRY_TEST_TARGET := $(TEST_OUT_DIR)/test_asymptotic_entry
+ASYMPTOTIC_QUADRATIC_TEST_TARGET := $(TEST_OUT_DIR)/test_asymptotic_quadratic
+ASYMPTOTIC_SCHWARZSCHILD_TEST_TARGET := $(TEST_OUT_DIR)/test_asymptotic_schwarzschild
+TERMINATION_ORACLE_TEST_TARGET := $(TEST_OUT_DIR)/test_termination_oracle
+FRAME_TEST_TARGET := $(TEST_OUT_DIR)/test_frame
+SCHWARZSCHILD_TEST_TARGET := $(TEST_OUT_DIR)/test_schwarzschild
+ALCUBIERRE_TEST_TARGET := $(TEST_OUT_DIR)/test_alcubierre
+OBSERVER_TRACK_TEST_TARGET := $(TEST_OUT_DIR)/test_observer_track
+CATALOG_PREFETCH_TEST_TARGET := $(TEST_OUT_DIR)/test_catalog_prefetch
+HIP_PSF_TEST_TARGET := $(TEST_OUT_DIR)/test_hip_psf
+HIP_PSF_BENCH_TARGET := $(TEST_OUT_DIR)/benchmark_hip_psf
+CAMERA_TEST_TARGETS := $(TEST_OUT_DIR)/test_observer_minkowski $(TEST_OUT_DIR)/test_observer_schwarzschild
+FAST_PSF_FFTW_TEST_TARGET := $(TEST_OUT_DIR)/test_fast_psf_fftw
+FAST_PSF_FFTW_BENCH_TARGET := $(TEST_OUT_DIR)/benchmark_fast_psf_fftw
+TONE_MAP_TEST_TARGET := $(TEST_OUT_DIR)/test_tone_map
+MOVIE_OUTPUT_TEST_TARGET := $(TEST_OUT_DIR)/test_movie_output
+SENSOR_BLOOM_TEST_TARGET := $(TEST_OUT_DIR)/test_sensor_bloom
+SENSOR_BLOOM_BENCH_TARGET := $(TEST_OUT_DIR)/benchmark_sensor_bloom
+MESH_OVERLAY_TEST_TARGET := $(TEST_OUT_DIR)/test_mesh_overlay
+
 ifeq ($(PSF_BACKEND),hip)
 TARGET := $(BUILD_DIR)/$(TARGET_BASENAME)_hip
+else ifeq ($(PSF_BACKEND),dummy)
+TARGET := $(BUILD_DIR)/$(TARGET_BASENAME)_dummy
 else
 TARGET := $(BUILD_DIR)/$(TARGET_BASENAME)
 endif
 RENDER_SOURCES := $(COMMON_SOURCES) $(PROVIDER_SOURCE) src/main.c
+RENDER_SOURCES += $(CPU_FFTW_SOURCES)
+ifeq ($(PSF_BACKEND),dummy)
+RENDER_SOURCES += src/dummy_psf.c
+endif
 RENDER_OBJECTS := $(patsubst %.c,$(OBJECT_DIR)/$(HDR_BUILD_TAG)/%.o,$(RENDER_SOURCES))
 ifeq ($(PSF_BACKEND),hip)
 HIP_PSF_OBJECT := $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/hip_psf.o
@@ -95,7 +153,7 @@ RENDER_DEPS := $(RENDER_OBJECTS:.o=.d)
 ifneq ($(filter command\ line environment environment\ override,$(origin SPACETIME)),)
 all: backend
 else
-all: minkowski schwarzschild
+all: minkowski schwarzschild alcubierre
 endif

 minkowski:
@@ -104,6 +162,9 @@ minkowski:
 schwarzschild:
 	$(MAKE) SPACETIME=schwarzschild ENABLE_HDR=$(ENABLE_HDR) backend

+alcubierre:
+	$(MAKE) SPACETIME=alcubierre ENABLE_HDR=$(ENABLE_HDR) backend
+
 # Build exactly the selected backend/configuration, e.g.
 # make SPACETIME=schwarzschild ENABLE_HDR=1 backend
 backend: $(TARGET)
@@ -128,42 +189,171 @@ $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/hip_psf.o: src/hip_psf.hip src/hip_psf.h src/
 # It requires PSF_BACKEND=hip and an actual HIP GPU agent at execution time.
 ifeq ($(PSF_BACKEND),hip)
 hip-psf-test: $(HIP_PSF_TEST_TARGET)
+hip-psf-bench: $(HIP_PSF_BENCH_TARGET)

-$(HIP_PSF_TEST_TARGET): tests/test_hip_psf.hip $(HIP_PSF_OBJECT) $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/optics.o | $(BUILD_DIR)
-	$(HIPCC) $(HIP_CXXFLAGS) $(OPENMP_FLAGS) -Isrc -x hip $< -x none $(filter-out $<,$^) $(LDLIBS) -o $@
+$(HIP_PSF_BENCH_TARGET): tests/benchmark_hip_psf.hip $(HIP_PSF_OBJECT) $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/optics.o | $(TEST_OUT_DIR)
+	$(HIPCC) $(HIP_CXXFLAGS) $(OPENMP_FLAGS) -Isrc -x hip $< -x none $(filter-out $<,$^) $(LDLIBS) $(HDR_LDLIBS) -o $@
+
+$(HIP_PSF_TEST_TARGET): tests/test_hip_psf.hip $(HIP_PSF_OBJECT) $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/optics.o | $(TEST_OUT_DIR)
+	$(HIPCC) $(HIP_CXXFLAGS) $(OPENMP_FLAGS) -Isrc -x hip $< -x none $(filter-out $<,$^) $(LDLIBS) $(HDR_LDLIBS) -o $@
 else
-hip-psf-test:
-	$(error hip-psf-test requires PSF_BACKEND=hip)
+hip-psf-test hip-psf-bench:
+	$(error HIP PSF checks require PSF_BACKEND=hip)
 endif

 run: $(TARGET)
 	mkdir -p output/imgs
 	./$(TARGET) --catalog assets/sky_grid_5deg.csv --output output/imgs/$(SPACETIME)_sky.$(IMAGE_EXT)

-$(TEST_TARGET): tests/test_geodesic.c $(CORE_MINKOWSKI_SOURCES) | $(BUILD_DIR)
+$(TEST_OUT_DIR): | $(BUILD_DIR)
+	mkdir -p $@
+
+$(TEST_TARGET): tests/test_geodesic.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
 	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@

-$(FRAME_TEST_TARGET): tests/test_frame.c $(CORE_MINKOWSKI_SOURCES) | $(BUILD_DIR)
+# Explicit adaptive DP5(4) core and RayPool regression.  The test textually
+# includes both analytic providers (renaming spacetime_create_default), so the
+# link line deliberately omits src/spacetime_{minkowski,schwarzschild}.c.
+$(ADAPTIVE_GEODESIC_TEST_TARGET): tests/test_geodesic_adaptive.c $(COMMON_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -DGEODESIC_EVENT_TESTING -Isrc $^ $(LDLIBS) -o $@
+
+$(ASYMPTOTIC_TEST_TARGET): tests/test_asymptotic.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
 	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@

-$(SCHWARZSCHILD_TEST_TARGET): tests/test_schwarzschild.c $(COMMON_SOURCES) src/spacetime_schwarzschild.c | $(BUILD_DIR)
+# The test includes asymptotic.c to cover its private floating-point kernel.
+$(ASYMPTOTIC_QUADRATIC_TEST_TARGET): tests/test_asymptotic_quadratic.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $(filter-out src/asymptotic.c,$^) $(LDLIBS) -o $@
+
+$(ASYMPTOTIC_SCHWARZSCHILD_TEST_TARGET): tests/test_asymptotic_schwarzschild.c $(COMMON_SOURCES) src/spacetime_schwarzschild.c $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -DSPACETIME_SCHWARZSCHILD -Isrc $^ $(LDLIBS) -o $@
+
+# Independent core regression for the backend-free numerical entry localizer.
+# It links only the new module and the shared spacetime dispatch wrapper: no
+# analytic backend, no geodesic integrator and no asymptotic.c are required,
+# so it stays exercisable independently of the route integration.
+$(ASYMPTOTIC_ENTRY_TEST_TARGET): tests/test_asymptotic_entry.c src/asymptotic_entry.c src/spacetime_common.c src/asymptotic_entry.h src/asymptotic.h src/geodesic.h src/spacetime.h src/observer.h | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/test_asymptotic_entry.c src/asymptotic_entry.c src/spacetime_common.c $(LDLIBS) -o $@
+
+$(FRAME_TEST_TARGET): tests/test_frame.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
 	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@

-$(OBSERVER_TRACK_TEST_TARGET): tests/test_observer_track.c $(COMMON_SOURCES) | $(BUILD_DIR)
+$(SCHWARZSCHILD_TEST_TARGET): tests/test_schwarzschild.c $(COMMON_SOURCES) src/spacetime_schwarzschild.c $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
 	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@

-$(CATALOG_PREFETCH_TEST_TARGET): tests/test_catalog_prefetch.c $(CORE_MINKOWSKI_SOURCES) | $(BUILD_DIR)
+# Independent physics oracle for the termination policy (plan P0); links the
+# analytic Schwarzschild backend and its exterior module.
+$(TERMINATION_ORACLE_TEST_TARGET): tests/test_termination_oracle.c $(COMMON_SOURCES) src/spacetime_schwarzschild.c $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -DSPACETIME_SCHWARZSCHILD -Isrc $^ $(LDLIBS) -o $@
+
+$(ALCUBIERRE_TEST_TARGET): tests/test_alcubierre.c $(COMMON_SOURCES) src/spacetime_alcubierre.c $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
 	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@

-test: $(TEST_TARGET) $(FRAME_TEST_TARGET) $(SCHWARZSCHILD_TEST_TARGET) $(OBSERVER_TRACK_TEST_TARGET) $(CATALOG_PREFETCH_TEST_TARGET)
-	./$(TEST_TARGET)
-	./$(FRAME_TEST_TARGET)
-	./$(SCHWARZSCHILD_TEST_TARGET)
-	./$(OBSERVER_TRACK_TEST_TARGET)
-	./$(CATALOG_PREFETCH_TEST_TARGET)
+$(OBSERVER_TRACK_TEST_TARGET): tests/test_observer_track.c $(COMMON_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@
+
+$(CATALOG_PREFETCH_TEST_TARGET): tests/test_catalog_prefetch.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@
+
+$(TEST_OUT_DIR)/test_observer_minkowski: tests/test_observer.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@
+
+$(TEST_OUT_DIR)/test_observer_schwarzschild: tests/test_observer.c $(COMMON_SOURCES) src/spacetime_schwarzschild.c $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -DSPACETIME_SCHWARZSCHILD -Isrc $^ $(LDLIBS) -o $@
+
+$(FAST_PSF_FFTW_TEST_TARGET): tests/test_fast_psf_fftw.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@
+
+# The tone-map regression links production optics.c only, so it neither needs a
+# catalog nor touches ray tracing, the mesh, or any image writer at runtime.
+$(TONE_MAP_TEST_TARGET): tests/test_tone_map.c src/optics.c src/optics.h $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/test_tone_map.c src/optics.c $(CPU_FFTW_SOURCES) $(LDLIBS) -o $@
+
+# The movie-output queue links production optics, mesh overlay and FFTW only, so it
+# needs neither a catalog nor ray tracing.
+$(MOVIE_OUTPUT_TEST_TARGET): tests/test_movie_output.c src/movie_output.c src/movie_output.h src/mesh_overlay.c src/mesh_overlay.h src/optics.c src/optics.h $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/test_movie_output.c src/movie_output.c src/mesh_overlay.c src/optics.c $(CPU_FFTW_SOURCES) $(LDLIBS) -o $@
+
+$(FAST_PSF_FFTW_BENCH_TARGET): tests/benchmark_fast_psf_fftw.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $^ $(LDLIBS) -o $@
+
+# The sensor-bloom checks link only the standalone model, so they need neither
+# a catalog nor ray tracing, and build in every ENABLE_HDR/PSF_BACKEND
+# configuration.
+$(SENSOR_BLOOM_TEST_TARGET): tests/test_sensor_bloom.c src/sensor_bloom.c src/sensor_bloom.h | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/test_sensor_bloom.c src/sensor_bloom.c $(LDLIBS) -o $@
+
+$(SENSOR_BLOOM_BENCH_TARGET): tests/benchmark_sensor_bloom.c src/sensor_bloom.c src/sensor_bloom.h | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/benchmark_sensor_bloom.c src/sensor_bloom.c $(LDLIBS) -o $@
+
+# The mesh-overlay regression links only the standalone overlay module: it
+# needs neither a catalog, ray tracing, FFTW, nor an output writer.
+$(MESH_OVERLAY_TEST_TARGET): tests/test_mesh_overlay.c src/mesh_overlay.c src/mesh_overlay.h | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc tests/test_mesh_overlay.c src/mesh_overlay.c $(LDLIBS) -o $@
+
+# The FFTW-vs-spatial test is meaningful only in the CPU PSF build.
+ifneq ($(CPU_FFTW_SOURCES),)
+FAST_PSF_FFTW_TEST_DEP := $(FAST_PSF_FFTW_TEST_TARGET)
+FAST_PSF_FFTW_TEST_RUN := $(FAST_PSF_FFTW_TEST_TARGET)
+else
+FAST_PSF_FFTW_TEST_DEP :=
+FAST_PSF_FFTW_TEST_RUN :=
+endif
+
+test: $(CAMERA_TEST_TARGETS) $(TEST_TARGET) $(ADAPTIVE_GEODESIC_TEST_TARGET) $(ASYMPTOTIC_TEST_TARGET) $(ASYMPTOTIC_ENTRY_TEST_TARGET) $(ASYMPTOTIC_QUADRATIC_TEST_TARGET) $(ASYMPTOTIC_SCHWARZSCHILD_TEST_TARGET) $(TERMINATION_ORACLE_TEST_TARGET) $(FRAME_TEST_TARGET) $(SCHWARZSCHILD_TEST_TARGET) $(ALCUBIERRE_TEST_TARGET) $(OBSERVER_TRACK_TEST_TARGET) $(CATALOG_PREFETCH_TEST_TARGET) $(FAST_PSF_FFTW_TEST_DEP) $(TONE_MAP_TEST_TARGET) $(MOVIE_OUTPUT_TEST_TARGET) $(SENSOR_BLOOM_TEST_TARGET) $(MESH_OVERLAY_TEST_TARGET)
+	$(TEST_OUT_DIR)/test_observer_minkowski
+	$(TEST_OUT_DIR)/test_observer_schwarzschild
+	$(TEST_TARGET)
+	$(ADAPTIVE_GEODESIC_TEST_TARGET)
+	$(ASYMPTOTIC_TEST_TARGET)
+	$(ASYMPTOTIC_ENTRY_TEST_TARGET)
+	$(ASYMPTOTIC_QUADRATIC_TEST_TARGET)
+	$(ASYMPTOTIC_SCHWARZSCHILD_TEST_TARGET)
+	$(TERMINATION_ORACLE_TEST_TARGET)
+	$(FRAME_TEST_TARGET)
+	$(SCHWARZSCHILD_TEST_TARGET)
+	$(ALCUBIERRE_TEST_TARGET)
+	$(OBSERVER_TRACK_TEST_TARGET)
+	$(CATALOG_PREFETCH_TEST_TARGET)
+	$(FAST_PSF_FFTW_TEST_RUN)
+	$(TONE_MAP_TEST_TARGET)
+	$(MOVIE_OUTPUT_TEST_TARGET)
+	$(SENSOR_BLOOM_TEST_TARGET)
+	$(MESH_OVERLAY_TEST_TARGET)
+	python3 tests/test_camera_cli.py $(BUILD_DIR) $(TEST_OUT_DIR)
+	python3 tests/test_adaptive_cli.py $(BUILD_DIR) $(TEST_OUT_DIR)
+	python3 tests/test_ray_diagnostics.py $(BUILD_DIR) $(TEST_OUT_DIR)
+	python3 tests/test_output_streams.py $(BUILD_DIR) $(TEST_OUT_DIR)
+	python3 tests/test_mesh_overlay_cli.py $(BUILD_DIR)
+
+tone-map-test: $(TONE_MAP_TEST_TARGET)
+	$(TONE_MAP_TEST_TARGET)
+
+sensor-bloom-test: $(SENSOR_BLOOM_TEST_TARGET)
+	$(SENSOR_BLOOM_TEST_TARGET)
+
+mesh-overlay-test: $(MESH_OVERLAY_TEST_TARGET)
+	$(MESH_OVERLAY_TEST_TARGET)
+
+sensor-bloom-bench: $(SENSOR_BLOOM_BENCH_TARGET)
+
+fast-psf-fftw-bench: $(FAST_PSF_FFTW_BENCH_TARGET)

 clean:
 	rm -rf build

 -include $(RENDER_DEPS)
 include mk/reference_images.mk
+
+# Test-only producer consumer: never linked into a renderer.
+.PHONY: psf-capture
+psf-capture: $(TEST_OUT_DIR)/capture_psf
+$(TEST_OUT_DIR)/capture_psf: tests/capture_psf.c $(CORE_MINKOWSKI_SOURCES) $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $< $(filter-out src/frame.c,$(CORE_MINKOWSKI_SOURCES)) $(CPU_FFTW_SOURCES) $(LDLIBS) -o $@
+
+.PHONY: hip-psf-replay
+hip-psf-replay: $(TEST_OUT_DIR)/replay_psf
+$(TEST_OUT_DIR)/replay_psf: tests/replay_psf.hip src/hip_psf.hip src/hip_psf.h src/optics.h $(OBJECT_DIR)/$(HDR_BUILD_TAG)/src/optics.o | $(TEST_OUT_DIR)
+	$(HIPCC) $(HIP_CXXFLAGS) $(OPENMP_FLAGS) -Isrc -x hip $< -x none $(filter %.o,$^) $(LDLIBS) $(HDR_LDLIBS) -o $@
+
+$(TEST_OUT_DIR)/make_psf_fixture: tests/make_psf_fixture.c src/optics.c src/optics.h $(CPU_FFTW_SOURCES) | $(TEST_OUT_DIR)
+	$(CC) $(CPPFLAGS) $(BUILD_CPPFLAGS) $(CFLAGS) $(BUILD_CFLAGS) $(OPENMP_FLAGS) -Isrc $< src/optics.c $(CPU_FFTW_SOURCES) $(LDLIBS) -o $@
@@ -10,25 +10,36 @@ four-dimensional spacetime.
 [![Schwarzschild black-hole lensing of the 2MASS Galactic-center star field](assets/images/schwarzschild_galactic_center.png)](assets/images/schwarzschild_galactic_center.png)

 *The 2MASS Galactic-center star field seen through Schwarzschild spacetime,
-from a camera at radius 100 M. Click the image for the full 4K render;
+from a camera at radius 100 M. This reference image uses the legacy Reinhard
+tone map (`--tone-map reinhard`). Click the image for the full 4K render;
 [rendering command below](#example-galactic-center-field-through-schwarzschild-spacetime).*

 Stars are individual catalog point sources with direction, temperature, and
 amplitude. The renderer maps them into the camera image, accounting for
 multiple images, gravitational lensing magnification, and frequency shifts,
 then accumulates their sub-pixel point-spread functions (PSFs) into an HDR
-image. Moving cameras are described by worldline and tetrad tracks.
+image. Movie cameras are described by worldline and tetrad tracks.
+
+Single images support independent coordinate position and look direction,
+coordinate velocity, and camera roll in both backends. For example,
+`--observer-position 1.75 0 0 --observer-velocity -0.5 0 0 --look-ra-deg 0 --look-dec-deg 0`
+specifies an inward-moving Schwarzschild camera looking outward from inside
+the horizon. See [single-frame camera parameters and complete commands](usage.md#single-frame-camera).

 ## Current status

-The current implementation supports analytic **Minkowski** and
-**Schwarzschild** spacetimes, single images and observer-track image sequences,
+The current implementation supports analytic **Minkowski**,
+**Schwarzschild**, and moving **Alcubierre** warp-bubble spacetimes,
+single images and observer-track image sequences,
 adaptive lens meshes, and reusable lens-map files. It is written primarily in
 C with OpenMP CPU parallelism; an optional HIP backend accelerates PSF
 accumulation.

+HIP retains parallel CPU catalog mapping and uses bounded, completion-protected
+event uploads. See [HIP configuration and bounded performance checks](build.md#optional-hip-psf-acceleration).
+
 The [Nmesh](https://github.com/nmeshsource/nmesh) numerical-spacetime backend and BBH rendering are still planned.
-The current scope is black-hole capture and distant stellar backgrounds;
+The current scope is black-hole shadows and distant stellar backgrounds;
 local matter emission, accretion disks, and plasma are outside this stage.
 See the [design document](nr_spacetime_movie_renderer_design.md) for the
 architecture and development roadmap.
@@ -42,8 +53,8 @@ libpng development files. From the repository root:
 make -j
 ```

-This builds both `build/Release/minkowski_sky` and
-`build/Release/schwarzschild_sky`. For individual backends, Debug builds,
+This builds `build/Release/minkowski_sky`, `build/Release/schwarzschild_sky`,
+and `build/Release/alcubierre_sky`. For individual backends, Debug builds,
 optional HDR/FITS output, HIP support, and regression checks, see
 [build.md](build.md).

@@ -83,12 +94,14 @@ mkdir -p output/imgs
  --all-sky-catalog assets/2mass/processed/all_sky \
  --look-ra-deg 296 --look-dec-deg 27 --fov-deg 72 \
  --width 3840 --height 2160 --exposure 1e12 \
+  --tone-map reinhard \
  --output output/imgs/summer_triangle.png
 ```

 [![Summer Triangle in flat spacetime, exposure 1e12](assets/images/summer_triangle.png)](assets/images/summer_triangle.png)

-*4K reference image with exposure `1e12`. Click to view at full resolution.*
+*4K reference image with exposure `1e12`; it uses the legacy Reinhard tone
+map (`--tone-map reinhard`). Click to view at full resolution.*

 Angles are in degrees; `--fov-deg` is the horizontal field of view. Exposure
 is an adjustable display multiplier. Use `--verbose` for progress during long
@@ -110,26 +123,79 @@ mkdir -p output/imgs
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 \
  --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 \
  --catalog-load-workers 4 \
+  --tone-map reinhard \
  --output output/imgs/schwarzschild_galactic_center.png
 ```

-This uses the reference image's rendering settings, including its
-`--max-cache-psf-flux 1e8` preview approximation, which clips bright PSF wings
-to the cache radius. The [original benchmark record](benchmarks/2mass_galactic_center_blackhole.md)
-preserves the command and terminal output; the command above omits the optional
-HDR export.
+This uses the updated reference image's rendering settings. The
+`--max-cache-psf-flux 1e8` setting permits bright PSF wings to be clipped to the
+cache radius, but this run reported no wing clipping or direct fallbacks.
+The [CPU/HIP benchmark record](benchmarks/2mass_galactic_center_cpu_hip_2026-09-07.md)
+preserves the commands and terminal output, and records bit-identical CPU/HIP
+PNGs. The command above omits the optional HDR and lens-map exports.

-The Schwarzschild camera points toward the hole. Adaptive refinement should
+This example infers a position facing the hole from its look direction and radius. Adaptive refinement should
 be configured for the desired image accuracy; it is disabled by default.
+Tone-mapped PNG/PPM output uses a per-channel soft-clip display transform by
+default (`--tone-map softclip --tone-map-p 2`); `--tone-map reinhard` restores
+the historical curve used by the reference images above. The linear HDR FITS
+output never applies it. An optional limited-response sensor bloom
+(`--sensor-bloom-limit E --sensor-bloom-transfer e`, default disabled) can be
+applied to the linear HDR before display; it never changes the FITS output. See
+[tone mapping and display](usage.md#tone-mapping-and-display).
 Camera controls, movie sequences, lens-map reuse, PSF settings, and HDR output
-are described in [usage.md](usage.md). Both binaries provide a complete option
-list with `--help`.
+are described in [usage.md](usage.md). For fast single-frame previews,
+`--fast-mode` replaces per-event PSF splats with a supersampled delta deposit
+plus one global PSF convolution and downsample. Its nearest-deposit path is not
+qualified for temporally coherent movie output; see [usage.md](usage.md) for
+the spatial and temporal accuracy limits. Both binaries provide a complete
+option list with `--help`.
+
+### Example: Looking outward just above the Schwarzschild horizon
+
+This camera is static at `(2.1, 0, 0)` in Cartesian Kerr–Schild coordinates,
+just outside the horizon at `r=2M` (`M=1`). RA=0°, Dec=0° points along +X,
+radially outward. Its coordinate velocity is zero: this is a static
+observer, not a freely falling one. The scene uses the bundled synthetic
+stellar grid, so no survey download is needed.
+
+```sh
+mkdir -p output/imgs
+./build/Release/schwarzschild_sky \
+  --catalog assets/sky_grid_5deg.csv \
+  --observer-position 2.1 0 0 \
+  --observer-velocity 0 0 0 \
+  --look-ra-deg 0 --look-dec-deg 0 \
+  --camera-roll-deg 0 \
+  --width 3840 --height 2160 --fov-deg 90 \
+  --coarse-cell-pixels 16 --refine-max-level 3 \
+  --exposure 0.01 \
+  --tone-map reinhard \
+  --output output/imgs/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png
+```
+
+[![Synthetic stellar sky seen outward by a static observer at r=2.1M](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)
+
+*4K render with a 90° horizontal field of view, exposure `0.01`, and maximum
+refinement level 3; it uses the legacy Reinhard tone map (`--tone-map
+reinhard`). Click to view at full resolution.*
+
+The distant sky occupies a bounded angular region around the outward
+direction, with repeated images crowded near its edge. Strong gravitational
+blueshift pushes both the 3000 K and 12000 K test stars toward blue-white.

 ### Example: Synthetic test grid with mesh overlay

 This example uses `assets/sky_grid_5deg.csv` to inspect lensing and adaptive
-mesh refinement in Schwarzschild spacetime. `--draw-mesh` overlays the final
-image-plane triangles.
+mesh refinement in Schwarzschild spacetime. The main output is the clean
+tone-mapped image; `--draw-mesh` additionally writes the final image-plane
+triangles, so one command produces both
+`output/imgs/schwarzschild_test_grid.png` (no mesh) and
+`output/imgs/schwarzschild_test_grid_mesh.png` (mesh overlay).
+The antialiased mesh is drawn after tone mapping: gray escape half-edges,
+purple dark half-edges, yellow budget-unresolved half-edges, and red failure
+half-edges, using Catppuccin Mocha defaults. Color and opacity settings are
+documented in `usage.md`.

 ```sh
 mkdir -p output/imgs
@@ -142,9 +208,61 @@ mkdir -p output/imgs
  --coarse-cell-pixels 32 \
  --observer-radius 100 --exposure 0.2 \
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --draw-mesh \
+  --tone-map reinhard \
  --output output/imgs/schwarzschild_test_grid.png
 ```

-[![Synthetic stellar grid lensed by a Schwarzschild black hole, with adaptive mesh overlay](assets/images/schwarzschild_test_grid.png)](assets/images/schwarzschild_test_grid.png)
+[![Synthetic stellar grid lensed by a Schwarzschild black hole, with adaptive mesh overlay](assets/images/schwarzschild_test_grid_mesh.png)](assets/images/schwarzschild_test_grid_mesh.png)

-*4K test-grid reference image. Click to view at full resolution.*
+*4K test-grid reference image showing the `_mesh.png` overlay; it uses the
+legacy Reinhard tone map (`--tone-map reinhard`). Click to view at full
+resolution.*
+
+### Freely falling Schwarzschild movie camera
+
+`scripts/schwarzschild_camera_track.py` generates the canonical 21-column observer
+CSV in ingoing Cartesian Kerr–Schild coordinates (`G=c=M=1`, matching the renderer).
+It requires Python 3, NumPy and SciPy. Position is `(x,y,z)`; velocity is coordinate
+`(dx/dt,dy/dt,dz/dt)`. Look RA/Dec and roll construct the initial rest-frame
+forward/up/right legs with the same convention as the single-image camera. Without
+look angles, the camera initially points toward the origin. The orientation then
+follows Fermi–Walker transport; for free fall this is parallel transport, so it does
+not keep pointing at the black hole. `--tetrad` alternatively accepts 16 row-major
+components `(e0t,e0x,...,e3z)` of an orthonormal tetrad, with `e0` matching velocity.
+
+```sh
+python3 scripts/schwarzschild_camera_track.py \
+  --position 8 0 0 --velocity 0 0 0 \
+  --look-ra-deg 0 --look-dec-deg 0 --roll-deg 0 \
+  --fps 30 --duration 10 --output /tmp/freefall_camera.csv
+make SPACETIME=schwarzschild all
+mkdir -p output/freefall_frames
+./build/Release/schwarzschild_sky \
+  --observer-track /tmp/freefall_camera.csv --movie-track-samples \
+  --frames-dir output/freefall_frames --catalog assets/sky_grid_5deg.csv \
+  --width 640 --height 360 --fov-deg 60 --exposure 0.2
+ffmpeg -framerate 30 -i output/freefall_frames/frame_%06d.png \
+  -c:v libx264 -pix_fmt yuv420p output/freefall.mp4
+```
+
+Here `--duration` is elapsed **proper time**, and `--fps` is samples per unit proper
+time. CSV rows occur at `tau=k/fps <= duration`, including the initial event and an
+endpoint only if it lies on that cadence (10 at 30 fps gives 301 rows). `tau` starts
+at zero; `--t0` sets the initial coordinate time. `--movie-track-samples` uses each
+row exactly once and ignores renderer `--start-time`, `--duration`, and `--fps`;
+encode the PNG sequence at the generator's fps. Without this flag the existing
+movie mode resamples at uniform coordinate time, which changes the proper-time cadence.
+
+DOP853 jointly integrates the geodesic and all tetrad legs using analytic metric
+derivatives. Defaults: `--rtol 1e-10 --atol 1e-12 --stop-radius 0.001`.
+Integration crosses the horizon and stops at this numerical guard before the
+singularity, reporting its proper time and retaining only regular cadence samples.
+The guard is not the exact singularity; reduce it and tolerances to check convergence.
+The renderer no longer uses a position capture cutoff: cameras at and inside the
+old `r=1.5M` guard are valid targets, and a normal dark pixel comes from the
+redshift-threshold truncation `log(alpha p^0) >= 8`. Budget-exhausted and
+data/integration failures are separate unresolved/incomplete outcomes and are not
+silently rendered as dark.
+The script reports maximum tetrad drift and rejects errors above `1e-6` rather
+than silently repairing the transported frame. Run the orbit, transport and CSV
+render regressions after building with `python3 tests/test_schwarzschild_camera_track.py`.
@@ -6,14 +6,21 @@

 [![Schwarzschild 黑洞对 2MASS 银心方向星场的引力透镜效果](assets/images/schwarzschild_galactic_center.png)](assets/images/schwarzschild_galactic_center.png)

-*从半径 100 M 处的相机观察 Schwarzschild 时空中的 2MASS 银心方向星场。点击图片查看完整 4K 图像；[渲染命令见下文](#示例schwarzschild-时空中的银心方向星场)。*
+*从半径 100 M 处的相机观察 Schwarzschild 时空中的 2MASS 银心方向星场。该参考图像使用 legacy Reinhard tone map（`--tone-map reinhard`）。点击图片查看完整 4K 图像；[渲染命令见下文](#示例schwarzschild-时空中的银心方向星场)。*

-恒星以独立的星表点源表示，保留方向、温度和振幅。渲染器将它们映射到相机图像中，处理多像、引力透镜放大和频移，再将保留亚像素位置的点扩散函数（PSF）累积到 HDR 图像。运动相机由世界线与四标架（tetrad）轨迹描述。
+恒星以独立的星表点源表示，保留方向、温度和振幅。渲染器将它们映射到相机图像中，处理多像、引力透镜放大和频移，再将保留亚像素位置的点扩散函数（PSF）累积到 HDR 图像。电影中的运动相机由世界线与四标架（tetrad）轨迹描述。
+
+单张模式在两个 backend 中都支持独立的位置、指向、坐标速度和 roll。例如
+`--observer-position 1.75 0 0 --observer-velocity -0.5 0 0 --look-ra-deg 0 --look-dec-deg 0`
+表示位于史瓦西视界内、向内运动且朝外看的相机，无需借用电影模式。
+参数语义与完整命令见 [单张相机指南](usage.md#single-frame-camera)。

 ## 当前进展

 当前实现支持解析 **Minkowski** 与 **Schwarzschild** 时空、单张图像、基于观测者轨迹的图像序列、自适应透镜网格，以及可复用的透镜映射文件。程序主要使用 C 编写，通过 OpenMP 实现 CPU 并行；可选的 HIP 后端用于加速 PSF 累积。

+HIP 保留并行 CPU catalog 映射，并使用由完成事件保护的有界上传缓冲。配置与小规模性能检查见 [HIP 构建说明](build.md#optional-hip-psf-acceleration)。
+
 [Nmesh](https://github.com/nmeshsource/nmesh) 数值时空后端和双黑洞（BBH）渲染仍在规划中。当前范围为黑洞捕获与远处恒星背景，暂不包含局域物质辐射、吸积盘或等离子体。架构与开发路线参见[设计文档](nr_spacetime_movie_renderer_design.md)。

 ## 编译
@@ -48,12 +55,13 @@ mkdir -p output/imgs
  --all-sky-catalog assets/2mass/processed/all_sky \
  --look-ra-deg 296 --look-dec-deg 27 --fov-deg 72 \
  --width 3840 --height 2160 --exposure 1e12 \
+  --tone-map reinhard \
  --output output/imgs/summer_triangle.png
 ```

 [![平直时空中的夏季大三角，曝光为 1e12](assets/images/summer_triangle.png)](assets/images/summer_triangle.png)

-*曝光为 `1e12` 的 4K 参考图像。点击查看完整分辨率。*
+*曝光为 `1e12` 的 4K 参考图像；使用 legacy Reinhard tone map（`--tone-map reinhard`）。点击查看完整分辨率。*

 角度单位为度，`--fov-deg` 表示水平视场角。曝光是可调节的显示倍率。长时间渲染时可使用 `--verbose` 查看进度。

@@ -72,16 +80,46 @@ mkdir -p output/imgs
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 \
  --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 \
  --catalog-load-workers 4 \
+  --tone-map reinhard \
  --output output/imgs/schwarzschild_galactic_center.png
 ```

-这里使用参考图像的渲染设置，包括 `--max-cache-psf-flux 1e8` 这一预览近似：它将明亮 PSF 的翼部截断在缓存半径内。[原始 benchmark 记录](benchmarks/2mass_galactic_center_blackhole.md)保留了命令与终端输出；上述命令省略了可选的 HDR 导出。
+这里使用更新后的参考图像的渲染设置。`--max-cache-psf-flux 1e8` 允许将明亮 PSF 的翼部截断在缓存半径内，但本次运行没有发生翼部裁剪或 direct fallback。[CPU/HIP benchmark 记录](benchmarks/2mass_galactic_center_cpu_hip_2026-09-07.md)保留了命令、终端输出，以及 CPU/HIP PNG 比特级一致的结果；上述命令省略了可选的 HDR 和 lens-map 导出。

-Schwarzschild 相机朝向黑洞。自适应细分默认关闭，应根据所需图像精度配置。相机控制、图像序列、透镜映射复用、PSF 设置及 HDR 输出参见 [usage.md](usage.md)（英文）。两个可执行文件都可通过 `--help` 查看完整选项。
+上述 Schwarzschild 示例省略位置，因此按指向与半径推导出朝向黑洞的相机。自适应细分默认关闭，应根据所需图像精度配置。tone-mapped PNG/PPM 默认使用逐通道 soft-clip 显示变换（`--tone-map softclip --tone-map-p 2`）；`--tone-map reinhard` 恢复上方参考图像使用的历史曲线，线性 HDR FITS 输出不受其影响。可选的有限响应 sensor bloom（`--sensor-bloom-limit E --sensor-bloom-transfer e`，默认关闭）在显示前作用于线性 HDR，且不会改变 FITS 输出。相机控制、图像序列、透镜映射复用、PSF 设置及 HDR 输出参见 [usage.md](usage.md)（英文）。两个可执行文件都可通过 `--help` 查看完整选项。
+
+### 示例：紧贴史瓦西视界向外看
+
+相机位于 Cartesian Kerr–Schild 坐标 `(2.1, 0, 0)`，紧贴 `r=2M` 的视界外侧
+（`M=1`）。RA=0°、Dec=0° 对应沿 +X 径向向外看；坐标速度为零，表示静态观者，
+而非自由落体相机。这里使用仓库自带的合成测试星表，无需下载巡天数据。
+
+```sh
+mkdir -p output/imgs
+./build/Release/schwarzschild_sky \
+  --catalog assets/sky_grid_5deg.csv \
+  --observer-position 2.1 0 0 \
+  --observer-velocity 0 0 0 \
+  --look-ra-deg 0 --look-dec-deg 0 \
+  --camera-roll-deg 0 \
+  --width 3840 --height 2160 --fov-deg 90 \
+  --coarse-cell-pixels 16 --refine-max-level 3 \
+  --exposure 0.01 \
+  --tone-map reinhard \
+  --output output/imgs/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png
+```
+
+[![r=2.1M 处的静态观者向外观察合成恒星天空](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)](assets/images/schwarzschild_near_horizon_outward_R2.1_0.01_refine3.png)
+
+*水平视场角 90°、曝光 `0.01`、最大细分级别 3 的 4K 图像；使用 legacy Reinhard tone map（`--tone-map reinhard`）。点击查看完整分辨率。*
+
+远方天空集中在朝外方向的有限角域中，多级成像在边缘附近密集堆叠。
+强烈的引力蓝移使 3000 K 和 12000 K 的测试恒星都被推向蓝白色。

 ### 示例：叠加网格的合成测试星表

-这个示例使用 `assets/sky_grid_5deg.csv` 检查 Schwarzschild 时空中的引力透镜效果与自适应网格细分。`--draw-mesh` 会叠加显示最终的像平面三角网格。
+这个示例使用 `assets/sky_grid_5deg.csv` 检查 Schwarzschild 时空中的引力透镜效果与自适应网格细分。主输出是不带网格的成品图；`--draw-mesh` 会额外写出最终的像平面三角网格，因此同一次命令会同时生成 `output/imgs/schwarzschild_test_grid.png`（无网格）和 `output/imgs/schwarzschild_test_grid_mesh.png`（网格叠加）。
+网格在 tone mapping 后以抗锯齿半边叠加。默认采用 Catppuccin Mocha：逃逸为灰色、暗终态为紫色、预算耗尽未决为黄色、真实失败为红色，未追踪为蓝色。颜色与透明度配置详见 `usage.md`。

 ```sh
 mkdir -p output/imgs
@@ -94,9 +132,51 @@ mkdir -p output/imgs
  --coarse-cell-pixels 32 \
  --observer-radius 100 --exposure 0.2 \
  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --draw-mesh \
+  --tone-map reinhard \
  --output output/imgs/schwarzschild_test_grid.png
 ```

-[![Schwarzschild 黑洞对合成恒星网格的透镜效果，叠加自适应网格](assets/images/schwarzschild_test_grid.png)](assets/images/schwarzschild_test_grid.png)
+[![Schwarzschild 黑洞对合成恒星网格的透镜效果，叠加自适应网格](assets/images/schwarzschild_test_grid_mesh.png)](assets/images/schwarzschild_test_grid_mesh.png)

-*4K 测试网格参考图像。点击查看完整分辨率。*
+*4K 测试网格参考图像，展示 `_mesh.png` 网格叠加结果；使用 legacy Reinhard tone map（`--tone-map reinhard`）。点击查看完整分辨率。*
+
+### Schwarzschild 自由落体相机轨迹
+
+`scripts/schwarzschild_camera_track.py` 生成 movie 使用的 21 列相机 CSV，采用
+入射 Cartesian Kerr–Schild 坐标及 `G=c=M=1`，依赖 Python 3、NumPy、SciPy。
+`--position` 是坐标位置，`--velocity` 是 `dx/dt,dy/dt,dz/dt`，不是局域三速度。
+初始标架由 RA/Dec 与 roll 构造，约定与单张相机一致；省略指向时初始朝向原点。
+也可用 `--tetrad` 提供 16 个按行排列的四标架分量，顺序为 `e0t,e0x,...,e3z`，
+要求正交归一、定向正确，且 `e0` 与指定速度一致。自由落体中费米–沃克输运等同于
+平行输运；初始之后不再强制朝向黑洞。
+
+```sh
+python3 scripts/schwarzschild_camera_track.py \
+  --position 8 0 0 --velocity 0 0 0 \
+  --look-ra-deg 0 --look-dec-deg 0 --roll-deg 0 \
+  --fps 30 --duration 10 --output /tmp/freefall_camera.csv
+make SPACETIME=schwarzschild all
+mkdir -p output/freefall_frames
+./build/Release/schwarzschild_sky \
+  --observer-track /tmp/freefall_camera.csv --movie-track-samples \
+  --frames-dir output/freefall_frames --catalog assets/sky_grid_5deg.csv \
+  --width 640 --height 360 --fov-deg 60 --exposure 0.2
+ffmpeg -framerate 30 -i output/freefall_frames/frame_%06d.png \
+  -c:v libx264 -pix_fmt yuv420p output/freefall.mp4
+```
+
+脚本的 `--duration` 是持续本征时（单位 M），`--fps` 是每单位本征时的采样数。
+采样为 `tau=k/fps <= duration`，包含初始帧，只在终点恰好满足采样节奏时包含终点；
+10 M、30 fps 共 301 行。`tau` 从零开始，`--t0` 指定初始坐标时间。
+新增 `--movie-track-samples` 让每行恰好对应一帧，保留真实坐标时间，并忽略 renderer
+的 `--start-time/--duration/--fps`；编码时使用生成脚本的 fps。
+不加此选项时原有 movie 仍按坐标时间等间隔采样，不能保持这里的本征时节奏。
+
+脚本以解析 metric 导数及 DOP853 联合积分测地线与四标架，默认
+`--rtol 1e-10 --atol 1e-12 --stop-radius 0.001`。轨迹穿过视界继续积分，在该小半径
+数值保护边界停止，报告终止本征时，只保留此前的规则采样；不声称到达精确的 `r=0`。
+可减小半径及误差容限检查收敛。现有 renderer 的光线捕获边界仍为 `r=1.5M`：
+CSV 可以记录更深处的相机，但目前 renderer 会把这些相机发出的光线立即判为捕获。
+脚本报告标架正交归一误差，超过 `1e-6` 时直接报错，不自动修正输运后的标架。
+构建后运行 `python3 tests/test_schwarzschild_camera_track.py`，检查解析径向落体、
+圆轨道及标架输运收敛、非法初值和实际 CSV 渲染。
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+740,0.000690078600,0.0002492000000,0.000000000000
+741,0.000640515600,0.0002313019000,0.000000000000
+742,0.000594502100,0.0002146856000,0.000000000000
+743,0.000551864600,0.0001992884000,0.000000000000
+744,0.000512429000,0.0001850475000,0.000000000000
+745,0.000476021300,0.0001719000000,0.000000000000
+746,0.000442453600,0.0001597781000,0.000000000000
+747,0.000411511700,0.0001486044000,0.000000000000
+748,0.000382981400,0.0001383016000,0.000000000000
+749,0.000356649100,0.0001287925000,0.000000000000
+750,0.000332301100,0.0001200000000,0.000000000000
+751,0.000309758600,0.0001118595000,0.000000000000
+752,0.000288887100,0.0001043224000,0.000000000000
+753,0.000269539400,0.0000973356000,0.000000000000
+754,0.000251568200,0.0000908458700,0.000000000000
+755,0.000234826100,0.0000848000000,0.000000000000
+756,0.000219171000,0.0000791466700,0.000000000000
+757,0.000204525800,0.0000738580000,0.000000000000
+758,0.000190840500,0.0000689160000,0.000000000000
+759,0.000178065400,0.0000643026700,0.000000000000
+760,0.000166150500,0.0000600000000,0.000000000000
+761,0.000155023600,0.0000559818700,0.000000000000
+762,0.000144621900,0.0000522256000,0.000000000000
+763,0.000134909800,0.0000487184000,0.000000000000
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+770,0.000083075270,0.0000300000000,0.000000000000
+771,0.000077512690,0.0000279912500,0.000000000000
+772,0.000072313040,0.0000261135600,0.000000000000
+773,0.000067457780,0.0000243602400,0.000000000000
+774,0.000062928440,0.0000227246100,0.000000000000
+775,0.000058706520,0.0000212000000,0.000000000000
+776,0.000054770280,0.0000197785500,0.000000000000
+777,0.000051099180,0.0000184528500,0.000000000000
+778,0.000047676540,0.0000172168700,0.000000000000
+779,0.000044485670,0.0000160645900,0.000000000000
+780,0.000041509940,0.0000149900000,0.000000000000
+781,0.000038733240,0.0000139872800,0.000000000000
+782,0.000036142030,0.0000130515500,0.000000000000
+783,0.000033723520,0.0000121781800,0.000000000000
+784,0.000031464870,0.0000113625400,0.000000000000
+785,0.000029353260,0.0000106000000,0.000000000000
+786,0.000027375730,0.0000098858770,0.000000000000
+787,0.000025524330,0.0000092173040,0.000000000000
+788,0.000023793760,0.0000085923620,0.000000000000
+789,0.000022178700,0.0000080091330,0.000000000000
+790,0.000020673830,0.0000074657000,0.000000000000
+791,0.000019272260,0.0000069595670,0.000000000000
+792,0.000017966400,0.0000064879950,0.000000000000
+793,0.000016749910,0.0000060486990,0.000000000000
+794,0.000015616480,0.0000056393960,0.000000000000
+795,0.000014559770,0.0000052578000,0.000000000000
+796,0.000013573870,0.0000049017710,0.000000000000
+797,0.000012654360,0.0000045697200,0.000000000000
+798,0.000011797230,0.0000042601940,0.000000000000
+799,0.000010998440,0.0000039717390,0.000000000000
+800,0.000010253980,0.0000037029000,0.000000000000
+801,0.000009559646,0.0000034521630,0.000000000000
+802,0.000008912044,0.0000032183020,0.000000000000
+803,0.000008308358,0.0000030003000,0.000000000000
+804,0.000007745769,0.0000027971390,0.000000000000
+805,0.000007221456,0.0000026078000,0.000000000000
+806,0.000006732475,0.0000024312200,0.000000000000
+807,0.000006276423,0.0000022665310,0.000000000000
+808,0.000005851304,0.0000021130130,0.000000000000
+809,0.000005455118,0.0000019699430,0.000000000000
+810,0.000005085868,0.0000018366000,0.000000000000
+811,0.000004741466,0.0000017122300,0.000000000000
+812,0.000004420236,0.0000015962280,0.000000000000
+813,0.000004120783,0.0000014880900,0.000000000000
+814,0.000003841716,0.0000013873140,0.000000000000
+815,0.000003581652,0.0000012934000,0.000000000000
+816,0.000003339127,0.0000012058200,0.000000000000
+817,0.000003112949,0.0000011241430,0.000000000000
+818,0.000002902121,0.0000010480090,0.000000000000
+819,0.000002705645,0.0000009770578,0.000000000000
+820,0.000002522525,0.0000009109300,0.000000000000
+821,0.000002351726,0.0000008492513,0.000000000000
+822,0.000002192415,0.0000007917212,0.000000000000
+823,0.000002043902,0.0000007380904,0.000000000000
+824,0.000001905497,0.0000006881098,0.000000000000
+825,0.000001776509,0.0000006415300,0.000000000000
+826,0.000001656215,0.0000005980895,0.000000000000
+827,0.000001544022,0.0000005575746,0.000000000000
+828,0.000001439440,0.0000005198080,0.000000000000
+829,0.000001341977,0.0000004846123,0.000000000000
+830,0.000001251141,0.0000004518100,0.000000000000
@@ -0,0 +1,40 @@
+# CIE 1931 blackbody LUT
+
+`cie1931_2deg_xyz_1024.grbblut` is the sole repository LUT. It contains 1,024
+XYZ nodes uniformly spaced in `log(T)` over `[670.146556, 101408.88] K`.
+Wolfram integrates the Planck spectrum against the piecewise-linear 1 nm data
+in `assets/CIE_xyz_1931_2deg.csv` at 40-digit working precision and rounds each
+stored value once to little-endian IEEE binary64.
+
+The 160-byte `GRBBLUT3` header records the CIE 1931 2-degree, 360--830 nm,
+1 nm-linear reference definition, node count, temperature limits, physical
+constants, generator description, and payload FNV-1a checksum. The C loader
+validates the header, exact payload size, and checksum, and rejects trailing
+bytes. Runtime table generation and the former `GRBBLUT1`/`GRBBLUT2` formats are
+not supported. The evaluator uses four-point cubic Lagrange interpolation in
+`log(T)`.
+
+- file size: 24,736 bytes
+- payload FNV-1a: `0e39867b0e70a809`
+- file SHA-256:
+  `850446663212fe488c88fca3ac2f54d6f8119a04801dda84fc1a62acdec37d63`
+- all 1,023 interval midpoints versus independent Gauss-16 integration:
+  max XYZ-channel relative `5.4633e-5`, no negative XYZ
+
+The LUT interpolation acceptance limit is `1e-4`. A separate `5e-4` overall
+relative error budget accounts for the estimated error of linearly
+interpolating the 1 nm CIE samples; the LUT's much smaller internal error must
+not be mistaken for physical-reference accuracy.
+
+Outside the stored range, the same CSV reference supplies both models. Above
+101408.88 K the evaluator uses three integrated Rayleigh--Jeans terms
+`A T+B+C/T` (maximum validated XYZ-channel relative error `1.6635e-5`
+through `10*Tmax`). Below 670.146556 K it uses a six-segment, degree-eight
+inverse-temperature/log-XYZ Chebyshev--Lobatto crossover down to 4.097321 K
+and channel-specific endpoint forms below that. Their maximum sampled XYZ
+relative errors are `8.16e-5` and `6.69e-5`.
+
+The Wolfram generation/validation scripts that produced this table, together
+with the bounded performance and accuracy evidence, are preserved on the
+experiment branch `codex/blackbody-cost-experiment` (tag
+`blackbody-cost-experiment-2026-09-12`) and are not part of the mainline tree.
@@ -0,0 +1,82 @@
+ra_deg,dec_deg,temperature_K,amplitude_sr
+-0.500000,0.500000,2500,1.288768695e-13
+-0.375000,0.500000,2500,5.130680588e-14
+-0.250000,0.500000,2500,2.042560732e-14
+-0.125000,0.500000,2500,8.131580736e-15
+0.000000,0.500000,2500,3.237240599e-15
+0.125000,0.500000,2500,1.288768695e-15
+0.250000,0.500000,2500,5.130680588e-16
+0.375000,0.500000,2500,2.042560732e-16
+0.500000,0.500000,2500,8.131580736e-17
+-0.500000,0.375000,3044.7082,5.529309491e-14
+-0.375000,0.375000,3044.7082,2.201257756e-14
+-0.250000,0.375000,3044.7082,8.763364971e-15
+-0.125000,0.375000,3044.7082,3.488758433e-15
+0.000000,0.375000,3044.7082,1.388899748e-15
+0.125000,0.375000,3044.7082,5.529309491e-16
+0.250000,0.375000,3044.7082,2.201257756e-16
+0.375000,0.375000,3044.7082,8.763364971e-17
+0.500000,0.375000,3044.7082,3.488758433e-17
+-0.500000,0.250000,3708.0992,2.727501648e-14
+-0.375000,0.250000,3708.0992,1.085837964e-14
+-0.250000,0.250000,3708.0992,4.322798794e-15
+-0.125000,0.250000,3708.0992,1.720937197e-15
+0.000000,0.250000,3708.0992,6.851174381e-16
+0.125000,0.250000,3708.0992,2.727501648e-16
+0.250000,0.250000,3708.0992,1.085837964e-16
+0.375000,0.250000,3708.0992,4.322798794e-17
+0.500000,0.250000,3708.0992,1.720937197e-17
+-0.500000,0.125000,4516.0321,1.501787774e-14
+-0.375000,0.125000,4516.0321,5.978724815e-15
+-0.250000,0.125000,4516.0321,2.380173219e-15
+-0.125000,0.125000,4516.0321,9.475640258e-16
+0.000000,0.125000,4516.0321,3.772320332e-16
+0.125000,0.125000,4516.0321,1.501787774e-16
+0.250000,0.125000,4516.0321,5.978724815e-17
+0.375000,0.125000,4516.0321,2.380173219e-17
+0.500000,0.125000,4516.0321,9.475640258e-18
+-0.500000,0.000000,5500,9.010857559e-15
+-0.375000,0.000000,5500,3.587287007e-15
+-0.250000,0.000000,5500,1.428124680e-15
+-0.125000,0.000000,5500,5.685466757e-16
+0.000000,0.000000,5500,2.263425084e-16
+0.125000,0.000000,5500,9.010857559e-17
+0.250000,0.000000,5500,3.587287007e-17
+0.375000,0.000000,5500,1.428124680e-17
+0.500000,0.000000,5500,5.685466757e-18
+-0.500000,-0.125000,7067.9722,5.170563867e-15
+-0.375000,-0.125000,7067.9722,2.058438551e-15
+-0.250000,-0.125000,7067.9722,8.194791473e-16
+-0.125000,-0.125000,7067.9722,3.262405247e-16
+0.000000,-0.125000,7067.9722,1.298786922e-16
+0.125000,-0.125000,7067.9722,5.170563867e-17
+0.250000,-0.125000,7067.9722,2.058438551e-17
+0.375000,-0.125000,7067.9722,8.194791473e-18
+0.500000,-0.125000,7067.9722,3.262405247e-18
+-0.500000,-0.250000,9082.9511,3.209818520e-15
+-0.375000,-0.250000,9082.9511,1.277851769e-15
+-0.250000,-0.250000,9082.9511,5.087219521e-16
+-0.125000,-0.250000,9082.9511,2.025258569e-16
+0.000000,-0.250000,9082.9511,8.062699587e-17
+0.125000,-0.250000,9082.9511,3.209818520e-17
+0.250000,-0.250000,9082.9511,1.277851769e-17
+0.375000,-0.250000,9082.9511,5.087219521e-18
+0.500000,-0.250000,9082.9511,2.025258569e-18
+-0.500000,-0.375000,11672.372,2.109932559e-15
+-0.375000,-0.375000,11672.372,8.399792812e-16
+-0.250000,-0.375000,11672.372,3.344017750e-16
+-0.125000,-0.375000,11672.372,1.331277445e-16
+0.000000,-0.375000,11672.372,5.299910967e-17
+0.125000,-0.375000,11672.372,2.109932559e-17
+0.250000,-0.375000,11672.372,8.399792812e-18
+0.375000,-0.375000,11672.372,3.344017750e-18
+0.500000,-0.375000,11672.372,1.331277445e-18
+-0.500000,-0.500000,15000,1.446233663e-15
+-0.375000,-0.500000,15000,5.757559917e-16
+-0.250000,-0.500000,15000,2.292125888e-16
+-0.125000,-0.500000,15000,9.125117517e-17
+0.000000,-0.500000,15000,3.632774716e-17
+0.125000,-0.500000,15000,1.446233663e-17
+0.250000,-0.500000,15000,5.757559917e-18
+0.375000,-0.500000,15000,2.292125888e-18
+0.500000,-0.500000,15000,9.125117517e-19
@@ -1,3 +1,7 @@
+> 历史记录：此运行早于 `265d7b95d5b916ec4768d174d73ad963a43f0088` 的伪像修复。
+> 当前 CPU/HIP 配对基准及优化提交 hash 见 [完整 4K 新记录](2mass_galactic_center_cpu_hip_2026-09-07.md)。
+> 下方原始命令与输出保留，不用于新版本计数对照。
+
 Git hash: dd8cf29dac557c881e5df1db15a58fae15294967

 ```
@@ -0,0 +1,89 @@
+# 2MASS 银河中心完整 4K：CPU / 优化 HIP（2026-09-07 归档）
+
+## 代码版本与证据来源
+
+HIP 优化提交：**`e1ec480669b0d24a0266ee135edf8a64a0d80ec9`**
+（`HIP: accelerate PSF accumulation and restore parallel producers`）。
+该提交包含 32-thread/event kernel、并行 CPU producer、有界双缓冲、全批次计时及回归测试。
+HIP 完整运行发生在提交之前，对应此次提交的实现；运行日志本身没有嵌入 Git 或 binary hash。
+
+用户指定本页 CPU 运行作为可比较基准，并说明
+`265d7b95d5b916ec4768d174d73ad963a43f0088` 修复了此前的一些伪像。
+因此，旧 `dd8cf29` 记录的 598,308,919 星像和 1,365 wing-clipped 不用于本次性能/正确性配对。
+CPU 日志同样未嵌入 binary hash，不将代码版本说明冒充运行时二进制校验。
+
+两份完整命令与原始终端输出均由用户提供：
+
+- [CPU 原始日志](2mass_galactic_center_cpu_hip_2026-09-07/cpu.log)：生成并导出 lens map。
+- [HIP 原始日志](2mass_galactic_center_cpu_hip_2026-09-07/hip.log)：导入同一 lens map；保留全部
+  worker 进度、每五秒 batch 进度、最终计数及 zsh `time` 输出，未删减成汇总。
+
+用户确认：**两个 PNG 比特级完全一致。** 本次归档没有重跑渲染，也没有重新执行文件比较；
+原始比较命令和两个 PNG 的 SHA256 未提供。不将 PNG 一致性扩大为完整任务的 linear HDR
+逐样本一致性声明。此前有界样本的 HDR 验证另见
+[有界排查记录](hip_psf_2026-09-07.md)。
+
+## 工作负载与环境
+
+- 主机沿用有界排查的 AMD Radeon RX 9070（gfx1201）与 HIP 7.2 环境；用户说明测试时段无其他
+  持续负载。完整日志没有独立输出驱动/编译器版本，前期环境证据见
+  [metadata.log](hip_psf_2026-09-07/metadata.log)。
+- Release CPU/HIP 可执行文件，启用 HDR 输出；完整运行的实际编译命令未附在用户日志中。
+- 3840×2160，45° FOV，RA 262.5° / Dec −30°，observer radius 100 M。
+- CPU coarse cell 16，refine max level 4，Jacobian min 0.2；导出的 lens map 包含
+  65,817 vertices 和 130,882 triangles，HIP 直接导入它。
+- 两次均请求并加载 64,440 tiles、343,363,141 stars，无 unavailable tile；catalog loaders=4。
+- HIP 明确报告 16 producer workers。CPU 日志报告 1521% CPU，没有单独打印 worker 数。
+- PSF FWHM 2.7 px、Moffat beta 4.5、relative tail 1e-8、min-Y=0、max-cache-psf-flux=1e8、
+  exposure=1e13；cache 为 64×64 phases、radius 47 px。
+- 用户原始 CPU/HIP 命令使用相同 PNG 输出路径，且 CPU 命令的文件名也带 `full-gpu`；
+  原样保留此命名，不根据文件名判断 backend。未来复现应分别指定输出文件名，避免覆盖对照。
+
+## 完整运行结果
+
+| 项目 | CPU | 优化 HIP |
+| --- | ---: | ---: |
+| 总墙钟时间 | 1474.32 s（24:34.32） | 533.06 s（8:53.06） |
+| user | 22234.08 s | 7733.61 s |
+| system | 200.30 s | 61.18 s |
+| CPU 百分比 | 1521% | 1462% |
+| PSF cache build | 0.676 s | 0.691 s |
+| catalog prefetch | 49.253 s | 48.201 s |
+| 星像 / cached | 598264924 | 598264924 |
+| wing-clipped | 0 | 0 |
+| direct fallback | 0 | 0 |
+| discarded below min-Y | 0 | 0 |
+
+总墙钟时间比 `1474.32 / 533.06 = 2.76577`，耗时减少约 **63.84%**，节省 **941.26 秒**
+（15 分 41.26 秒）。这是两次工作流的端到端时间比：CPU 包含 tracing 与 lens-map 写出，
+HIP 导入文件；没有独立的 CPU PSF 阶段计时，不能把该比值称作严格隔离的 PSF backend 加速比。
+
+HIP 全程诊断：
+
+| 项目 | 结果 |
+| --- | ---: |
+| producer/splat wall | 481.155 s（frame 日志四舍五入为481.2 s） |
+| GPU kernel | 476.906037 s |
+| event upload | 1.504570 s |
+| HDR download | 0.021966 s |
+| batch / timed batch | 36526 / 36526 |
+| summed worker generation | 3302.459 s |
+| summed worker submission/fallback | 4395.356 s |
+
+GPU kernel 时间约为 producer/splat wall 的 **99.12%**，kernel 吞吐约 **125.45 万事件/秒**。
+上传占比很小，CPU producer 在中段能够持续供给 GPU；下一步性能工作应优先研究 kernel，
+而不是仅增加 CPU worker 或上传带宽。这不单独证明 atomic contention 是 kernel 的主导成本。
+
+多数进度行的 submitted−completed=32,768，等于两个 16,384-event staging slot，符合
+有界队列与计时回收的设计。最后全部 36,526 批计时，没有沿用旧版前 64 批采样限制。
+
+两个 worker 时间是线程墙钟之和，其中 submission/fallback 包含锁与设备等待：
+`3302.459 + 4395.356 = 7697.815 ≈ 16 × 481.155`。不能将它们当作额外串行时间加到
+GPU 或总墙钟时间上，1462% CPU 也不能全部解释为有效计算。
+
+## 比较结论
+
+本次完整任务确认了优化的实际收益，星像及 PSF 分类计数全部匹配，PNG 比特级一致由用户确认。
+旧 CPU 文档中的计数差异属于不同修复版本，已不构成本次 CPU/HIP 配对的疑点。
+原有完整日志、硬件/构建证据的限制与 tracing/import 差异均保留，不用小规模 kernel 加速比
+替代这里的完整运行结果。
@@ -0,0 +1,23 @@
+❯ time ./build/Release/schwarzschild_sky \
+  --psf-relative-tail 1e-8 \
+  --psf-min-y 0 \
+  --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky \
+  --refine-max-level 4 \
+  --refine-jacobian-min 0.2 \
+  --width 3840 --height 2160 \
+  --look-ra-deg 262.5 --look-dec-deg -30 \
+  --fov-deg 45 \
+  --coarse-cell-pixels 16 \
+  --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 \
+  --catalog-load-workers 4 \
+  --observer-radius 100 \
+  --hdr-output --lens-map-output output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens \
+  --output output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.676 s
+Wrote lens map: output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens (65817 vertices, 130882 triangles)
+Catalog prefetch: 64440 requested, 64440 newly loaded (343363141 stars), 0 unavailable in 49.253 s; 4 loader workers
+Rendered 598264924 images from 343363141 catalog stars to output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png (ok)
+PSF splats: cached 598264924, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+./build/Release/schwarzschild_sky --psf-relative-tail 1e-8 --psf-min-y 0  1e8  22234.08s user 200.30s system 1521% cpu 24:34.32 total
@@ -0,0 +1,315 @@
+❯ time ./build/Release/schwarzschild_sky_hip --verbose \
+  --psf-relative-tail 1e-8 \
+  --psf-min-y 0 \
+  --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky \
+  --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 \
+  --catalog-load-workers 4 \
+  --hdr-output --lens-map-input output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens \
+  --output output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.691 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 64440 newly loaded (343363141 stars), 0 unavailable in 48.201 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: splat worker 13/16 started.
+Frame 0: splat worker 1/16 started.
+Frame 0: splat worker 10/16 started.
+Frame 0: splat worker 4/16 started.
+Frame 0: splat worker 8/16 started.
+Frame 0: splat worker 11/16 started.
+Frame 0: splat worker 3/16 started.
+Frame 0: splat worker 15/16 started.
+Frame 0: splat worker 14/16 started.
+Frame 0: splat worker 6/16 started.
+Frame 0: splat worker 5/16 started.
+Frame 0: splat worker 9/16 started.
+Frame 0: splat worker 16/16 started.
+Frame 0: splat worker 7/16 started.
+Frame 0: splat worker 12/16 started.
+Frame 0: splat worker 2/16 started.
+Frame 0: splat worker 2/16 reached 8 local triangles.
+Frame 0: splat worker 12/16 reached 8 local triangles.
+Frame 0: splat worker 10/16 reached 8 local triangles.
+Frame 0: splat worker 1/16 reached 8 local triangles.
+Frame 0: splat worker 11/16 reached 8 local triangles.
+Frame 0: splat worker 5/16 reached 8 local triangles.
+Frame 0: splat worker 4/16 reached 8 local triangles.
+Frame 0: splat worker 6/16 reached 8 local triangles.
+Frame 0: splat worker 9/16 reached 8 local triangles.
+Frame 0: splat worker 3/16 reached 8 local triangles.
+Frame 0: splat worker 16/16 reached 8 local triangles.
+Frame 0: splat worker 7/16 reached 8 local triangles.
+Frame 0: splat worker 15/16 reached 8 local triangles.
+Frame 0: splat worker 8/16 reached 8 local triangles.
+Frame 0: splat worker 13/16 reached 8 local triangles.
+Frame 0: splat worker 14/16 reached 8 local triangles.
+Frame 0: splat worker 6/16 reached 16 local triangles.
+Frame 0: splat worker 10/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 16 local triangles.
+Frame 0: splat worker 4/16 reached 16 local triangles.
+Frame 0: splat worker 16/16 reached 16 local triangles.
+Frame 0: splat worker 12/16 reached 16 local triangles.
+Frame 0: splat worker 13/16 reached 16 local triangles.
+Frame 0: splat worker 5/16 reached 16 local triangles.
+Frame 0: splat worker 14/16 reached 16 local triangles.
+Frame 0: splat worker 11/16 reached 16 local triangles.
+Frame 0: splat worker 7/16 reached 16 local triangles.
+Frame 0: splat worker 15/16 reached 16 local triangles.
+Frame 0: splat worker 8/16 reached 16 local triangles.
+Frame 0: splat worker 2/16 reached 16 local triangles.
+Frame 0: splat worker 3/16 reached 16 local triangles.
+Frame 0: splat worker 9/16 reached 16 local triangles.
+Frame 0: splat worker 12/16 reached 32 local triangles.
+Frame 0: splat worker 13/16 reached 32 local triangles.
+Frame 0: splat worker 1/16 reached 32 local triangles.
+Frame 0: splat worker 4/16 reached 32 local triangles.
+Frame 0: splat worker 6/16 reached 32 local triangles.
+Frame 0: splat worker 12/16 reached 64 local triangles.
+Frame 0: splat worker 13/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 32 local triangles.
+Frame 0: splat worker 5/16 reached 32 local triangles.
+Frame 0: splat worker 10/16 reached 32 local triangles.
+Frame 0: splat worker 15/16 reached 32 local triangles.
+Frame 0: splat worker 2/16 reached 32 local triangles.
+Frame 0: splat worker 7/16 reached 32 local triangles.
+Frame 0: splat worker 11/16 reached 32 local triangles.
+Frame 0: splat worker 16/16 reached 32 local triangles.
+Frame 0: splat worker 3/16 reached 32 local triangles.
+Frame 0: splat worker 9/16 reached 32 local triangles.
+Frame 0: splat worker 8/16 reached 32 local triangles.
+Frame 0: splat worker 1/16 reached 64 local triangles.
+Frame 0: splat worker 4/16 reached 64 local triangles.
+Frame 0: splat worker 6/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 64 local triangles.
+Frame 0: splat worker 9/16 reached 64 local triangles.
+Frame 0: splat worker 3/16 reached 64 local triangles.
+Frame 0: splat worker 16/16 reached 64 local triangles.
+Frame 0: splat worker 7/16 reached 64 local triangles.
+Frame 0: splat worker 8/16 reached 64 local triangles.
+Frame 0: splat worker 11/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 128 local triangles.
+Frame 0: splat worker 5/16 reached 64 local triangles.
+Frame 0: splat worker 13/16 reached 128 local triangles.
+Frame 0: splat worker 1/16 reached 128 local triangles.
+Frame 0: splat worker 15/16 reached 64 local triangles.
+Frame 0: splat worker 10/16 reached 64 local triangles.
+Frame 0: splat worker 2/16 reached 64 local triangles.
+Frame 0: splat worker 4/16 reached 128 local triangles.
+Frame 0: splat worker 9/16 reached 128 local triangles.
+Frame 0: splat worker 3/16 reached 128 local triangles.
+Frame 0: splat worker 8/16 reached 128 local triangles.
+Frame 0: splat worker 6/16 reached 128 local triangles.
+Frame 0: splat worker 11/16 reached 128 local triangles.
+Frame 0: splat worker 14/16 reached 128 local triangles.
+Frame 0: splat worker 16/16 reached 128 local triangles.
+Frame 0: splat worker 5/16 reached 128 local triangles.
+Frame 0: splat worker 10/16 reached 128 local triangles.
+Frame 0: splat worker 7/16 reached 128 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
+Frame 0: splat worker 15/16 reached 128 local triangles.
+Frame 0: splat worker 13/16 reached 256 local triangles.
+Frame 0: splat worker 12/16 reached 256 local triangles.
+Frame 0: splat worker 1/16 reached 256 local triangles.
+Frame 0: splat worker 4/16 reached 256 local triangles.
+Frame 0: splat worker 3/16 reached 256 local triangles.
+Frame 0: splat worker 14/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 256 local triangles.
+Frame 0: splat worker 9/16 reached 256 local triangles.
+Frame 0: splat worker 10/16 reached 256 local triangles.
+Frame 0: splat worker 5/16 reached 256 local triangles.
+Frame 0: splat worker 7/16 reached 256 local triangles.
+Frame 0: splat worker 6/16 reached 256 local triangles.
+Frame 0: splat worker 16/16 reached 256 local triangles.
+Frame 0: splat worker 15/16 reached 256 local triangles.
+Frame 0: splat worker 11/16 reached 256 local triangles.
+Frame 0: splat worker 2/16 reached 256 local triangles.
+Frame 0: splat worker 4/16 reached 512 local triangles.
+Frame 0: splat worker 12/16 reached 512 local triangles.
+Frame 0: splat worker 13/16 reached 512 local triangles.
+Frame 0: splat worker 9/16 reached 512 local triangles.
+Frame 0: splat worker 10/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 512 local triangles.
+Frame 0: splat worker 3/16 reached 512 local triangles.
+Frame 0: splat worker 1/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 512 local triangles.
+Frame 0: splat worker 6/16 reached 512 local triangles.
+Frame 0: splat worker 15/16 reached 512 local triangles.
+Frame 0: splat worker 5/16 reached 512 local triangles.
+Frame 0: splat worker 11/16 reached 512 local triangles.
+Frame 0: splat worker 16/16 reached 512 local triangles.
+Frame 0: splat worker 7/16 reached 512 local triangles.
+Frame 0: splat worker 2/16 reached 512 local triangles.
+HIP PSF progress: 4816896 submitted / 4784128 completed events; 292 / 294 batches timed; kernel 4.083 s
+Frame 0: splat worker 1/16 reached 1024 local triangles.
+Frame 0: splat worker 4/16 reached 1024 local triangles.
+Frame 0: splat worker 13/16 reached 1024 local triangles.
+Frame 0: splat worker 12/16 reached 1024 local triangles.
+Frame 0: splat worker 14/16 reached 1024 local triangles.
+Frame 0: splat worker 8/16 reached 1024 local triangles.
+Frame 0: splat worker 9/16 reached 1024 local triangles.
+Frame 0: splat worker 6/16 reached 1024 local triangles.
+Frame 0: splat worker 3/16 reached 1024 local triangles.
+Frame 0: splat worker 10/16 reached 1024 local triangles.
+Frame 0: splat worker 7/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 1024 local triangles.
+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 1024 local triangles.
+HIP PSF progress: 11206656 submitted / 11173888 completed events; 682 / 684 batches timed; kernel 9.065 s
+Frame 0: splat worker 11/16 reached 1024 local triangles.
+Frame 0: splat worker 5/16 reached 1024 local triangles.
+HIP PSF progress: 17547264 submitted / 17514496 completed events; 1069 / 1071 batches timed; kernel 14.057 s
+HIP PSF progress: 23838720 submitted / 23805952 completed events; 1453 / 1455 batches timed; kernel 19.045 s
+HIP PSF progress: 30081024 submitted / 30048256 completed events; 1834 / 1836 batches timed; kernel 24.036 s
+HIP PSF progress: 36306944 submitted / 36274176 completed events; 2214 / 2216 batches timed; kernel 29.028 s
+HIP PSF progress: 42483712 submitted / 42450944 completed events; 2591 / 2593 batches timed; kernel 34.020 s
+HIP PSF progress: 48660480 submitted / 48627712 completed events; 2968 / 2970 batches timed; kernel 39.014 s
+HIP PSF progress: 54755328 submitted / 54722560 completed events; 3340 / 3342 batches timed; kernel 43.998 s
+HIP PSF progress: 60850176 submitted / 60817408 completed events; 3712 / 3714 batches timed; kernel 48.971 s
+Frame 0: splat worker 14/16 reached 2048 local triangles.
+Frame 0: splat worker 12/16 reached 2048 local triangles.
+Frame 0: splat worker 4/16 reached 2048 local triangles.
+Frame 0: splat worker 9/16 reached 2048 local triangles.
+HIP PSF progress: 66977792 submitted / 66945024 completed events; 4086 / 4088 batches timed; kernel 53.963 s
+Frame 0: splat worker 1/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 2048 local triangles.
+Frame 0: splat worker 8/16 reached 2048 local triangles.
+Frame 0: splat worker 16/16 reached 2048 local triangles.
+Frame 0: splat worker 7/16 reached 2048 local triangles.
+Frame 0: splat worker 13/16 reached 2048 local triangles.
+Frame 0: splat worker 5/16 reached 2048 local triangles.
+Frame 0: splat worker 15/16 reached 2048 local triangles.
+Frame 0: splat worker 2/16 reached 2048 local triangles.
+HIP PSF progress: 73138176 submitted / 73105408 completed events; 4462 / 4464 batches timed; kernel 58.945 s
+Frame 0: splat worker 6/16 reached 2048 local triangles.
+Frame 0: splat worker 10/16 reached 2048 local triangles.
+Frame 0: splat worker 11/16 reached 2048 local triangles.
+HIP PSF progress: 79216640 submitted / 79183872 completed events; 4833 / 4835 batches timed; kernel 63.931 s
+HIP PSF progress: 85393408 submitted / 85360640 completed events; 5210 / 5212 batches timed; kernel 68.919 s
+HIP PSF progress: 91537408 submitted / 91504640 completed events; 5585 / 5587 batches timed; kernel 73.903 s
+HIP PSF progress: 97779712 submitted / 97746944 completed events; 5966 / 5968 batches timed; kernel 78.894 s
+HIP PSF progress: 103890944 submitted / 103858176 completed events; 6339 / 6341 batches timed; kernel 83.877 s
+HIP PSF progress: 110215168 submitted / 110182400 completed events; 6725 / 6727 batches timed; kernel 88.859 s
+HIP PSF progress: 116506624 submitted / 116473856 completed events; 7109 / 7111 batches timed; kernel 93.844 s
+HIP PSF progress: 123224064 submitted / 123191296 completed events; 7519 / 7521 batches timed; kernel 98.830 s
+HIP PSF progress: 130007040 submitted / 129974272 completed events; 7933 / 7935 batches timed; kernel 103.809 s
+HIP PSF progress: 136577024 submitted / 136544256 completed events; 8334 / 8336 batches timed; kernel 108.791 s
+HIP PSF progress: 142950400 submitted / 142917632 completed events; 8723 / 8725 batches timed; kernel 113.777 s
+HIP PSF progress: 149487616 submitted / 149454848 completed events; 9122 / 9124 batches timed; kernel 118.758 s
+HIP PSF progress: 156352512 submitted / 156319744 completed events; 9541 / 9543 batches timed; kernel 123.748 s
+HIP PSF progress: 163250176 submitted / 163217408 completed events; 9962 / 9964 batches timed; kernel 128.732 s
+HIP PSF progress: 169689088 submitted / 169656320 completed events; 10355 / 10357 batches timed; kernel 133.705 s
+HIP PSF progress: 176259072 submitted / 176226304 completed events; 10756 / 10758 batches timed; kernel 138.691 s
+HIP PSF progress: 183222272 submitted / 183189504 completed events; 11181 / 11183 batches timed; kernel 143.674 s
+HIP PSF progress: 190251008 submitted / 190218240 completed events; 11610 / 11612 batches timed; kernel 148.656 s
+HIP PSF progress: 197181440 submitted / 197148672 completed events; 12033 / 12035 batches timed; kernel 153.645 s
+HIP PSF progress: 203554816 submitted / 203522048 completed events; 12422 / 12424 batches timed; kernel 158.639 s
+HIP PSF progress: 210452480 submitted / 210419712 completed events; 12843 / 12845 batches timed; kernel 163.627 s
+HIP PSF progress: 217448448 submitted / 217415680 completed events; 13270 / 13272 batches timed; kernel 168.608 s
+HIP PSF progress: 224083968 submitted / 224051200 completed events; 13675 / 13677 batches timed; kernel 173.601 s
+HIP PSF progress: 230670336 submitted / 230637568 completed events; 14077 / 14079 batches timed; kernel 178.581 s
+HIP PSF progress: 237600768 submitted / 237568000 completed events; 14500 / 14502 batches timed; kernel 183.570 s
+HIP PSF progress: 244121600 submitted / 244088832 completed events; 14898 / 14900 batches timed; kernel 188.555 s
+HIP PSF progress: 250937344 submitted / 250904576 completed events; 15314 / 15316 batches timed; kernel 193.537 s
+HIP PSF progress: 257392640 submitted / 257359872 completed events; 15708 / 15710 batches timed; kernel 198.520 s
+HIP PSF progress: 264028160 submitted / 263995392 completed events; 16113 / 16115 batches timed; kernel 203.508 s
+HIP PSF progress: 270680064 submitted / 270647296 completed events; 16519 / 16521 batches timed; kernel 208.496 s
+HIP PSF progress: 277184512 submitted / 277151744 completed events; 16916 / 16918 batches timed; kernel 213.465 s
+HIP PSF progress: 283721728 submitted / 283688960 completed events; 17315 / 17317 batches timed; kernel 218.447 s
+Frame 0: splat worker 14/16 reached 4096 local triangles.
+HIP PSF progress: 290193408 submitted / 290160640 completed events; 17710 / 17712 batches timed; kernel 223.428 s
+Frame 0: splat worker 16/16 reached 4096 local triangles.
+HIP PSF progress: 296779776 submitted / 296747008 completed events; 18112 / 18114 batches timed; kernel 228.403 s
+Frame 0: splat worker 2/16 reached 4096 local triangles.
+HIP PSF progress: 303333376 submitted / 303300608 completed events; 18512 / 18514 batches timed; kernel 233.386 s
+Frame 0: splat worker 13/16 reached 4096 local triangles.
+Frame 0: splat worker 10/16 reached 4096 local triangles.
+Frame 0: splat worker 7/16 reached 4096 local triangles.
+HIP PSF progress: 309755904 submitted / 309723136 completed events; 18904 / 18906 batches timed; kernel 238.369 s
+Frame 0: splat worker 4/16 reached 4096 local triangles.
+Frame 0: splat worker 5/16 reached 4096 local triangles.
+Frame 0: splat worker 8/16 reached 4096 local triangles.
+HIP PSF progress: 315932672 submitted / 315899904 completed events; 19281 / 19283 batches timed; kernel 243.183 s
+Frame 0: splat worker 3/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 4096 local triangles.
+HIP PSF progress: 322338816 submitted / 322306048 completed events; 19672 / 19674 batches timed; kernel 248.175 s
+Frame 0: splat worker 1/16 reached 4096 local triangles.
+Frame 0: splat worker 6/16 reached 4096 local triangles.
+Frame 0: splat worker 9/16 reached 4096 local triangles.
+Frame 0: splat worker 15/16 reached 4096 local triangles.
+Frame 0: splat worker 12/16 reached 4096 local triangles.
+HIP PSF progress: 328597504 submitted / 328564736 completed events; 20054 / 20056 batches timed; kernel 253.161 s
+HIP PSF progress: 334741504 submitted / 334708736 completed events; 20429 / 20431 batches timed; kernel 258.149 s
+HIP PSF progress: 340819968 submitted / 340787200 completed events; 20800 / 20802 batches timed; kernel 263.138 s
+HIP PSF progress: 346865664 submitted / 346832896 completed events; 21169 / 21171 batches timed; kernel 268.124 s
+HIP PSF progress: 352894976 submitted / 352862208 completed events; 21537 / 21539 batches timed; kernel 273.097 s
+HIP PSF progress: 358973440 submitted / 358940672 completed events; 21908 / 21910 batches timed; kernel 278.083 s
+HIP PSF progress: 364986368 submitted / 364953600 completed events; 22275 / 22277 batches timed; kernel 283.074 s
+HIP PSF progress: 370900992 submitted / 370868224 completed events; 22636 / 22638 batches timed; kernel 288.068 s
+HIP PSF progress: 376946688 submitted / 376913920 completed events; 23005 / 23007 batches timed; kernel 293.054 s
+HIP PSF progress: 382844928 submitted / 382812160 completed events; 23365 / 23367 batches timed; kernel 298.052 s
+HIP PSF progress: 388923392 submitted / 388890624 completed events; 23736 / 23738 batches timed; kernel 303.033 s
+HIP PSF progress: 394772480 submitted / 394739712 completed events; 24093 / 24095 batches timed; kernel 308.019 s
+HIP PSF progress: 400621568 submitted / 400588800 completed events; 24450 / 24452 batches timed; kernel 313.006 s
+HIP PSF progress: 406536192 submitted / 406503424 completed events; 24811 / 24813 batches timed; kernel 317.991 s
+HIP PSF progress: 412499968 submitted / 412467200 completed events; 25175 / 25177 batches timed; kernel 322.978 s
+HIP PSF progress: 418316288 submitted / 418283520 completed events; 25530 / 25532 batches timed; kernel 327.973 s
+HIP PSF progress: 424148992 submitted / 424116224 completed events; 25886 / 25888 batches timed; kernel 332.964 s
+HIP PSF progress: 429948928 submitted / 429916160 completed events; 26240 / 26242 batches timed; kernel 337.956 s
+HIP PSF progress: 435961856 submitted / 435929088 completed events; 26607 / 26609 batches timed; kernel 342.950 s
+HIP PSF progress: 441942016 submitted / 441909248 completed events; 26972 / 26974 batches timed; kernel 347.936 s
+HIP PSF progress: 447741952 submitted / 447709184 completed events; 27326 / 27328 batches timed; kernel 352.922 s
+HIP PSF progress: 453541888 submitted / 453509120 completed events; 27680 / 27682 batches timed; kernel 357.894 s
+HIP PSF progress: 459390976 submitted / 459358208 completed events; 28037 / 28039 batches timed; kernel 362.875 s
+HIP PSF progress: 465387520 submitted / 465354752 completed events; 28403 / 28405 batches timed; kernel 367.848 s
+HIP PSF progress: 471400448 submitted / 471367680 completed events; 28770 / 28772 batches timed; kernel 372.843 s
+HIP PSF progress: 476987392 submitted / 476954624 completed events; 29111 / 29113 batches timed; kernel 377.672 s
+HIP PSF progress: 482525184 submitted / 482492416 completed events; 29449 / 29451 batches timed; kernel 382.488 s
+HIP PSF progress: 488357888 submitted / 488325120 completed events; 29805 / 29807 batches timed; kernel 387.481 s
+HIP PSF progress: 494190592 submitted / 494157824 completed events; 30161 / 30163 batches timed; kernel 392.467 s
+HIP PSF progress: 500432896 submitted / 500400128 completed events; 30542 / 30544 batches timed; kernel 397.454 s
+HIP PSF progress: 506445824 submitted / 506413056 completed events; 30909 / 30911 batches timed; kernel 402.437 s
+HIP PSF progress: 512344064 submitted / 512311296 completed events; 31269 / 31271 batches timed; kernel 407.423 s
+HIP PSF progress: 518455296 submitted / 518422528 completed events; 31642 / 31644 batches timed; kernel 412.408 s
+HIP PSF progress: 524484608 submitted / 524451840 completed events; 32010 / 32012 batches timed; kernel 417.391 s
+HIP PSF progress: 530628608 submitted / 530595840 completed events; 32385 / 32387 batches timed; kernel 422.377 s
+HIP PSF progress: 536739840 submitted / 536707072 completed events; 32758 / 32760 batches timed; kernel 427.370 s
+HIP PSF progress: 542867456 submitted / 542834688 completed events; 33132 / 33134 batches timed; kernel 432.358 s
+HIP PSF progress: 549044224 submitted / 549011456 completed events; 33509 / 33511 batches timed; kernel 437.340 s
+HIP PSF progress: 555220992 submitted / 555188224 completed events; 33886 / 33888 batches timed; kernel 442.323 s
+HIP PSF progress: 561397760 submitted / 561364992 completed events; 34263 / 34265 batches timed; kernel 447.309 s
+HIP PSF progress: 567607296 submitted / 567574528 completed events; 34642 / 34644 batches timed; kernel 452.300 s
+HIP PSF progress: 573849600 submitted / 573816832 completed events; 35023 / 35025 batches timed; kernel 457.284 s
+HIP PSF progress: 580124672 submitted / 580091904 completed events; 35406 / 35408 batches timed; kernel 462.268 s
+HIP PSF progress: 586432512 submitted / 586399744 completed events; 35791 / 35793 batches timed; kernel 467.253 s
+HIP PSF progress: 592773120 submitted / 592740352 completed events; 36178 / 36180 batches timed; kernel 472.247 s
+Frame 0: splat worker 14/16 reached 8192 local triangles.
+Frame 0: splat worker 16/16 reached 8192 local triangles.
+Frame 0: splat worker 2/16 reached 8192 local triangles.
+Frame 0: splat worker 13/16 reached 8192 local triangles.
+Frame 0: splat worker 10/16 reached 8192 local triangles.
+HIP PSF progress: 597475328 submitted / 597442560 completed events; 36465 / 36467 batches timed; kernel 476.352 s
+Frame 0: splat worker 11/16 reached 8192 local triangles.
+Frame 0: splat worker 3/16 finished after 8097 local triangles.
+Frame 0: splat worker 12/16 finished after 7940 local triangles.
+Frame 0: splat worker 13/16 finished after 8379 local triangles.
+Frame 0: splat worker 1/16 finished after 8046 local triangles.
+Frame 0: splat worker 16/16 finished after 8763 local triangles.
+Frame 0: splat worker 9/16 finished after 7982 local triangles.
+Frame 0: splat worker 11/16 finished after 8200 local triangles.
+Frame 0: splat worker 8/16 finished after 8121 local triangles.
+Frame 0: splat worker 14/16 finished after 8831 local triangles.
+Frame 0: splat worker 4/16 finished after 7936 local triangles.
+Frame 0: splat worker 6/16 finished after 8100 local triangles.
+Frame 0: splat worker 5/16 finished after 7905 local triangles.
+Frame 0: splat worker 15/16 finished after 7625 local triangles.
+Frame 0: splat worker 7/16 finished after 8084 local triangles.
+Frame 0: splat worker 10/16 finished after 8367 local triangles.
+Frame 0: splat worker 2/16 finished after 8506 local triangles.
+HIP producers: 16 workers; summed generation 3302.459 s, submission/fallback 4395.356 s; wall 481.155 s
+Frame 0: catalog splatting finished in 481.2 s; writing image...
+Rendered 598264924 images from 343363141 catalog stars to output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png (ok; imported lens map)
+PSF splats: cached 598264924, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 598264924 events in 36526 batches (36526 timed); upload 1.504570 s, kernel 476.906037 s, download 0.021966 s
+./build/Release/schwarzschild_sky_hip --verbose --psf-relative-tail 1e-8  0    7733.61s user 61.18s system 1462% cpu 8:53.06 total
@@ -0,0 +1,224 @@
+# adaptive_step_bounds_2026-10-05
+
+Long-term benchmark for calibrating the DP54 adaptive-integrator step bounds
+(`min_step` / `max_step`) of the past-directed null-geodesic tracer, and the
+public record of the one authorised 4K Schwarzschild `max_step` 2-vs-8 pair.
+
+The benchmark runs the public endpoint `geodesic_trace_past()`, the production
+DP core, and bounded adaptive-mesh renders against the analytic
+Minkowski / Schwarzschild / Alcubierre backends.  It does not modify production
+sources.
+
+## Build (required before renderer scripts)
+
+The Python mesh/4K drivers start from an existing renderer binary. The shell
+endpoint/core drivers compile their own small harnesses against production code.
+
+```
+make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend
+# binary: build/Release/schwarzschild_sky
+```
+
+## Files
+
+| file | role |
+|---|---|
+| `a_public_endpoints.c` | Experiment A: step-bound scans through the public endpoint, tol=1e-12 reference, RK4 h-halving on near-critical rays. |
+| `b_actual_h.c` | Experiment B: textually includes `src/geodesic.c`, drives the production `dp_advance_one` on finite trusted intervals to measure observed accepted `h`. |
+| `critical_ref_check.c` | Critical-classification probe (r30/r100 inward, r2.1 outward; `theta_crit` and `theta_crit±1e-7`; tol/max_step ladder). |
+| `mesh_maps.py` | Pure GRLENS v3 `load`/`compare`; no renderer, no untracked import. |
+| `run_mesh.py` | 8 bounded 320x180 candidates (R100 and R2.1, `max_step` .5/2/8/32). |
+| `run_mesh_reference.py` | 2 tight-tolerance references and comparisons against the 8 maps. |
+| `summarize_4k.py` | Postprocess existing maps only; never invokes a renderer. |
+| `run_4k_pair.py` | One-task, at-most-two-attempt 4K pair; refuses to run without `--authorize-two-4k`. |
+| `record_environment.py` | Provenance (git/hashes/compiler/cpu/build/run commands); no render. |
+| `failure_floor.c` | Failure-path floor diagnostic; includes `../../tests/test_geodesic_adaptive.c`. |
+| `run_failure_floor.sh` | Builds/runs `failure_floor.c` with `-DGEODESIC_EVENT_TESTING`. |
+| `run_limited.sh` | Builds/runs Experiment A + B; all output under `OUT_DIR`. |
+| `run_critical_ref.sh` | Builds/runs `critical_ref_check.c`; all output under `OUT_DIR`. |
+| `summarize.py` | `OUT_DIR` CLI arg (default `local/adaptive_step_bounds_2026-10-05`); writes `OUT_DIR/logs/summary.txt`. |
+| `results/` | Tracked long-term evidence (see below). |
+
+## Reproduction
+
+```
+AB_OUT="$PWD/local/adaptive_step_bounds_2026-10-05"
+OUT="$PWD/local/adaptive_bounds_mesh"
+
+bash  benchmarks/adaptive_step_bounds_2026-10-05/run_limited.sh "$AB_OUT"
+bash  benchmarks/adaptive_step_bounds_2026-10-05/run_critical_ref.sh "$AB_OUT"
+python3 benchmarks/adaptive_step_bounds_2026-10-05/summarize.py "$AB_OUT"
+
+python3 benchmarks/adaptive_step_bounds_2026-10-05/run_mesh.py "$OUT"
+python3 benchmarks/adaptive_step_bounds_2026-10-05/run_mesh_reference.py "$OUT"
+bash  benchmarks/adaptive_step_bounds_2026-10-05/run_failure_floor.sh "$OUT"
+
+# 4K only after explicit fresh user authorization for that task:
+python3 benchmarks/adaptive_step_bounds_2026-10-05/run_4k_pair.py \
+        --authorize-two-4k --out local/adaptive_bounds_4k
+```
+
+Defaults: A/B `OUT_DIR` is `local/adaptive_step_bounds_2026-10-05`; mesh
+`OUT_DIR` is `local/adaptive_bounds_mesh`; 4K `--out` default is
+`local/adaptive_bounds_4k`.  All logs/CSV go to `OUT_DIR`; the tracked
+benchmark directory holds only sources and `results/`.  Scratch binaries go to
+`/tmp/opencode/step_bounds/`.
+
+The `run_4k_pair.py` driver refuses to run without `--authorize-two-4k`, keeps
+an attempt ledger, and has no automatic retry.  Authorisation does not extend to
+later tasks or routine tests.
+
+All catalog inputs are generated inline by the scripts (column header
+`longitude_deg,latitude_deg,temperature_K,amplitude`, one 1e-30 star); no
+external survey CSV is read.
+
+## Results
+
+### 1. Public-endpoint step-bound scan (Experiment A/B)
+
+Environment and full table inputs: `results/source_environment.txt`,
+`results/summary_tables.txt`; full stdout: `results/expA.log`,
+`results/expB.log`.  Per-ray raw CSV (not tracked) is reproduced by
+`run_limited.sh`.
+
+| backend | worst near-critical sky error vs tol=1e-12 ref | notes |
+|---|---|---|
+| Schwarzschild r30 | 2.82e-4 rad (`max_step`≥1); 8.67e-5 rad at 0.25 | r100 8.0e-5 / 2.6e-5; r2.1 2.87e-4 |
+| Minkowski | Δn = 0, Δg/g = 0 (analytic) | crossing x/t ≤ 7.7e-11 at `max_step`≤256 |
+| Alcubierre | ≤1.8e-10 rad, no class change | 8x vs 1x `initial` RHS cost 4.3x–5.7x |
+
+- Dark terminal `L−L0` margin agrees with the reference to ≤2.1e-13 in every
+  config; near-critical dark stop times differ up to ~41 time units between
+  tol=1e-9 and tol=1e-12 (orbit-count sensitivity, reported not hidden).
+- Schwarzschild floor plateau: `min_step` `1e-14 … 1e-2` give bit-identical
+  results and RHS; only `0.1` breaks one r1.5 ray
+  (`INCOMPLETE/INTEGRATION_ERROR`).  No evidence to raise the default floor,
+  and no evidence that `1e-12` is uniquely optimal (it is never active).
+- Observed accepted `h` (Experiment B, finite window `T=min(20, ref span)`):
+  **Schwarzschild only** — r1.5 radial 0.0921, all other sampled Schwarzschild
+  rays ≥0.1; Alcubierre minimum = its initial step (0.05 / 0.005 / 0.0005);
+  Minkowski 1.0.  This is a finite-window diagnostic, **not** a full-trajectory
+  minimum.
+- RK4 h-halving worst (r2.1, `theta_crit−1e-7`): 1.04e-5 rad.
+
+### 2. Bounded 320x180 adaptive mesh
+
+Numeric inputs: `results/mesh_summary.json`,
+`results/mesh_reference_summary.json`.  Scene: R100/FOV45/jacobian0.2 and
+R2.1/outward/FOV90; DP54, hmin 1e-12, initial 0.1, tol 1e-9 (tight reference
+1e-12), 8 threads, one-point dim catalog.
+
+| scene | `max_step` | persistent vertices | RHS | wall (s) |
+|---|---:|---:|---:|---:|
+| R100 | 0.5 | 3158 | 16813349 | 2.071 |
+| R100 | 2 | 3158 | 6030185 | 0.979 |
+| R100 | 8 | 3158 | 4230835 | 0.823 |
+| R100 | 32 | 3158 | 4081609 | 0.830 |
+| R2.1 | 0.5 | 5496 | 20136508 | 1.974 |
+| R2.1 | 2 | 5496 | 9548434 | 1.178 |
+| R2.1 | 8 | 5496 | 7389760 | 0.970 |
+| R2.1 | 32 | 5496 | 7197806 | 0.972 |
+
+- 2→8 RHS reduction 29.84% (R100) / 22.61% (R2.1); 8→32 only 3.53% / 2.60%.
+- Identical terminal classifications and mesh/sample counts for all four caps.
+- Error vs tight reference: R100 max sky 9.216e-8 (hmax2) / 8.744e-8 (hmax8),
+  mutual 2-vs-8 difference 7.063e-9 rad; R2.1 max sky 1.4772e-5 rad at both,
+  mutual difference 8.370e-11 rad.  The larger R2.1 reference error is
+  tolerance/conditioning sensitive and is not cured by a smaller `max_step`.
+- Max log-frequency differences ≤8.51e-10 (R100) / ≤2.10e-9 (R2.1).
+- Short single-run wall times include setup/cache/output; not a timing study.
+
+### 3. One authorised 4K pair (R100, 3840x2160, FOV45)
+
+Raw terminal output (byte-for-byte): `results/4k_hmax2.log`,
+`results/4k_hmax8.log`; provenance: `results/4k_metadata.json`,
+`results/4k_attempts.json`; postprocessed: `results/4k_final_summary.json`,
+`results/4k_raw_summary.log`.
+
+| metric | `max_step`=2 | `max_step`=8 |
+|---|---:|---:|
+| persistent vertices / triangles | 66045 / 131338 | 66045 / 131338 |
+| outcomes | 62419 ESC, 3626 DARK | 62419 ESC, 3626 DARK |
+| unresolved / error | 0 | 0 |
+| persistent accepted | 15,768,677 | 10,183,020 |
+| persistent rejected | 97,176 | 194,781 |
+| persistent RHS | 130,409,139 | 91,991,144 |
+| trace+refine time (s) | 10.774 | 7.805 |
+| process wall (s) | 11.3893 | 8.38925 |
+
+- Triangle payload is bit-identical; shared film identities 66045, terminal
+  mismatches 0; max mutual endpoint sky difference 7.9544e-7 rad, max logg
+  difference 3.4711e-11.
+- Persistent-vertex RHS reduction −29.46%; accepted −35.42%; wall −26.34%.
+- **Cost scope:** the v3 map stores final persistent vertices only.  The
+  requested-sample count including discarded refinement probes is 116308
+  (> 66045), so discarded probes contribute no stored cost and these sums must
+  not be read as full-render executed RHS totals.
+- **Timing:** one sequential pair only; no statistical timing confidence.
+- PSF splat cached/direct = 0 and `--psf-min-y` discarded 1965 (hmax2) / 1954
+  (hmax8) events; this does not measure image error.  The PNGs are dark
+  diagnostic backgrounds; no 2MASS catalog was used.
+
+### 4. Critical-classification reference check
+
+Full output: `results/critical_ref.log`, `results/critical_ref.csv` (36
+endpoint traces).  The exact `theta_crit` direction is a classification
+separatrix; it is reported, never asserted.
+
+- r2.1 `theta_crit`: ref tol1e-12/h0.25 vs tol1e-13/h0.125 sky difference
+  **2.33638 rad** — the exactly-critical escape direction is not
+  independently converged.  `EXACT_CRITICAL_REFERENCE_NOT_CONVERGED`.
+- r30 `theta_crit` (DARK) stop-time difference 13.056; r100 `theta_crit` (DARK)
+  12.700.  At tol1e-11, h2-vs-h8 at r2.1 `theta_crit` is 5.09e-5 rad.
+- Neighbours `±1e-7`: both reference tiers agree (same outcome/reason/end,
+  clean, positive steps) at every neighbour.  Escaped-neighbour sky differences
+  between the layers are ~1e-7 rad (9.47e-8 r30, 2.74e-8 r100, 1.42e-7 r2.1),
+  consistent with the loose 1e-4 magnitude trend; DARK neighbours report
+  stop-time differences 1.5e-7 … 7.5e-7.
+- `CRITICAL_REFERENCE_CHECK status=0` (no neighbour reference disagreement or
+  error endpoint).
+
+## Decision summary
+
+- **Schwarzschild `max_step = 8`**: supported by the far-field cost plateau
+  (2→8 saves ~23–30% persistent RHS; 8→32 only ~3%) together with the tight
+  reference and 4K 2-vs-8 comparisons.  This is not claimed as globally optimal
+  and gives no guarantee for arbitrary near-critical/shadow directions.
+- **`min_step = 1e-12`**: retained as a non-binding numerical guard; not a
+  measured optimum.
+- **Minkowski `max_step = 16`** and **Alcubierre `max_step = 8 × initial`**:
+  retained as conservative caps. Their bounded accuracy checks support keeping
+  these values, not claiming cost optimality; larger Alcubierre caps still
+  reduce RHS, but have larger frequency errors in some cases.
+- The R2.1 exactly-critical difference is tolerance-sensitive;
+  `critical_ref_check.c` confirms the exact direction is not
+  independently converged and the report does not treat it as certified.
+
+## Caveats
+
+- Analytic backends only; no time-dependent numerical-relativity metric was
+  exercised.  Bounds and the `unit = 1` calibration are not transferable to NR.
+- Experiment B samples `T = min(20, reference span)`; no full-trajectory
+  minimum-step claim is made.
+- The 4K numbers are one sequential pair; no timing-stability confidence and
+  no image-error bound (inverse-lens-map Jacobian amplification is separate).
+- Sky-angle differences divided by pixel angle are not inverse-lens-map image
+  error bounds.
+- `failure_floor.c` reuses the regression invalid-metric temporal-domain
+  fixture; it is not a physical shadow or floor calibration.
+
+## Verification of the selected defaults and reproduction tools
+
+`make -B -j4 BUILD_TYPE=Debug test` passed after selecting the Schwarzschild
+cap of 8 and adding CLI provenance assertions for the default bounds. Full
+terminal output is retained locally at
+`local/step_bounds_mesh/final_debug_tests.log` (`STEP_BOUNDS_FULL_DEBUG_EXIT=0`).
+The explicit-RK4 HDR reference tests remain bit-identical. The Release
+Schwarzschild binary was rebuilt with the selected default.
+
+The self-contained limited driver was also executed with the relative output
+path `local/step_bounds_reproduction`: 1500 endpoint traces and 2427 observed
+finite-window steps completed, including summary generation. Small angular
+differences use `atan2(|cross|,dot)` rather than rounded `acos(dot)`. Running the
+4K driver without fresh explicit authorization refuses with exit code 2;
+this check launches no renderer. No further 4K attempt was made.
@@ -0,0 +1,867 @@
+/*
+ * Experiment A: DP54 step-bound scan through the *public* production
+ * endpoint geodesic_trace_past().
+ *
+ * Sub-commands:
+ *   schwarzschild : r30/r100 static inward, r2.1 static outward, r1.5 free-fall
+ *   minkowski     : moving observer, escape sphere 64, analytic flat check
+ *   alcubierre    : comoving bubble-center camera, vs .3/.9, sigma 1/10/100
+ *
+ * Each sub-command computes one DP54 tol=1e-12 reference per ray, then scans
+ *   - upper scan : max_step over a list, min_step fixed
+ *   - min scan   : min_step over a list, max_step fixed
+ * and compares every result against the reference (class, sky angle, g,
+ * dark threshold margin / stop time, cost).  Raw per-ray CSV and stdout
+ * summaries are produced.  No production source is modified.
+ *
+ * Link line (do NOT link geodesic.c twice; the backends are textually included
+ * below, so only the common sources are linked):
+ *   cc -std=c11 -O2 -Isrc a_public_endpoints.c geodesic.c asymptotic.c \
+ *      asymptotic_schwarzschild.c spacetime_common.c observer.c -lm
+ */
+#define _POSIX_C_SOURCE 200809L
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+
+/* Textually include all three analytic backends with renamed default
+ * constructors so one binary can exercise every provider (the files each
+ * define spacetime_create_default, which would collide at link time). */
+#define spacetime_create_default spacetime_create_default_minkowski_local
+#include "../../src/spacetime_minkowski.c"
+#undef spacetime_create_default
+#define spacetime_create_default spacetime_create_default_schwarzschild_local
+#include "../../src/spacetime_schwarzschild.c"
+#undef spacetime_create_default
+#define spacetime_create_default spacetime_create_default_alcubierre_local
+#include "../../src/spacetime_alcubierre.c"
+#undef spacetime_create_default
+
+#include "geodesic.h"
+#include "observer.h"
+#include "spacetime.h"
+
+#define PI 3.14159265358979323846
+#define MAX_CASES 16
+#define MAX_DIRS 16
+#define RAY_CAP 2500
+
+static long g_rays = 0;
+
+/* ------------------------------------------------------------------ */
+/* Small helpers                                                      */
+/* ------------------------------------------------------------------ */
+
+static double dot3(const double a[3], const double b[3]) {
+  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+}
+
+static double ang_delta(const double a[3], const double b[3]) {
+  const double na = sqrt(dot3(a, a)), nb = sqrt(dot3(b, b));
+  if (!(na > 0.0) || !(nb > 0.0))
+    return NAN;
+  const double ca = dot3(a, b) / (na * nb);
+  const double cross[3] = {a[1] * b[2] - a[2] * b[1],
+                           a[2] * b[0] - a[0] * b[2],
+                           a[0] * b[1] - a[1] * b[0]};
+  const double sn = sqrt(dot3(cross, cross)) / (na * nb);
+  return atan2(sn, ca);
+}
+
+static double now_s(void) {
+  struct timespec ts;
+  clock_gettime(CLOCK_MONOTONIC, &ts);
+  return (double)ts.tv_sec + 1e-9 * (double)ts.tv_nsec;
+}
+
+static int is_dark(int outcome) { return outcome == RAY_OUTCOME_DARK; }
+static int is_escaped(int outcome) { return outcome == RAY_OUTCOME_ESCAPED; }
+
+/* Critical local angle (static observer, M=1) for the Schwarzschild monopole.
+ * theta_c = asin(3 sqrt(3) sqrt(1-2/r) / r). */
+static double critical_angle(double r) {
+  const double b = 3.0 * sqrt(3.0) * sqrt(1.0 - 2.0 / r) / r;
+  if (!(b < 1.0))
+    return PI / 2.0;
+  return asin(b);
+}
+
+/* ------------------------------------------------------------------ */
+/* Case / result / comparison structures                              */
+/* ------------------------------------------------------------------ */
+
+typedef struct {
+  char name[32];
+  int prov; /* 0 schwarzschild, 1 minkowski, 2 alcubierre */
+  double mass, escape_radius;
+  double alc_vs, alc_radius, alc_sigma;
+  double look_ra_deg, look_dec_deg;
+  double position[3], velocity[3];
+  double initial_step, lookback;
+  unsigned int max_steps;
+  unsigned int ref_max_steps; /* budget for the tol=1e-12 reference only */
+  double max_step_for_min_scan; /* fixed upper during the min scan */
+  int n_dirs;
+  double dirs[MAX_DIRS][3];
+  double theta[MAX_DIRS]; /* NAN for non-angle direction sets */
+} Case;
+
+typedef struct {
+  int outcome, reason, end_id;
+  double stop_t, g, thr;
+  double n[3];
+  unsigned int steps, rejected;
+  unsigned long rhs;
+  double wall;
+} Res;
+
+typedef struct {
+  int has_ref;
+  int class_match;
+  double dn_ang, dlogg, dgrel, dstopT, dmargin;
+} Cmp;
+
+typedef struct {
+  long n, class_mismatch;
+  double max_dn_ang, max_dlogg, max_dgrel, max_dstopT, max_dmargin;
+  unsigned long sum_rhs, max_rhs;
+  unsigned int max_rejected;
+  double sum_wall;
+  long escaped, dark, unresolved, incomplete;
+} Agg;
+
+static void agg_init(Agg *a) {
+  memset(a, 0, sizeof *a);
+  a->max_dn_ang = a->max_dlogg = a->max_dgrel = a->max_dstopT =
+      a->max_dmargin = -1.0;
+}
+
+static void bump(double *m, double v) {
+  if (!isfinite(v))
+    return;
+  if (v > *m)
+    *m = v;
+}
+
+static void agg_add(Agg *a, const Res *r, const Cmp *c) {
+  ++a->n;
+  if (c->has_ref && !c->class_match)
+    ++a->class_mismatch;
+  if (c->has_ref) {
+    bump(&a->max_dn_ang, c->dn_ang);
+    bump(&a->max_dlogg, c->dlogg);
+    bump(&a->max_dgrel, c->dgrel);
+    bump(&a->max_dstopT, c->dstopT);
+    bump(&a->max_dmargin, c->dmargin);
+  }
+  a->sum_rhs += r->rhs;
+  if (r->rhs > a->max_rhs)
+    a->max_rhs = r->rhs;
+  if (r->rejected > a->max_rejected)
+    a->max_rejected = r->rejected;
+  a->sum_wall += r->wall;
+  if (is_dark(r->outcome))
+    ++a->dark;
+  else if (is_escaped(r->outcome))
+    ++a->escaped;
+  else if (r->outcome == RAY_OUTCOME_UNRESOLVED)
+    ++a->unresolved;
+  else
+    ++a->incomplete;
+}
+
+/* ------------------------------------------------------------------ */
+/* Config builders                                                    */
+/* ------------------------------------------------------------------ */
+
+static GeodesicTraceConfig make_dp(double initial, double min_step,
+                                   double max_step, double tol,
+                                   unsigned int max_steps, double lookback) {
+  GeodesicTraceConfig c;
+  memset(&c, 0, sizeof c);
+  c.coordinate_time_step = initial;
+  c.max_steps = max_steps;
+  c.threshold.kind = THRESHOLD_LOG_ENERGY_GROWTH;
+  c.threshold.value = 8.0;
+  c.threshold.policy_version = 3;
+  c.stepper = GEODESIC_STEPPER_DP54;
+  c.atol_x = tol;
+  c.atol_Pi = tol;
+  c.atol_L = tol;
+  c.rtol = tol;
+  c.min_step = min_step;
+  c.max_step = max_step;
+  c.consecutive_rejection_limit = 32;
+  c.max_lookback_time = lookback;
+  return c;
+}
+
+static GeodesicTraceConfig make_rk4(double step, unsigned int max_steps) {
+  GeodesicTraceConfig c;
+  memset(&c, 0, sizeof c);
+  c.coordinate_time_step = step;
+  c.max_steps = max_steps;
+  c.threshold.kind = THRESHOLD_LOG_ENERGY_GROWTH;
+  c.threshold.value = 8.0;
+  c.threshold.policy_version = 3;
+  c.stepper = GEODESIC_STEPPER_RK4;
+  return c;
+}
+
+/* ------------------------------------------------------------------ */
+/* Trace + compare                                                    */
+/* ------------------------------------------------------------------ */
+
+static Res run_ray(const SpacetimeSource *source, const ObserverState *observer,
+                   const double dir[3], const GeodesicTraceConfig *config) {
+  Res r;
+  memset(&r, 0, sizeof r);
+  ++g_rays;
+  if (g_rays > RAY_CAP) {
+    fprintf(stderr, "FATAL: ray cap %d exceeded\n", RAY_CAP);
+    exit(3);
+  }
+  const double t0 = now_s();
+  const RayEndpoint e = geodesic_trace_past(source, observer, dir, config);
+  r.wall = now_s() - t0;
+  r.outcome = e.outcome;
+  r.reason = e.reason;
+  r.end_id = e.end_id;
+  r.stop_t = e.stop_coordinate_time;
+  r.g = e.frequency_ratio;
+  r.thr = e.threshold_value;
+  for (int i = 0; i < 3; ++i)
+    r.n[i] = e.n_infinity[i];
+  r.steps = e.accepted_steps;
+  r.rejected = e.rejected_steps;
+  r.rhs = e.rhs_evaluations;
+  return r;
+}
+
+static void compare(const Res *a, const Res *ref, Cmp *c) {
+  memset(c, 0, sizeof *c);
+  c->has_ref = 1;
+  c->class_match = (a->outcome == ref->outcome && a->reason == ref->reason);
+  if (is_escaped(a->outcome) && is_escaped(ref->outcome)) {
+    c->dn_ang = ang_delta(a->n, ref->n);
+    if (a->g > 0.0 && ref->g > 0.0 && isfinite(a->g) && isfinite(ref->g)) {
+      c->dlogg = fabs(log(a->g) - log(ref->g));
+      c->dgrel = fabs(a->g / ref->g - 1.0);
+    } else {
+      c->dlogg = c->dgrel = NAN;
+    }
+  } else {
+    c->dn_ang = c->dlogg = c->dgrel = NAN;
+  }
+  c->dstopT = (isfinite(a->stop_t) && isfinite(ref->stop_t))
+                  ? fabs(a->stop_t - ref->stop_t)
+                  : NAN;
+  c->dmargin = (is_dark(a->outcome) && is_dark(ref->outcome) &&
+                isfinite(a->thr) && isfinite(ref->thr))
+                   ? fabs(a->thr - ref->thr)
+                   : NAN;
+}
+
+static void write_row(FILE *f, const char *phase, const Case *c, int di,
+                      double upper, double min_step, double tol, const Res *r,
+                      const Cmp *cmp) {
+  fprintf(f,
+          "%s,%s,%d,%.17g,%.6g,%.6g,%.6g,%d,%d,%u,%.17g,%u,%u,%lu,%.6g,"
+          "%.17g,%.17g,%.17g,%.17g,%.17g",
+          phase, c->name, di, c->theta[di], upper, min_step, tol, r->outcome,
+          r->reason, r->end_id, r->stop_t, r->steps, r->rejected, r->rhs,
+          r->wall, r->n[0], r->n[1], r->n[2], r->g, r->thr);
+  if (cmp->has_ref)
+    fprintf(f, ",%d,%.17g,%.17g,%.17g,%.17g,%.17g", cmp->class_match,
+            cmp->dn_ang, cmp->dlogg, cmp->dgrel, cmp->dstopT, cmp->dmargin);
+  else
+    fprintf(f, ",,nan,nan,nan,nan,nan");
+  fprintf(f, "\n");
+}
+
+static const char *ROW_HEADER =
+    "phase,case,dir,theta,upper,min_step,tol,outcome,reason,end_id,stop_t,"
+    "steps,rejected,rhs,wall_s,nx,ny,nz,g,thr,class_match,dn_ang,dlogg,dgrel,"
+    "dstopT,dmargin\n";
+
+static void write_agg(FILE *f, const char *phase, const Case *c, double upper,
+                      double min_step, double tol, const Agg *a) {
+  fprintf(f,
+          "%s,%s,%.6g,%.6g,%.6g,%ld,%ld,%.6g,%.6g,%.6g,%.6g,%.6g,%lu,%lu,%u,"
+          "%.4f,%ld,%ld,%ld,%ld\n",
+          phase, c->name, upper, min_step, tol, a->n, a->class_mismatch,
+          a->max_dn_ang, a->max_dlogg, a->max_dgrel, a->max_dstopT,
+          a->max_dmargin, a->sum_rhs, a->max_rhs, a->max_rejected, a->sum_wall,
+          a->escaped, a->dark, a->unresolved, a->incomplete);
+}
+
+static const char *AGG_HEADER =
+    "phase,case,upper,min_step,tol,n,class_mismatch,max_dn_ang,max_dlogg,"
+    "max_dgrel,max_dstopT,max_dmargin,sum_rhs,max_rhs,max_rejected,sum_wall,"
+    "escaped,dark,unresolved,incomplete\n";
+
+/* ------------------------------------------------------------------ */
+/* Case builders                                                      */
+/* ------------------------------------------------------------------ */
+
+static void dir_from_theta(double th, double n[3]) {
+  if (th == 0.0) {
+    n[0] = 1.0;
+    n[1] = n[2] = 0.0;
+  } else if (th == PI) {
+    n[0] = -1.0;
+    n[1] = n[2] = 0.0;
+  } else {
+    n[0] = cos(th);
+    n[1] = sin(th);
+    n[2] = 0.0;
+  }
+  const double nn = sqrt(dot3(n, n));
+  for (int i = 0; i < 3; ++i)
+    n[i] /= nn;
+}
+
+static void fill_static_dirs(Case *c, double r) {
+  const double tc = critical_angle(r);
+  const double th[MAX_DIRS] = {0.0,        PI,          PI / 2.0,    tc,
+                               tc - 1e-3,  tc + 1e-3,   tc - 1e-5,   tc + 1e-5,
+                               tc - 1e-7,  tc + 1e-7,   tc + 0.05,   tc - 0.05};
+  c->n_dirs = 12;
+  for (int i = 0; i < c->n_dirs; ++i) {
+    c->theta[i] = th[i];
+    dir_from_theta(th[i], c->dirs[i]);
+  }
+}
+
+static void case_static(Case *c, const char *name, double r, double look_ra) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "%s", name);
+  c->prov = 0;
+  c->mass = 1.0;
+  c->escape_radius = 256.0;
+  c->look_ra_deg = look_ra;
+  c->look_dec_deg = 0.0;
+  c->position[0] = r;
+  c->position[1] = c->position[2] = 0.0;
+  c->velocity[0] = c->velocity[1] = c->velocity[2] = 0.0;
+  c->initial_step = 0.1;
+  c->lookback = 6553.6;
+  c->max_steps = 65536;
+  c->ref_max_steps = 65536;
+  c->max_step_for_min_scan = 2.0;
+  fill_static_dirs(c, r);
+}
+
+static void case_freefall(Case *c, const char *name, double r) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "%s", name);
+  c->prov = 0;
+  c->mass = 1.0;
+  c->escape_radius = 256.0;
+  c->look_ra_deg = 180.0;
+  c->look_dec_deg = 0.0;
+  c->position[0] = r;
+  c->position[1] = c->position[2] = 0.0;
+  /* Free-fall from rest at infinity, coordinate velocity dx/dt (the formula
+   * used by local/p2d_validation/observer_endpoints.c). */
+  const double y = sqrt(2.0 / r);
+  c->velocity[0] = -y * (1.0 + y) / (1.0 + y + y * y);
+  c->velocity[1] = c->velocity[2] = 0.0;
+  c->initial_step = 0.1;
+  c->lookback = 6553.6;
+  c->max_steps = 65536;
+  c->ref_max_steps = 65536;
+  c->max_step_for_min_scan = 2.0;
+  {
+    const double th[4] = {0.0, PI / 2.0, PI, 3.0 * PI / 4.0};
+    c->n_dirs = 4;
+    for (int i = 0; i < 4; ++i) {
+      c->theta[i] = th[i];
+      dir_from_theta(th[i], c->dirs[i]);
+    }
+  }
+}
+
+static void case_minkowski(Case *c) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "mink_moving");
+  c->prov = 1;
+  c->escape_radius = 64.0;
+  c->look_ra_deg = 0.0;
+  c->look_dec_deg = 0.0;
+  c->position[0] = 10.0;
+  c->position[1] = 20.0;
+  c->position[2] = -15.0;
+  c->velocity[0] = 0.3;
+  c->velocity[1] = 0.2;
+  c->velocity[2] = 0.1;
+  c->initial_step = 1.0;
+  c->lookback = 2048.0;
+  c->max_steps = 2048;
+  c->ref_max_steps = 4096;
+  c->max_step_for_min_scan = 16.0;
+  {
+    const double d[6][3] = {{1.0, 0.0, 0.0},  {-1.0, 0.0, 0.0},
+                            {0.0, 1.0, 0.0},  {0.0, 0.0, 1.0},
+                            {0.6, 0.8, 0.0},  {-0.6, 0.8, 0.0}};
+    c->n_dirs = 6;
+    for (int i = 0; i < 6; ++i) {
+      c->theta[i] = NAN;
+      for (int k = 0; k < 3; ++k)
+        c->dirs[i][k] = d[i][k];
+    }
+  }
+}
+
+static void case_alcubierre(Case *c, const char *name, double vs, double sigma) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "%s", name);
+  c->prov = 2;
+  c->alc_vs = vs;
+  c->alc_radius = 1.0;
+  c->alc_sigma = sigma;
+  c->look_ra_deg = 0.0;
+  c->look_dec_deg = 0.0;
+  c->position[0] = c->position[1] = c->position[2] = 0.0;
+  c->velocity[0] = vs; /* comoving with the bubble center */
+  c->velocity[1] = c->velocity[2] = 0.0;
+  c->initial_step = fmin(0.1, 0.05 / sigma);
+  c->max_steps = 100000;
+  c->ref_max_steps = 200000;
+  {
+    const double esc = spacetime_alcubierre_escape_radius(1.0, sigma);
+    c->lookback = 1.25 * 4.0 * esc / (1.0 - fabs(vs));
+  }
+  c->max_step_for_min_scan = c->initial_step * 8.0;
+  {
+    const double d[6][3] = {{1.0, 0.0, 0.0},  {-1.0, 0.0, 0.0},
+                            {0.0, 1.0, 0.0},  {0.0, 0.0, 1.0},
+                            {0.6, 0.8, 0.0},  {-0.6, 0.8, 0.0}};
+    c->n_dirs = 6;
+    for (int i = 0; i < 6; ++i) {
+      c->theta[i] = NAN;
+      for (int k = 0; k < 3; ++k)
+        c->dirs[i][k] = d[i][k];
+    }
+  }
+}
+
+/* ------------------------------------------------------------------ */
+/* Source/observer construction                                       */
+/* ------------------------------------------------------------------ */
+
+static int build_source(const Case *c, SpacetimeSource *s) {
+  if (c->prov == 0)
+    return spacetime_create_schwarzschild_ks(s, c->mass, c->escape_radius);
+  if (c->prov == 1)
+    return spacetime_create_minkowski(s, c->escape_radius);
+  return spacetime_create_alcubierre(s, c->alc_vs, c->alc_radius,
+                                     c->alc_sigma);
+}
+
+static int build_observer(const Case *c, const SpacetimeSource *s,
+                          ObserverState *o) {
+  MetricData m;
+  if (spacetime_eval(s, 0.0, c->position, &m) != SPACETIME_POINT_OK)
+    return -1;
+  ObserverCamera cam;
+  memset(&cam, 0, sizeof cam);
+  cam.coordinate_time = 0.0;
+  for (int i = 0; i < 3; ++i) {
+    cam.position[i] = c->position[i];
+    cam.velocity[i] = c->velocity[i];
+  }
+  cam.look_ra_deg = c->look_ra_deg;
+  cam.look_dec_deg = c->look_dec_deg;
+  cam.roll_deg = 0.0;
+  return observer_from_coordinate_camera(&m, &cam, o, NULL) ==
+                 OBSERVER_BUILD_OK
+             ? 0
+             : -1;
+}
+
+/* ------------------------------------------------------------------ */
+/* Generic scan driver                                                */
+/* ------------------------------------------------------------------ */
+
+static void run_grid(const Case *cases, int ncases, const double *uppers,
+                     int n_up, const double *floors, int n_fl, double tol,
+                     const char *phase, const char *rows_path,
+                     const char *agg_path, Res refs[][MAX_DIRS]) {
+  FILE *rf = fopen(rows_path, "w");
+  FILE *af = fopen(agg_path, "w");
+  if (!rf || !af) {
+    fprintf(stderr, "FATAL: cannot open %s / %s\n", rows_path, agg_path);
+    exit(2);
+  }
+  fprintf(rf, "%s", ROW_HEADER);
+  fprintf(af, "%s", AGG_HEADER);
+  for (int ci = 0; ci < ncases; ++ci) {
+    const Case *c = &cases[ci];
+    SpacetimeSource source;
+    ObserverState observer;
+    if (build_source(c, &source) || build_observer(c, &source, &observer)) {
+      fprintf(stderr, "FATAL: cannot build case %s\n", c->name);
+      exit(2);
+    }
+    for (int ui = 0; ui < n_up; ++ui) {
+      for (int fi = 0; fi < n_fl; ++fi) {
+        Agg agg;
+        agg_init(&agg);
+        for (int di = 0; di < c->n_dirs; ++di) {
+          const GeodesicTraceConfig cfg =
+              make_dp(c->initial_step, floors[fi], uppers[ui], tol, c->max_steps,
+                      c->lookback);
+          const Res r = run_ray(&source, &observer, c->dirs[di], &cfg);
+          Cmp cmp;
+          compare(&r, &refs[ci][di], &cmp);
+          write_row(rf, phase, c, di, uppers[ui], floors[fi], tol, &r, &cmp);
+          agg_add(&agg, &r, &cmp);
+        }
+        write_agg(af, phase, c, uppers[ui], floors[fi], tol, &agg);
+        printf("SUMMARY %s %s upper=%.6g min=%.6g n=%ld mismatch=%ld "
+               "max_dn_ang=%.6g max_dgrel=%.6g max_dstopT=%.6g sum_rhs=%lu "
+               "esc=%ld dark=%ld unres=%ld inc=%ld wall=%.3fs\n",
+               phase, c->name, uppers[ui], floors[fi], agg.n,
+               agg.class_mismatch, agg.max_dn_ang, agg.max_dgrel,
+               agg.max_dstopT, agg.sum_rhs, agg.escaped, agg.dark,
+               agg.unresolved, agg.incomplete, agg.sum_wall);
+        fflush(stdout);
+      }
+    }
+    spacetime_destroy(&source);
+  }
+  fclose(rf);
+  fclose(af);
+}
+
+/* Compute DP tol=1e-12 reference for every direction of every case.
+ * upper_ref <= 0 means "use the case's own initial step" as the max_step. */
+static void compute_refs(const Case *cases, int ncases, double upper_ref,
+                         const char *path, Res refs[][MAX_DIRS]) {
+  FILE *f = fopen(path, "w");
+  if (!f) {
+    fprintf(stderr, "FATAL: cannot open %s\n", path);
+    exit(2);
+  }
+  fprintf(f, "%s", ROW_HEADER);
+  for (int ci = 0; ci < ncases; ++ci) {
+    const Case *c = &cases[ci];
+    SpacetimeSource source;
+    ObserverState observer;
+    if (build_source(c, &source) || build_observer(c, &source, &observer)) {
+      fprintf(stderr, "FATAL: cannot build case %s\n", c->name);
+      exit(2);
+    }
+    const double upper = (upper_ref > 0.0) ? upper_ref : c->initial_step;
+    for (int di = 0; di < c->n_dirs; ++di) {
+      const GeodesicTraceConfig cfg = make_dp(c->initial_step, 1e-12, upper,
+                                              1e-12, c->ref_max_steps,
+                                              c->lookback);
+      refs[ci][di] = run_ray(&source, &observer, c->dirs[di], &cfg);
+      Cmp none;
+      memset(&none, 0, sizeof none);
+      write_row(f, "ref", c, di, upper, 1e-12, 1e-12, &refs[ci][di], &none);
+      printf("REF %s dir=%d theta=%.6g outcome=%d reason=%d stop_t=%.9g "
+             "steps=%u rejected=%u rhs=%lu g=%.12g thr=%.12g\n",
+             c->name, di, c->theta[di], refs[ci][di].outcome,
+             refs[ci][di].reason, refs[ci][di].stop_t, refs[ci][di].steps,
+             refs[ci][di].rejected, refs[ci][di].rhs, refs[ci][di].g,
+             refs[ci][di].thr);
+      fflush(stdout);
+    }
+    spacetime_destroy(&source);
+  }
+  fclose(f);
+}
+
+/* ------------------------------------------------------------------ */
+/* Sub-command: Schwarzschild                                         */
+/* ------------------------------------------------------------------ */
+
+static void cmd_schwarzschild(void) {
+  static Case cases[MAX_CASES];
+  static Res refs[MAX_CASES][MAX_DIRS];
+  memset(refs, 0, sizeof refs);
+  int nc = 0;
+  case_static(&cases[nc++], "r30_inward", 30.0, 180.0);
+  case_static(&cases[nc++], "r100_inward", 100.0, 180.0);
+  case_static(&cases[nc++], "r2p1_outward", 2.1, 0.0);
+  case_freefall(&cases[nc++], "r1p5_freefall", 1.5);
+
+  compute_refs(cases, nc, 0.25, "raw/a_sch_reference.csv", refs);
+
+  static const double uppers[9] = {0.25, 0.5, 1.0, 2.0, 4.0,
+                                   8.0,  16.0, 32.0, 64.0};
+  static const double floors[10] = {1e-1, 1e-2, 1e-3, 1e-4, 1e-5,
+                                    1e-6, 1e-8, 1e-10, 1e-12, 1e-14};
+  run_grid(cases, nc, uppers, 9, (double[]){1e-12}, 1, 1e-9, "upper",
+           "raw/a_sch_upper.csv", "raw/a_sch_upper_summary.csv", refs);
+  run_grid(cases, nc, (double[]){2.0}, 1, floors, 10, 1e-9, "min",
+           "raw/a_sch_min.csv", "raw/a_sch_min_summary.csv", refs);
+
+  /* Sensitive-ray RK4 h-halving reference (extra independent check).
+   * (case index, dir index): r30 and r2.1, theta_c +- 1e-5 / +- 1e-7. */
+  const int sens[8][2] = {{0, 8}, {0, 9}, {0, 6}, {0, 7},
+                          {2, 8}, {2, 9}, {2, 6}, {2, 7}};
+  FILE *f = fopen("raw/a_sch_rk4_sensitive.csv", "w");
+  if (!f) {
+    fprintf(stderr, "FATAL: cannot open rk4 csv\n");
+    exit(2);
+  }
+  fprintf(f, "%s", ROW_HEADER);
+  for (int k = 0; k < 8; ++k) {
+    const Case *c = &cases[sens[k][0]];
+    const int di = sens[k][1];
+    SpacetimeSource source;
+    ObserverState observer;
+    if (build_source(c, &source) || build_observer(c, &source, &observer)) {
+      fprintf(stderr, "FATAL: cannot build case %s\n", c->name);
+      exit(2);
+    }
+    GeodesicTraceConfig rk01 = make_rk4(0.01, 262144);
+    GeodesicTraceConfig rk005 = make_rk4(0.005, 262144);
+    Res r01 = run_ray(&source, &observer, c->dirs[di], &rk01);
+    Res r005 = run_ray(&source, &observer, c->dirs[di], &rk005);
+    Cmp hh, vsdp;
+    compare(&r005, &r01, &hh);
+    compare(&r005, &refs[sens[k][0]][di], &vsdp);
+    Cmp none;
+    memset(&none, 0, sizeof none);
+    write_row(f, "rk4_0.01", c, di, 0.01, 0.0, 0.0, &r01, &none);
+    write_row(f, "rk4_0.005", c, di, 0.005, 0.0, 0.0, &r005, &none);
+    printf("RK4 %s dir=%d theta=%.6g o01=%d/%d o005=%d/%d "
+           "hhalve_dn=%.6g hhalve_dgrel=%.6g vsdp_dn=%.6g vsdp_dgrel=%.6g "
+           "vsdp_class=%d\n",
+           c->name, di, c->theta[di], r01.outcome, r01.reason, r005.outcome,
+           r005.reason, hh.dn_ang, hh.dgrel, vsdp.dn_ang, vsdp.dgrel,
+           vsdp.class_match);
+    spacetime_destroy(&source);
+  }
+  fclose(f);
+}
+
+/* ------------------------------------------------------------------ */
+/* Sub-command: Minkowski (analytic flat verification)                */
+/* ------------------------------------------------------------------ */
+
+/* Analytic flat past escape from an observer at (t0,x0) with tetrad-frame
+ * direction n: coordinate photon velocity u = k_vec/k^0, crossing radius R at
+ * s = t-t0 < 0, sky direction n_inf = -u, frequency ratio g = 1/k^0. */
+static int mink_analytic(const Case *c, const ObserverState *o,
+                         const double n[3], double R, double *t_cross,
+                         double *xc, double *ninf, double *g) {
+  double k[4];
+  for (int mu = 0; mu < 4; ++mu)
+    k[mu] = o->tetrad[0][mu];
+  for (int a = 0; a < 3; ++a)
+    for (int mu = 0; mu < 4; ++mu)
+      k[mu] -= n[a] * o->tetrad[a + 1][mu];
+  if (!(k[0] > 0.0))
+    return -1;
+  double u[3];
+  for (int i = 0; i < 3; ++i)
+    u[i] = k[i + 1] / k[0];
+  const double uu = dot3(u, u);
+  const double B = 2.0 * dot3(c->position, u);
+  const double C = dot3(c->position, c->position) - R * R;
+  const double disc = B * B - 4.0 * uu * C;
+  if (disc < 0.0)
+    return -1;
+  const double sq = sqrt(disc);
+  const double s1 = (-B + sq) / (2.0 * uu);
+  const double s2 = (-B - sq) / (2.0 * uu);
+  const double s = (s1 < 0.0) ? fmin(s1, s2) : s2;
+  if (!(s < 0.0))
+    return -1;
+  *t_cross = o->coordinate_time + s;
+  for (int i = 0; i < 3; ++i)
+    xc[i] = c->position[i] + u[i] * s;
+  const double nu = sqrt(uu);
+  for (int i = 0; i < 3; ++i)
+    ninf[i] = -u[i] / nu;
+  *g = 1.0 / k[0];
+  return 0;
+}
+
+static void cmd_minkowski(void) {
+  Case c;
+  case_minkowski(&c);
+  static Res refs[MAX_CASES][MAX_DIRS];
+  memset(refs, 0, sizeof refs);
+  SpacetimeSource source;
+  ObserverState observer;
+  if (build_source(&c, &source) || build_observer(&c, &source, &observer)) {
+    fprintf(stderr, "FATAL: cannot build minkowski case\n");
+    exit(2);
+  }
+
+  FILE *mf = fopen("raw/a_mink_analytic.csv", "w");
+  if (!mf) {
+    fprintf(stderr, "FATAL: cannot open analytic csv\n");
+    exit(2);
+  }
+  fprintf(mf,
+          "case,dir,upper,min_step,tol,outcome,stop_t,x_err,t_err,dn_ang,"
+          "dgrel,g_analytic,stop_t_analytic\n");
+
+  /* Reference: tol=1e-12, max_step = initial (1.0). */
+  const GeodesicTraceConfig refcfg =
+      make_dp(c.initial_step, 1e-12, c.initial_step, 1e-12, c.max_steps,
+              c.lookback);
+  for (int di = 0; di < c.n_dirs; ++di)
+    refs[0][di] = run_ray(&source, &observer, c.dirs[di], &refcfg);
+
+  static const double uppers[5] = {1.0, 4.0, 16.0, 64.0, 256.0};
+  static const double floors[3] = {1e-1, 1e-6, 1e-12};
+  for (int ui = 0; ui < 5; ++ui) {
+    for (int fi = 0; fi < 3; ++fi) {
+      Agg agg;
+      agg_init(&agg);
+      for (int di = 0; di < c.n_dirs; ++di) {
+        const GeodesicTraceConfig cfg =
+            make_dp(c.initial_step, floors[fi], uppers[ui], 1e-9, c.max_steps,
+                    c.lookback);
+        const Res r = run_ray(&source, &observer, c.dirs[di], &cfg);
+        Cmp cmp;
+        compare(&r, &refs[0][di], &cmp);
+        agg_add(&agg, &r, &cmp);
+        double t_an, x_an[3], n_an[3], g_an;
+        const int ok = mink_analytic(&c, &observer, c.dirs[di], c.escape_radius,
+                                     &t_an, x_an, n_an, &g_an);
+        double x_err = NAN, t_err = NAN, dn_an = NAN, dg_an = NAN;
+        if (ok == 0 && is_escaped(r.outcome)) {
+          /* Crossing position is checked through the direct trace in
+           * a_mink_analytic_x.csv; here compare sky direction, g and time. */
+          t_err = fabs(r.stop_t - t_an);
+          dn_an = ang_delta(r.n, n_an);
+          if (r.g > 0.0 && g_an > 0.0)
+            dg_an = fabs(r.g / g_an - 1.0);
+        }
+        fprintf(mf,
+                "%s,%d,%.6g,%.6g,%.6g,%d,%.17g,%.17g,%.17g,%.17g,%.17g,%.17g,"
+                "%.17g\n",
+                c.name, di, uppers[ui], floors[fi], 1e-9, r.outcome, r.stop_t,
+                x_err, t_err, dn_an, dg_an, g_an, t_an);
+      }
+      printf("SUMMARY mink upper=%.6g min=%.6g n=%ld mismatch=%ld "
+             "max_dn_ang=%.6g max_dgrel=%.6g sum_rhs=%lu esc=%ld dark=%ld "
+             "unres=%ld inc=%ld\n",
+             uppers[ui], floors[fi], agg.n, agg.class_mismatch,
+             agg.max_dn_ang, agg.max_dgrel, agg.sum_rhs, agg.escaped, agg.dark,
+             agg.unresolved, agg.incomplete);
+      fflush(stdout);
+    }
+  }
+
+  /* Direct endpoint check for the crossing position (x) on a few configs. */
+  FILE *xf = fopen("raw/a_mink_analytic_x.csv", "w");
+  if (!xf) {
+    fprintf(stderr, "FATAL: cannot open analytic x csv\n");
+    exit(2);
+  }
+  fprintf(xf, "case,dir,upper,min_step,tol,outcome,x_err_x,x_err_y,x_err_z,"
+              "t_err\n");
+  for (int ui = 0; ui < 5; ++ui) {
+    for (int fi = 0; fi < 3; ++fi) {
+      for (int di = 0; di < c.n_dirs; ++di) {
+        const GeodesicTraceConfig cfg =
+            make_dp(c.initial_step, floors[fi], uppers[ui], 1e-9, c.max_steps,
+                    c.lookback);
+        const RayEndpoint e =
+            geodesic_trace_past(&source, &observer, c.dirs[di], &cfg);
+        ++g_rays;
+        double t_an, x_an[3], n_an[3], g_an;
+        const int ok = mink_analytic(&c, &observer, c.dirs[di], c.escape_radius,
+                                     &t_an, x_an, n_an, &g_an);
+        double ex = NAN, ey = NAN, ez = NAN, te = NAN;
+        if (ok == 0 && e.outcome == RAY_OUTCOME_ESCAPED) {
+          ex = fabs(e.final_x[0] - x_an[0]);
+          ey = fabs(e.final_x[1] - x_an[1]);
+          ez = fabs(e.final_x[2] - x_an[2]);
+          te = fabs(e.stop_coordinate_time - t_an);
+        }
+        fprintf(xf, "%s,%d,%.6g,%.6g,%.6g,%d,%.17g,%.17g,%.17g,%.17g\n",
+                c.name, di, uppers[ui], floors[fi], 1e-9, e.outcome, ex, ey, ez,
+                te);
+      }
+    }
+  }
+  fclose(xf);
+  fclose(mf);
+  spacetime_destroy(&source);
+}
+
+/* ------------------------------------------------------------------ */
+/* Sub-command: Alcubierre                                            */
+/* ------------------------------------------------------------------ */
+
+static void cmd_alcubierre(void) {
+  static Case cases[MAX_CASES];
+  static Res refs[MAX_CASES][MAX_DIRS];
+  memset(refs, 0, sizeof refs);
+  int nc = 0;
+  case_alcubierre(&cases[nc++], "alc_v3_s1", 0.3, 1.0);
+  case_alcubierre(&cases[nc++], "alc_v3_s10", 0.3, 10.0);
+  case_alcubierre(&cases[nc++], "alc_v9_s1", 0.9, 1.0);
+  case_alcubierre(&cases[nc++], "alc_v9_s10", 0.9, 10.0);
+  case_alcubierre(&cases[nc++], "alc_v9_s100", 0.9, 100.0);
+
+  compute_refs(cases, nc, -1.0, "raw/a_alc_reference.csv", refs);
+
+  /* Standard grid: upper = initial*{1,4,8,16,32,64}, floor {1e-4,1e-8,1e-12}. */
+  {
+    static const double floors[3] = {1e-4, 1e-8, 1e-12};
+    Case sub[4];
+    for (int i = 0; i < 4; ++i)
+      sub[i] = cases[i];
+    /* run_grid uses one upper array for all cases, so use per-case initial by
+     * calling run_grid four times. */
+    for (int i = 0; i < 4; ++i) {
+      char rp[128], ap[128];
+      snprintf(rp, sizeof rp, "raw/a_alc_%.31s_upper.csv", sub[i].name);
+      snprintf(ap, sizeof ap, "raw/a_alc_%.31s_upper_summary.csv", sub[i].name);
+      const double base = sub[i].initial_step;
+      const double up[6] = {base, 4 * base, 8 * base,
+                            16 * base, 32 * base, 64 * base};
+      run_grid(&sub[i], 1, up, 6, floors, 3, 1e-9, "upper", rp, ap, &refs[i]);
+    }
+  }
+
+  /* Focused lower-bound stress: vs=.9, sigma=100, upper = initial*8 = 0.004,
+   * floors {1e-4,1e-5,1e-6,1e-8,1e-12,1e-14}. */
+  {
+    const Case *c = &cases[4];
+    const double up[1] = {c->initial_step * 8.0};
+    const double floors[6] = {1e-4, 1e-5, 1e-6, 1e-8, 1e-12, 1e-14};
+    run_grid(c, 1, up, 1, floors, 6, 1e-9, "min_stress",
+             "raw/a_alc_v9_s100_min.csv", "raw/a_alc_v9_s100_min_summary.csv",
+             &refs[4]);
+  }
+}
+
+/* ------------------------------------------------------------------ */
+
+int main(int argc, char **argv) {
+  if (argc < 2) {
+    fprintf(stderr,
+            "usage: %s schwarzschild|minkowski|alcubierre\n",
+            argv[0]);
+    return 1;
+  }
+  if (!strcmp(argv[1], "schwarzschild"))
+    cmd_schwarzschild();
+  else if (!strcmp(argv[1], "minkowski"))
+    cmd_minkowski();
+  else if (!strcmp(argv[1], "alcubierre"))
+    cmd_alcubierre();
+  else {
+    fprintf(stderr, "unknown sub-command %s\n", argv[1]);
+    return 1;
+  }
+  printf("TOTAL_RAYS %ld\n", g_rays);
+  return 0;
+}
@@ -0,0 +1,404 @@
+/*
+ * Experiment B: observed accepted-step sizes of the production DP54 core.
+ *
+ * This translation unit textually includes src/geodesic.c so the real,
+ * production `dp_advance_one` driver and the real `State` (GeodesicRayState)
+ * are exercised directly on a finite trajectory interval.  The production
+ * initialization is reproduced exactly as `geodesic_trace_past` does for an
+ * INSIDE route: `geodesic_initialize_past_ray_metric` at the camera event,
+ * then `next_step = config->coordinate_time_step` (the init already sets
+ * `integration_start_time`, `log_alpha_p0` and `log_alpha_p0_0`).  This is the
+ * same initialization the public endpoint uses, not a re-implementation.
+ *
+ * For each selected ray we:
+ *   1. run the public endpoint with tol=1e-12 to get a trusted reference
+ *      stop time and terminal class (physical terminal class is owned by A);
+ *   2. integrate the same ray with the production DP core up to
+ *      T = min(20, ref_span) observed steps <= 2000, recording each accepted
+ *      step magnitude, boundary-limit flag, rejection/RHS deltas and the null
+ *      residual gamma^{ij} Pi_i Pi_j - 1.
+ *
+ * Link line (geodesic.c is textually included, so it is NOT linked; the
+ * analytic backends are also textually included here):
+ *   cc -std=c11 -O2 -Isrc b_actual_h.c asymptotic.c asymptotic_schwarzschild.c \
+ *      spacetime_common.c observer.c -lm
+ */
+#define _POSIX_C_SOURCE 200809L
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+
+#define spacetime_create_default spacetime_create_default_minkowski_b
+#include "../../src/spacetime_minkowski.c"
+#undef spacetime_create_default
+#define spacetime_create_default spacetime_create_default_schwarzschild_b
+#include "../../src/spacetime_schwarzschild.c"
+#undef spacetime_create_default
+#define spacetime_create_default spacetime_create_default_alcubierre_b
+#include "../../src/spacetime_alcubierre.c"
+#undef spacetime_create_default
+
+/* The production geodesic core, textually included.  Its static State,
+ * dp_advance_one and invert become visible to the code below. */
+#include "../../src/geodesic.c"
+
+#define PI 3.14159265358979323846
+#define MAX_BCASES 12
+#define MAX_BDIRS 8
+#define MAX_OBS_STEPS 2000
+
+typedef struct {
+  char name[32];
+  int prov; /* 0 sch, 1 mink, 2 alc */
+  double mass, esc;
+  double vs, radius, sigma;
+  double look_ra_deg, look_dec_deg;
+  double pos[3], vel[3];
+  double initial, max_step;
+  double ref_max_step, lookback;
+  unsigned int ref_max_steps;
+  int ndirs;
+  double dirs[MAX_BDIRS][3];
+} BCase;
+
+static double b_now(void) {
+  struct timespec ts;
+  clock_gettime(CLOCK_MONOTONIC, &ts);
+  return (double)ts.tv_sec + 1e-9 * (double)ts.tv_nsec;
+}
+
+static void b_dir(double th, double n[3]) {
+  if (th == 0.0) {
+    n[0] = 1.0;
+    n[1] = n[2] = 0.0;
+  } else if (th == PI) {
+    n[0] = -1.0;
+    n[1] = n[2] = 0.0;
+  } else {
+    n[0] = cos(th);
+    n[1] = sin(th);
+    n[2] = 0.0;
+  }
+  const double nn = sqrt(n[0] * n[0] + n[1] * n[1] + n[2] * n[2]);
+  for (int i = 0; i < 3; ++i)
+    n[i] /= nn;
+}
+
+static double b_critical_angle(double r) {
+  const double b = 3.0 * sqrt(3.0) * sqrt(1.0 - 2.0 / r) / r;
+  return (b < 1.0) ? asin(b) : PI / 2.0;
+}
+
+static GeodesicTraceConfig b_make_dp(double initial, double min_step,
+                                     double max_step, double tol,
+                                     unsigned int max_steps, double lookback) {
+  GeodesicTraceConfig c;
+  memset(&c, 0, sizeof c);
+  c.coordinate_time_step = initial;
+  c.max_steps = max_steps;
+  c.threshold.kind = THRESHOLD_LOG_ENERGY_GROWTH;
+  c.threshold.value = 8.0;
+  c.threshold.policy_version = 3;
+  c.stepper = GEODESIC_STEPPER_DP54;
+  c.atol_x = c.atol_Pi = c.atol_L = c.rtol = tol;
+  c.min_step = min_step;
+  c.max_step = max_step;
+  c.consecutive_rejection_limit = 32;
+  c.max_lookback_time = lookback;
+  return c;
+}
+
+static int b_build_source(const BCase *c, SpacetimeSource *s) {
+  if (c->prov == 0)
+    return spacetime_create_schwarzschild_ks(s, c->mass, c->esc);
+  if (c->prov == 1)
+    return spacetime_create_minkowski(s, c->esc);
+  return spacetime_create_alcubierre(s, c->vs, c->radius, c->sigma);
+}
+
+static int b_build_observer(const BCase *c, const SpacetimeSource *s,
+                            ObserverState *o) {
+  MetricData m;
+  if (spacetime_eval(s, 0.0, c->pos, &m) != SPACETIME_POINT_OK)
+    return -1;
+  ObserverCamera cam;
+  memset(&cam, 0, sizeof cam);
+  for (int i = 0; i < 3; ++i) {
+    cam.position[i] = c->pos[i];
+    cam.velocity[i] = c->vel[i];
+  }
+  cam.look_ra_deg = c->look_ra_deg;
+  cam.look_dec_deg = c->look_dec_deg;
+  return observer_from_coordinate_camera(&m, &cam, o, NULL) ==
+                 OBSERVER_BUILD_OK
+             ? 0
+             : -1;
+}
+
+static void b_add_sch(BCase *c, const char *name, double r, double look,
+                      const double *thetas, int nt) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "%s", name);
+  c->prov = 0;
+  c->mass = 1.0;
+  c->esc = 256.0;
+  c->look_ra_deg = look;
+  c->pos[0] = r;
+  c->initial = 0.1;
+  c->max_step = 2.0;
+  c->ref_max_step = 0.25;
+  c->lookback = 6553.6;
+  c->ref_max_steps = 65536;
+  c->ndirs = nt;
+  for (int i = 0; i < nt; ++i)
+    b_dir(thetas[i], c->dirs[i]);
+}
+
+static void b_add_mink(BCase *c) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "mink_moving");
+  c->prov = 1;
+  c->esc = 64.0;
+  c->look_ra_deg = 0.0;
+  c->pos[0] = 10.0;
+  c->pos[1] = 20.0;
+  c->pos[2] = -15.0;
+  c->vel[0] = 0.3;
+  c->vel[1] = 0.2;
+  c->vel[2] = 0.1;
+  c->initial = 1.0;
+  c->max_step = 16.0;
+  c->ref_max_step = 1.0;
+  c->lookback = 2048.0;
+  c->ref_max_steps = 4096;
+  c->ndirs = 2;
+  b_dir(0.0, c->dirs[0]);
+  b_dir(PI, c->dirs[1]);
+}
+
+static void b_add_alc(BCase *c, const char *name, double vs, double sigma,
+                      const double *thetas, int nt) {
+  memset(c, 0, sizeof *c);
+  snprintf(c->name, sizeof c->name, "%s", name);
+  c->prov = 2;
+  c->vs = vs;
+  c->radius = 1.0;
+  c->sigma = sigma;
+  c->look_ra_deg = 0.0;
+  c->vel[0] = vs;
+  c->initial = fmin(0.1, 0.05 / sigma);
+  c->max_step = c->initial * 8.0;
+  c->ref_max_step = c->initial;
+  const double esc = spacetime_alcubierre_escape_radius(1.0, sigma);
+  c->lookback = 1.25 * 4.0 * esc / (1.0 - fabs(vs));
+  c->ref_max_steps = 200000;
+  c->ndirs = nt;
+  for (int i = 0; i < nt; ++i)
+    b_dir(thetas[i], c->dirs[i]);
+}
+
+/* gamma^{ij} Pi_i Pi_j - 1; `invert` is the production static from
+ * geodesic.c, so this is the exact production metric contraction. */
+static double b_null_residual(const MetricData *m, const double Pi[3]) {
+  double g[3][3], inv[3][3];
+  for (int i = 0; i < 3; ++i)
+    for (int j = 0; j < 3; ++j)
+      g[i][j] = m->gamma[i][j];
+  if (invert(g, inv))
+    return NAN;
+  double v = 0.0;
+  for (int i = 0; i < 3; ++i)
+    for (int j = 0; j < 3; ++j)
+      v += inv[i][j] * Pi[i] * Pi[j];
+  return v - 1.0;
+}
+
+int main(void) {
+  static BCase cases[MAX_BCASES];
+  int nc = 0;
+
+  {
+    const double tc = b_critical_angle(30.0);
+    const double th[6] = {0.0, PI, tc - 1e-7, tc + 1e-7, tc - 1e-5, tc + 1e-5};
+    b_add_sch(&cases[nc++], "r30_inward", 30.0, 180.0, th, 6);
+  }
+  {
+    const double tc = b_critical_angle(100.0);
+    const double th[4] = {0.0, PI, tc, tc - 1e-7};
+    b_add_sch(&cases[nc++], "r100_inward", 100.0, 180.0, th, 4);
+  }
+  {
+    const double tc = b_critical_angle(2.1);
+    const double th[5] = {0.0, tc, tc - 1e-7, tc + 1e-7, PI};
+    b_add_sch(&cases[nc++], "r2p1_outward", 2.1, 0.0, th, 5);
+  }
+  {
+    const double th[2] = {0.0, PI};
+    b_add_sch(&cases[nc++], "r1p5_freefall", 1.5, 180.0, th, 2);
+    /* free-fall velocity is set below (b_add_sch leaves it zero). */
+  }
+  b_add_mink(&cases[nc++]);
+  {
+    const double th[2] = {0.0, PI};
+    b_add_alc(&cases[nc++], "alc_v3_s1", 0.3, 1.0, th, 2);
+    b_add_alc(&cases[nc++], "alc_v9_s10", 0.9, 10.0, th, 2);
+    b_add_alc(&cases[nc++], "alc_v9_s100", 0.9, 100.0, th, 2);
+  }
+  /* Free-fall coordinate velocity for r1.5 (same formula as A). */
+  {
+    BCase *c = &cases[3];
+    const double y = sqrt(2.0 / c->pos[0]);
+    c->vel[0] = -y * (1.0 + y) / (1.0 + y + y * y);
+  }
+
+  FILE *hf = fopen("raw/b_actual_h.csv", "w");
+  FILE *sf = fopen("raw/b_summary.csv", "w");
+  if (!hf || !sf) {
+    fprintf(stderr, "FATAL: cannot open b csv\n");
+    return 2;
+  }
+  fprintf(hf, "case,dir,step,t,h,boundary_limited,rhs_delta,reject_delta,"
+              "null_residual\n");
+  fprintf(sf, "case,dir,ref_outcome,ref_stop_t,span,target,observed_steps,"
+              "reached_target,terminated_reason,h_min,h_max,h_first,h_last,"
+              "boundary_steps,sum_rhs,sum_reject,max_reject_delta,"
+              "null_residual_max,final_t,wall_s\n");
+
+  long total_steps = 0;
+  for (int ci = 0; ci < nc; ++ci) {
+    BCase *c = &cases[ci];
+    SpacetimeSource source;
+    ObserverState observer;
+    if (b_build_source(c, &source) || b_build_observer(c, &source, &observer)) {
+      fprintf(stderr, "FATAL: cannot build B case %s\n", c->name);
+      return 2;
+    }
+    for (int di = 0; di < c->ndirs; ++di) {
+      /* 1. trusted reference via the public endpoint (physical terminal). */
+      GeodesicTraceConfig refcfg =
+          b_make_dp(c->initial, 1e-12, c->ref_max_step, 1e-12, c->ref_max_steps,
+                    c->lookback);
+      RayEndpoint ref =
+          geodesic_trace_past(&source, &observer, c->dirs[di], &refcfg);
+      const double span =
+          isfinite(ref.stop_coordinate_time)
+              ? (observer.coordinate_time - ref.stop_coordinate_time)
+              : 20.0;
+      const double finite_T = fmin(20.0, span > 0.0 ? span : 20.0);
+      const double target = observer.coordinate_time - finite_T;
+
+      /* 2. production-exact INSIDE-route initialization. */
+      MetricData metric;
+      if (spacetime_eval(&source, observer.coordinate_time,
+                         observer.coordinate_position, &metric) !=
+          SPACETIME_POINT_OK) {
+        fprintf(stderr, "FATAL: camera metric %s\n", c->name);
+        return 2;
+      }
+      State st;
+      if (geodesic_initialize_past_ray_metric(&metric, &observer, c->dirs[di],
+                                              &st)) {
+        fprintf(stderr, "FATAL: init %s dir %d\n", c->name, di);
+        return 2;
+      }
+      GeodesicTraceConfig cfg =
+          b_make_dp(c->initial, 1e-12, c->max_step, 1e-9, 0u, 0.0);
+      st.next_step = cfg.coordinate_time_step;
+
+      MetricSlab *slab = NULL;
+      if (spacetime_load_slab(&source, st.coordinate_time, target - 1.0,
+                              &slab)) {
+        fprintf(stderr, "FATAL: slab %s dir %d\n", c->name, di);
+        return 2;
+      }
+
+      double h_min = INFINITY, h_max = 0.0, h_first = NAN, h_last = NAN;
+      double null_max = 0.0, sum_wall = 0.0;
+      unsigned long sum_rhs = 0;
+      unsigned int sum_rej = 0, max_rej_delta = 0, boundary_steps = 0;
+      int reached = 0, terminated_reason = -1;
+      int step_index = 0;
+      const double start_wall = b_now();
+      while (st.coordinate_time > target && step_index < MAX_OBS_STEPS) {
+        const double before_t = st.coordinate_time;
+        unsigned long rhs = st.rhs_evaluations;
+        unsigned int rej = st.rejected_steps;
+        RayReason reason = RAY_REASON_INTEGRATION_ERROR;
+        const int rc =
+            dp_advance_one(slab, &cfg, &st, target, &reason, &rhs, &rej, NULL);
+        const unsigned long rhs_delta = rhs - st.rhs_evaluations;
+        const unsigned int rej_delta = rej - st.rejected_steps;
+        st.rhs_evaluations = rhs;
+        st.rejected_steps = rej;
+        sum_rhs += rhs_delta;
+        sum_rej += rej_delta;
+        if (rej_delta > max_rej_delta)
+          max_rej_delta = rej_delta;
+        if (rc) {
+          terminated_reason = (int)reason;
+          break;
+        }
+        const double h = before_t - st.coordinate_time;
+        const int boundary = (st.coordinate_time == target);
+        if (boundary)
+          ++boundary_steps;
+        if (h < h_min)
+          h_min = h;
+        if (h > h_max)
+          h_max = h;
+        if (step_index == 0)
+          h_first = h;
+        h_last = h;
+        ++step_index;
+        MetricData m;
+        double nr = NAN;
+        if (spacetime_slab_eval(slab, st.coordinate_time, st.x, &m) ==
+            SPACETIME_POINT_OK)
+          nr = b_null_residual(&m, st.Pi);
+        if (isfinite(nr) && fabs(nr) > null_max)
+          null_max = fabs(nr);
+        fprintf(hf, "%s,%d,%d,%.17g,%.17g,%d,%lu,%u,%.6g\n", c->name, di,
+                step_index, st.coordinate_time, h, boundary, rhs_delta,
+                rej_delta, nr);
+        if (st.coordinate_time <= target)
+          reached = 1;
+      }
+      sum_wall = b_now() - start_wall;
+      if (step_index >= MAX_OBS_STEPS)
+        reached = 0;
+      if (!isfinite(h_first)) {
+        h_first = NAN;
+        h_max = NAN;
+      }
+      if (!isfinite(h_min) || h_min == INFINITY)
+        h_min = NAN;
+      if (h_last < 0.0)
+        h_last = NAN;
+      fprintf(sf,
+              "%s,%d,%d,%.17g,%.17g,%.17g,%d,%d,%d,%.17g,%.17g,%.17g,%.17g,"
+              "%u,%lu,%u,%u,%.6g,%.17g,%.6g\n",
+              c->name, di, ref.outcome, ref.stop_coordinate_time, span, target,
+              step_index, reached, terminated_reason, h_min, h_max, h_first,
+              h_last, boundary_steps, sum_rhs, sum_rej, max_rej_delta, null_max,
+              st.coordinate_time, sum_wall);
+      printf("B %s dir=%d ref=%d refstop=%.9g span=%.6g T=%.6g target=%.6g "
+             "steps=%d reached=%d term=%d h=[%.6g,%.6g] first=%.6g last=%.6g "
+             "boundary=%u rhs=%lu rej=%u nullmax=%.3g final_t=%.9g wall=%.4fs\n",
+             c->name, di, ref.outcome, ref.stop_coordinate_time, span, finite_T,
+             target, step_index, reached, terminated_reason, h_min, h_max,
+             h_first, h_last, boundary_steps, sum_rhs, sum_rej, null_max,
+             st.coordinate_time, sum_wall);
+      fflush(stdout);
+      total_steps += step_index;
+      spacetime_free_slab(slab);
+    }
+    spacetime_destroy(&source);
+  }
+  fclose(hf);
+  fclose(sf);
+  printf("TOTAL_OBSERVED_STEPS %ld\n", total_steps);
+  return 0;
+}
@@ -0,0 +1,341 @@
+/*
+ * Standalone critical-classification reference check.
+ *
+ * Three static Schwarzschild cameras (M=1, escape sphere 256):
+ *   r30  look 180 (inward),  r100 look 180 (inward),  r2.1 look 0 (outward),
+ * each aimed at theta_crit exactly and at theta_crit +- 1e-7, where
+ *   theta_crit = asin(3 sqrt(3) sqrt(1 - 2/r) / r)
+ * is the local tetrad angle from the camera forward direction.
+ *
+ * For every direction four DP54 configs are run (initial step 0.1,
+ * min_step 1e-14, max_steps 65536, max_lookback_time 6553.6, reject limit 32,
+ * camera-relative dark threshold 8):
+ *
+ *   ref_tol1e-12_h0.25    tol 1e-12, max_step 0.25
+ *   ref_tol1e-13_h0.125   tol 1e-13, max_step 0.125
+ *   tol1e-11_h2           tol 1e-11, max_step 2
+ *   tol1e-11_h8           tol 1e-11, max_step 8
+ *
+ * Total 3 cameras * 3 directions * 4 configs = 36 endpoint traces.
+ *
+ * Raw per-run rows go to raw/critical_ref.csv; stdout prints, for all nine
+ * directions, ref_vs_tighter / h2_vs_h8 / ref_vs_h2 / ref_vs_h8 comparisons
+ * (outcome/reason/end, sky angle, relative g, dark stop-time and threshold
+ * shifts) and a NEIGHBOR_REFERENCE_CHECK that verifies the two reference
+ * tiers agree at the +-1e-7 neighbours.  The exactly-critical direction is a
+ * separatrix: a class flip or a large direction/stop-time difference there is
+ * reported as EXACT_CRITICAL_REFERENCE_NOT_CONVERGED and is diagnostic only.
+ *
+ * Exit status: 0 when the neighbours' reference tiers agree and no neighbour
+ * returned an error/unresolved endpoint or a zero-step trace; 1 when a
+ * neighbour reference check fails; 2 on setup error.  The exact-critical
+ * separatrix is never an assertion.
+ *
+ * Link line (the Schwarzschild backend is textually included):
+ *   cc -std=c11 -O2 -Isrc critical_ref_check.c geodesic.c asymptotic.c \
+ *      asymptotic_schwarzschild.c spacetime_common.c observer.c -lm
+ */
+#define _POSIX_C_SOURCE 200809L
+
+#include <math.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "../../src/spacetime_schwarzschild.c"
+
+#include "geodesic.h"
+#include "observer.h"
+#include "spacetime.h"
+
+#define PI 3.14159265358979323846
+
+typedef struct {
+  const char *name;
+  double tol;
+  double max_step;
+} CfgDef;
+
+static const CfgDef cfgs[4] = {
+    {"ref_tol1e-12_h0.25", 1e-12, 0.25},
+    {"ref_tol1e-13_h0.125", 1e-13, 0.125},
+    {"tol1e-11_h2", 1e-11, 2.0},
+    {"tol1e-11_h8", 1e-11, 8.0},
+};
+
+typedef struct {
+  const char *name;
+  double r;
+  double look_ra_deg;
+} CamDef;
+
+static const CamDef cams[3] = {
+    {"r30_inward", 30.0, 180.0},
+    {"r100_inward", 100.0, 180.0},
+    {"r2p1_outward", 2.1, 0.0},
+};
+
+typedef struct {
+  int outcome, reason;
+  unsigned int end_id;
+  double stop_t, g, thr;
+  double L, L0;
+  double n[3];
+  unsigned int steps, rejected;
+  unsigned long rhs;
+} Res;
+
+static double b_dot3(const double a[3], const double b[3]) {
+  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
+}
+
+static double b_ang_delta(const double a[3], const double b[3]) {
+  const double na = sqrt(b_dot3(a, a)), nb = sqrt(b_dot3(b, b));
+  if (!(na > 0.0) || !(nb > 0.0))
+    return NAN;
+  const double cross[3] = {a[1] * b[2] - a[2] * b[1],
+                           a[2] * b[0] - a[0] * b[2],
+                           a[0] * b[1] - a[1] * b[0]};
+  return atan2(sqrt(b_dot3(cross, cross)) / (na * nb),
+               b_dot3(a, b) / (na * nb));
+}
+
+static double critical_angle(double r) {
+  const double b = 3.0 * sqrt(3.0) * sqrt(1.0 - 2.0 / r) / r;
+  return (b < 1.0) ? asin(b) : PI / 2.0;
+}
+
+static void dir_from_theta(double th, double n[3]) {
+  n[0] = cos(th);
+  n[1] = sin(th);
+  n[2] = 0.0;
+  const double nn = sqrt(b_dot3(n, n));
+  for (int i = 0; i < 3; ++i)
+    n[i] /= nn;
+}
+
+static GeodesicTraceConfig make_cfg(const CfgDef *d) {
+  GeodesicTraceConfig c;
+  memset(&c, 0, sizeof c);
+  c.coordinate_time_step = 0.1;
+  c.max_steps = 65536;
+  c.threshold.kind = THRESHOLD_LOG_ENERGY_GROWTH;
+  c.threshold.value = 8.0;
+  c.threshold.policy_version = 3;
+  c.stepper = GEODESIC_STEPPER_DP54;
+  c.atol_x = c.atol_Pi = c.atol_L = c.rtol = d->tol;
+  c.min_step = 1e-14;
+  c.max_step = d->max_step;
+  c.consecutive_rejection_limit = 32;
+  c.max_lookback_time = 6553.6;
+  return c;
+}
+
+static int build_observer(const CamDef *cam, const SpacetimeSource *s,
+                          ObserverState *o) {
+  const double pos[3] = {cam->r, 0.0, 0.0};
+  MetricData m;
+  if (spacetime_eval(s, 0.0, pos, &m) != SPACETIME_POINT_OK)
+    return -1;
+  ObserverCamera camera;
+  memset(&camera, 0, sizeof camera);
+  camera.position[0] = pos[0];
+  camera.position[1] = pos[1];
+  camera.position[2] = pos[2];
+  camera.look_ra_deg = cam->look_ra_deg;
+  camera.look_dec_deg = 0.0;
+  return observer_from_coordinate_camera(&m, &camera, o, NULL) ==
+                 OBSERVER_BUILD_OK
+             ? 0
+             : -1;
+}
+
+static Res run_one(const SpacetimeSource *s, const ObserverState *o,
+                   const double dir[3], const GeodesicTraceConfig *cfg) {
+  Res r;
+  memset(&r, 0, sizeof r);
+  const RayEndpoint e = geodesic_trace_past(s, o, dir, cfg);
+  r.outcome = e.outcome;
+  r.reason = e.reason;
+  r.end_id = e.end_id;
+  r.stop_t = e.stop_coordinate_time;
+  r.g = e.frequency_ratio;
+  r.thr = e.threshold_value;
+  r.L = e.final_log_alpha_p0;
+  r.L0 = e.final_log_alpha_p0_0;
+  for (int i = 0; i < 3; ++i)
+    r.n[i] = e.n_infinity[i];
+  r.steps = e.accepted_steps;
+  r.rejected = e.rejected_steps;
+  r.rhs = e.rhs_evaluations;
+  return r;
+}
+
+static const char *outcome_name(int o) {
+  switch (o) {
+  case RAY_OUTCOME_ESCAPED:
+    return "ESC";
+  case RAY_OUTCOME_DARK:
+    return "DARK";
+  case RAY_OUTCOME_UNRESOLVED:
+    return "UNRES";
+  default:
+    return "INC";
+  }
+}
+
+static void print_pair(const char *cam, int di, double theta, const char *pn,
+                       const Res *a, const Res *b) {
+  const int same = a->outcome == b->outcome && a->reason == b->reason &&
+                   a->end_id == b->end_id;
+  const int esc = a->outcome == RAY_OUTCOME_ESCAPED &&
+                  b->outcome == RAY_OUTCOME_ESCAPED;
+  const double dn = esc ? b_ang_delta(a->n, b->n) : NAN;
+  const double dg =
+      (esc && a->g > 0.0 && b->g > 0.0) ? fabs(a->g / b->g - 1.0) : NAN;
+  const double dstop =
+      (isfinite(a->stop_t) && isfinite(b->stop_t)) ? a->stop_t - b->stop_t
+                                                   : NAN;
+  const double dthr = (isfinite(a->thr) && isfinite(b->thr))
+                          ? a->thr - b->thr
+                          : NAN;
+  printf("CAPAIR camera=%s dir=%d theta=%.17g pair=%s class=%s/%s same=%d "
+         "dn_ang=%.17g dgrel=%.17g dstop_t=%.17g dthr=%.17g end=%u/%u\n",
+         cam, di, theta, pn, outcome_name(a->outcome), outcome_name(b->outcome),
+         same, dn, dg, dstop, dthr, a->end_id, b->end_id);
+}
+
+/* A two-reference-tier agreement check for one neighbour direction.  Returns
+ * 1 when the pair is a valid, agreeing ESC/DARK reference, 0 otherwise. */
+static int neighbour_reference_check(const char *cam, int di, double theta,
+                                     const Res *a, const Res *b) {
+  const int class_same = a->outcome == b->outcome && a->reason == b->reason &&
+                         a->end_id == b->end_id;
+  const int clean = (a->outcome == RAY_OUTCOME_ESCAPED ||
+                     a->outcome == RAY_OUTCOME_DARK) &&
+                    (b->outcome == RAY_OUTCOME_ESCAPED ||
+                     b->outcome == RAY_OUTCOME_DARK);
+  const int stepped = a->steps > 0 && b->steps > 0;
+  const int esc = a->outcome == RAY_OUTCOME_ESCAPED &&
+                  b->outcome == RAY_OUTCOME_ESCAPED;
+  const double dn = esc ? b_ang_delta(a->n, b->n) : NAN;
+  const double dg =
+      (esc && a->g > 0.0 && b->g > 0.0) ? fabs(a->g / b->g - 1.0) : NAN;
+  const double dstop =
+      (isfinite(a->stop_t) && isfinite(b->stop_t)) ? a->stop_t - b->stop_t
+                                                   : NAN;
+  printf("NEIGHBOR_REFERENCE_CHECK camera=%s dir=%d theta=%.17g "
+         "ref_class0=%s/%d/%u ref_class1=%s/%d/%u same=%d clean=%d stepped=%d "
+         "dn_ang=%.17g dgrel=%.17g dstop_t=%.17g\n",
+         cam, di, theta, outcome_name(a->outcome), a->reason, a->end_id,
+         outcome_name(b->outcome), b->reason, b->end_id, class_same, clean,
+         stepped, dn, dg, dstop);
+  return class_same && clean && stepped;
+}
+
+int main(void) {
+  SpacetimeSource source;
+  if (spacetime_create_schwarzschild_ks(&source, 1.0, 256.0)) {
+    fprintf(stderr, "FATAL: cannot create Schwarzschild source\n");
+    return 2;
+  }
+
+  FILE *f = fopen("raw/critical_ref.csv", "w");
+  if (!f) {
+    fprintf(stderr, "FATAL: cannot open raw/critical_ref.csv\n");
+    return 2;
+  }
+  fprintf(f, "camera,dir,theta,cfg,outcome,reason,end_id,stop_t,steps,"
+             "rejected,rhs,nx,ny,nz,g,thr,L,L0\n");
+
+  Res res[3][3][4];
+  double thetas[3][3];
+  for (int ci = 0; ci < 3; ++ci) {
+    ObserverState observer;
+    if (build_observer(&cams[ci], &source, &observer)) {
+      fprintf(stderr, "FATAL: cannot build observer %s\n", cams[ci].name);
+      return 2;
+    }
+    const double tc = critical_angle(cams[ci].r);
+    const double th[3] = {tc - 1e-7, tc, tc + 1e-7};
+    for (int di = 0; di < 3; ++di) {
+      double dir[3];
+      dir_from_theta(th[di], dir);
+      thetas[ci][di] = th[di];
+      for (int fi = 0; fi < 4; ++fi) {
+        const GeodesicTraceConfig cfg = make_cfg(&cfgs[fi]);
+        const Res r = run_one(&source, &observer, dir, &cfg);
+        res[ci][di][fi] = r;
+        fprintf(f, "%s,%d,%.17g,%s,%d,%d,%u,%.17g,%u,%u,%lu,%.17g,%.17g,"
+                   "%.17g,%.17g,%.17g,%.17g,%.17g\n",
+                cams[ci].name, di, th[di], cfgs[fi].name, r.outcome, r.reason,
+                r.end_id, r.stop_t, r.steps, r.rejected, r.rhs, r.n[0], r.n[1],
+                r.n[2], r.g, r.thr, r.L, r.L0);
+        printf("RAW camera=%s dir=%d theta=%.17g cfg=%s outcome=%d reason=%d "
+               "end=%u stop_t=%.17g steps=%u rejected=%u rhs=%lu g=%.17g "
+               "thr=%.17g L=%.17g L0=%.17g nx=%.17g ny=%.17g nz=%.17g\n",
+               cams[ci].name, di, th[di], cfgs[fi].name, r.outcome, r.reason,
+               r.end_id, r.stop_t, r.steps, r.rejected, r.rhs, r.g, r.thr, r.L,
+               r.L0, r.n[0], r.n[1], r.n[2]);
+        fflush(stdout);
+      }
+    }
+  }
+  fclose(f);
+
+  /* All nine directions: ref_vs_tighter, h2_vs_h8, ref_vs_h2, ref_vs_h8. */
+  for (int ci = 0; ci < 3; ++ci) {
+    for (int di = 0; di < 3; ++di) {
+      print_pair(cams[ci].name, di, thetas[ci][di], "ref_vs_tighter",
+                 &res[ci][di][0], &res[ci][di][1]);
+      print_pair(cams[ci].name, di, thetas[ci][di], "h2_vs_h8",
+                 &res[ci][di][2], &res[ci][di][3]);
+      print_pair(cams[ci].name, di, thetas[ci][di], "ref_vs_h2",
+                 &res[ci][di][0], &res[ci][di][2]);
+      print_pair(cams[ci].name, di, thetas[ci][di], "ref_vs_h8",
+                 &res[ci][di][0], &res[ci][di][3]);
+    }
+  }
+
+  /* Exact-critical: diagnostic only, never asserted. */
+  for (int ci = 0; ci < 3; ++ci) {
+    const Res *a = &res[ci][1][0];
+    const Res *b = &res[ci][1][1];
+    const int same = a->outcome == b->outcome && a->reason == b->reason &&
+                     a->end_id == b->end_id;
+    const int esc = a->outcome == RAY_OUTCOME_ESCAPED &&
+                    b->outcome == RAY_OUTCOME_ESCAPED;
+    const int dark = a->outcome == RAY_OUTCOME_DARK &&
+                     b->outcome == RAY_OUTCOME_DARK;
+    const double dn = esc ? b_ang_delta(a->n, b->n) : NAN;
+    const double dstop =
+        (isfinite(a->stop_t) && isfinite(b->stop_t)) ? a->stop_t - b->stop_t
+                                                     : NAN;
+    const int nonconverged =
+        !same || (esc && !(dn <= 1e-6)) || (dark && fabs(dstop) > 1e-4);
+    printf("EXACT_CRITICAL_DIRECTION camera=%s theta=%.17g ref0=%s/%d/%u "
+           "ref1=%s/%d/%u same=%d dn_ang=%.17g dstop_t=%.17g\n",
+           cams[ci].name, thetas[ci][1], outcome_name(a->outcome), a->reason,
+           a->end_id, outcome_name(b->outcome), b->reason, b->end_id, same, dn,
+           dstop);
+    if (nonconverged)
+      printf("EXACT_CRITICAL_REFERENCE_NOT_CONVERGED camera=%s dn_ang=%.17g "
+             "dstop_t=%.17g class_same=%d\n",
+             cams[ci].name, dn, dstop, same);
+  }
+
+  /* Neighbour reference check: must pass; this is the assertion-valid path. */
+  int fail = 0;
+  for (int ci = 0; ci < 3; ++ci) {
+    for (int di = 0; di < 3; di += 2) {
+      if (!neighbour_reference_check(cams[ci].name, di, thetas[ci][di],
+                                     &res[ci][di][0], &res[ci][di][1]))
+        fail = 1;
+    }
+  }
+
+  spacetime_destroy(&source);
+  printf("CRITICAL_REFERENCE_CHECK status=%d\n", fail ? 1 : 0);
+  printf("CRITICAL_REF_DONE\n");
+  return fail ? 1 : 0;
+}
@@ -0,0 +1,26 @@
+/* Diagnostic only: reuse the production regression's invalid-metric fixture. */
+#define main adaptive_regression_main_not_called
+#include "../../tests/test_geodesic_adaptive.c"
+#undef main
+
+int main(void) {
+  const double floors[] = {1e-2,1e-4,1e-6,1e-8,1e-10,1e-12,1e-14};
+  for (unsigned i=0;i<sizeof floors/sizeof *floors;++i) {
+    FixtureContext context={.bad_status=SPACETIME_POINT_INVALID_METRIC,
+      .bad_lo=-10,.bad_hi=-.05,.radius=100};
+    SpacetimeSource source={.context=&context,.ops=&fixture_ops};
+    GeodesicTraceConfig config=dp_config(1e-9,.1,10);
+    config.min_step=floors[i]; config.max_step=1;
+    const ObserverState observer=flat_observer_at((double[3]){0,0,0});
+    const double direction[3]={1,0,0};
+    RayEndpoint endpoint=geodesic_trace_past(&source,&observer,direction,&config);
+    printf("FAILURE_FLOOR min=%.0e outcome=%d reason=%d t=%.17g distance_to_invalid=%.17g accepted=%u rejected=%u rhs=%lu\n",
+      floors[i],endpoint.outcome,endpoint.reason,endpoint.stop_coordinate_time,
+      endpoint.stop_coordinate_time+.05,endpoint.accepted_steps,
+      endpoint.rejected_steps,endpoint.rhs_evaluations);
+    if(endpoint.outcome!=RAY_OUTCOME_INCOMPLETE ||
+       endpoint.stop_coordinate_time<=-.05) return 1;
+  }
+  puts("FAILURE_FLOOR_EXIT=0");
+  return 0;
+}
@@ -0,0 +1,77 @@
+#!/usr/bin/env python3
+"""Pure GRLENS v3 map load/compare helpers.
+
+No renderer, no environment probing, no data generation: this module is only
+imported by the benchmark scripts under
+benchmarks/adaptive_step_bounds_2026-10-05/.  Keeping it here means the
+benchmark never imports an untracked module from local/.
+"""
+import collections
+import hashlib
+import math
+import struct
+import zlib
+
+
+def load(path):
+    """Parse one GRLENS v3 map; returns (info dict, {film_pos: vertex tuple})."""
+    data = path.read_bytes()
+    assert data[:8] == b'GRLENS\x01\x00'
+    assert struct.unpack_from('<I', data, 8)[0] == 3
+    assert struct.unpack_from('<Q', data, 32)[0] == 1
+    nv, nt = struct.unpack_from('<QQ', data, 200)
+    end = 224 + nv * 108 + nt * 32
+    assert end + 4 == len(data)
+    assert zlib.crc32(data[224:end]) == struct.unpack_from('<I', data, end)[0]
+    vertices = [struct.unpack_from('<9dIIIQQQ', data, 224 + i * 108)
+                for i in range(nv)]
+    costs = [sum(v[j] for v in vertices) for j in (12, 13, 14)]
+    result = dict(vertices=nv, triangles=nt,
+                  outcomes=dict(collections.Counter(v[10] for v in vertices)),
+                  reasons=dict(collections.Counter(v[11] for v in vertices)),
+                  accepted=costs[0], rejected=costs[1], rhs=costs[2])
+    names = ('atol_x', 'atol_Pi', 'atol_L', 'rtol', 'min_step', 'max_step',
+             'max_lookback_time', 'retry_lookback_increment',
+             'max_total_lookback_time')
+    result['provenance'] = dict(zip(names, struct.unpack_from('<9d', data, 100)))
+    result['provenance'].update(
+        integrator=struct.unpack_from('<I', data, 68)[0],
+        initial_step=struct.unpack_from('<d', data, 88)[0],
+        initial_max_steps=struct.unpack_from('<I', data, 96)[0],
+        threshold=struct.unpack_from('<d', data, 48)[0],
+        retry_step_increment=struct.unpack_from('<I', data, 56)[0],
+        max_total_steps=struct.unpack_from('<I', data, 60)[0])
+    for j, name in ((12, 'accepted'), (13, 'rejected'), (14, 'rhs')):
+        xs = sorted(v[j] for v in vertices)
+        result[name + '_percentiles'] = {
+            str(q): xs[min(len(xs) - 1, int(q * (len(xs) - 1)))]
+            for q in (0, .5, .9, .99, 1)}
+    result['sha256'] = hashlib.sha256(data).hexdigest()
+    result['triangle_sha256'] = hashlib.sha256(
+        data[224 + nv * 108:end]).hexdigest()
+    by_film = {(v[0], v[1]): v for v in vertices}
+    result['unique_film_positions'] = len(by_film)
+    result['duplicate_film_positions'] = len(vertices) - len(by_film)
+    return result, by_film
+
+
+def compare(a, b):
+    """Compare two {film_pos: vertex} maps by shared film-coordinate identity."""
+    keys = a.keys() & b.keys()
+    mismatches = 0
+    worst_sky = worst_logg = 0.
+    for k in keys:
+        x, y = a[k], b[k]
+        if x[9:12] != y[9:12]:
+            mismatches += 1
+        elif x[10] == 0:
+            n, m = x[5:8], y[5:8]
+            cross = (n[1] * m[2] - n[2] * m[1], n[2] * m[0] - n[0] * m[2],
+                     n[0] * m[1] - n[1] * m[0])
+            angle = math.atan2(math.sqrt(sum(v * v for v in cross)),
+                               sum(v * w for v, w in zip(n, m)))
+            worst_sky = max(worst_sky, angle)
+            worst_logg = max(worst_logg, abs(x[8] - y[8]))
+    return dict(shared=len(keys), only_a=len(a) - len(keys),
+                only_b=len(b) - len(keys), terminal_mismatches=mismatches,
+                max_sky_angle=worst_sky, max_logg_difference=worst_logg)
@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+"""Record provenance without launching a render.
+
+Usage:
+    record_environment.py [OUT_DIR]
+
+OUT_DIR defaults to <repo>/local/adaptive_bounds_mesh.  Writes metadata.json in
+OUT_DIR.  No renderer or test is run.
+"""
+import hashlib
+import json
+from pathlib import Path
+import subprocess
+import sys
+import time
+
+ROOT = Path(__file__).resolve().parents[2]
+OUT = Path(sys.argv[1]).resolve() if len(sys.argv) > 1 else \
+    ROOT / 'local/adaptive_bounds_mesh'
+PATHS = ['src/geodesic.c', 'src/main.c', 'src/frame.c',
+         'build/Release/schwarzschild_sky']
+
+metadata = {
+    'recorded_utc': time.strftime('%Y-%m-%dT%H:%M:%SZ', time.gmtime()),
+    'git_head': subprocess.check_output(
+        ['git', 'rev-parse', 'HEAD'], cwd=ROOT, text=True).strip(),
+    'hashes': {p: hashlib.sha256((ROOT / p).read_bytes()).hexdigest()
+               for p in PATHS},
+    'compiler': subprocess.check_output(['cc', '--version'], text=True),
+    'cpu': subprocess.check_output(['lscpu'], text=True),
+    'scope': '8 bounded 320x180 candidates plus 2 tight references; no 4K here',
+    'threads': 8,
+    'build_command': 'make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend',
+    'run_commands': [
+        'python3 benchmarks/adaptive_step_bounds_2026-10-05/run_mesh.py [OUT]',
+        'python3 benchmarks/adaptive_step_bounds_2026-10-05/run_mesh_reference.py [OUT]',
+        'bash benchmarks/adaptive_step_bounds_2026-10-05/run_failure_floor.sh [OUT]'],
+}
+OUT.mkdir(parents=True, exist_ok=True)
+(OUT / 'metadata.json').write_text(json.dumps(metadata, indent=2) + '\n')
+print(json.dumps(metadata, indent=2))
@@ -0,0 +1,16 @@
+[
+  {
+    "upper": 2,
+    "command": "/home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky --integrator dp54 --width 3840 --height 2160 --look-ra-deg 262.5 --look-dec-deg -30 --fov-deg 45 --observer-radius 100 --coarse-cell-pixels 16 --refine-max-level 4 --refine-jacobian-min .2 --catalog /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/single_dim_star.csv --exposure 1 --tone-map reinhard --psf-min-y 1e-20 --psf-relative-tail 1e-4 --ode-min-step 1e-12 --ode-max-step 2 --verbose --lens-map-output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.grlens --output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.png",
+    "state": "completed",
+    "returncode": 0,
+    "wall_seconds": 11.389317202148959
+  },
+  {
+    "upper": 8,
+    "command": "/home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky --integrator dp54 --width 3840 --height 2160 --look-ra-deg 262.5 --look-dec-deg -30 --fov-deg 45 --observer-radius 100 --coarse-cell-pixels 16 --refine-max-level 4 --refine-jacobian-min .2 --catalog /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/single_dim_star.csv --exposure 1 --tone-map reinhard --psf-min-y 1e-20 --psf-relative-tail 1e-4 --ode-min-step 1e-12 --ode-max-step 8 --verbose --lens-map-output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.grlens --output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.png",
+    "state": "completed",
+    "returncode": 0,
+    "wall_seconds": 8.389249739935622
+  }
+]
@@ -0,0 +1,160 @@
+{
+  "r100_4k_hmax2": {
+    "vertices": 66045,
+    "triangles": 131338,
+    "outcomes": {
+      "0": 62419,
+      "1": 3626
+    },
+    "reasons": {
+      "0": 62419,
+      "1": 3626
+    },
+    "accepted": 15768677,
+    "rejected": 97176,
+    "rhs": 130409139,
+    "provenance": {
+      "atol_x": 1e-09,
+      "atol_Pi": 1e-09,
+      "atol_L": 1e-09,
+      "rtol": 1e-09,
+      "min_step": 1e-12,
+      "max_step": 2.0,
+      "max_lookback_time": 6553.6,
+      "retry_lookback_increment": 6553.6,
+      "max_total_lookback_time": 26214.4,
+      "integrator": 1,
+      "initial_step": 0.1,
+      "initial_max_steps": 65536,
+      "threshold": 8.0,
+      "retry_step_increment": 65536,
+      "max_total_steps": 262144
+    },
+    "accepted_percentiles": {
+      "0": 162,
+      "0.5": 212,
+      "0.9": 328,
+      "0.99": 404,
+      "1": 520
+    },
+    "rejected_percentiles": {
+      "0": 0,
+      "0.5": 1,
+      "0.9": 3,
+      "0.99": 4,
+      "1": 5
+    },
+    "rhs_percentiles": {
+      "0": 1421,
+      "0.5": 1799,
+      "0.9": 2597,
+      "0.99": 3129,
+      "1": 3941
+    },
+    "sha256": "ef7267074338192f8597b1f2a0300fd36da8e25441e064719c7ad586c481ae7a",
+    "triangle_sha256": "2a943902e9b1401a16bc40fc547c19077bb12e396080074393636ee30761b7b2",
+    "unique_film_positions": 66045,
+    "duplicate_film_positions": 0,
+    "requested_samples_including_nonpersistent_probes": 116308,
+    "initial_samples": 32776,
+    "refinement_samples_per_generation": [
+      32686,
+      7900,
+      13375,
+      24826,
+      4403,
+      261,
+      67,
+      14
+    ],
+    "trace_wall_seconds": 10.774,
+    "wall_seconds": 11.389317202148959
+  },
+  "r100_4k_hmax8": {
+    "vertices": 66045,
+    "triangles": 131338,
+    "outcomes": {
+      "0": 62419,
+      "1": 3626
+    },
+    "reasons": {
+      "0": 62419,
+      "1": 3626
+    },
+    "accepted": 10183020,
+    "rejected": 194781,
+    "rhs": 91991144,
+    "provenance": {
+      "atol_x": 1e-09,
+      "atol_Pi": 1e-09,
+      "atol_L": 1e-09,
+      "rtol": 1e-09,
+      "min_step": 1e-12,
+      "max_step": 8.0,
+      "max_lookback_time": 6553.6,
+      "retry_lookback_increment": 6553.6,
+      "max_total_lookback_time": 26214.4,
+      "integrator": 1,
+      "initial_step": 0.1,
+      "initial_max_steps": 65536,
+      "threshold": 8.0,
+      "retry_step_increment": 65536,
+      "max_total_steps": 262144
+    },
+    "accepted_percentiles": {
+      "0": 80,
+      "0.5": 127,
+      "0.9": 259,
+      "0.99": 337,
+      "1": 432
+    },
+    "rejected_percentiles": {
+      "0": 0,
+      "0.5": 3,
+      "0.9": 5,
+      "0.99": 6,
+      "1": 7
+    },
+    "rhs_percentiles": {
+      "0": 868,
+      "0.5": 1204,
+      "0.9": 2114,
+      "0.99": 2646,
+      "1": 3318
+    },
+    "sha256": "b1897493b7fa5b88f86872e81d15ac876818a705fa0fefe8b1ee262da9de59bb",
+    "triangle_sha256": "2a943902e9b1401a16bc40fc547c19077bb12e396080074393636ee30761b7b2",
+    "unique_film_positions": 66045,
+    "duplicate_film_positions": 0,
+    "requested_samples_including_nonpersistent_probes": 116308,
+    "initial_samples": 32776,
+    "refinement_samples_per_generation": [
+      32686,
+      7900,
+      13375,
+      24826,
+      4403,
+      261,
+      67,
+      14
+    ],
+    "trace_wall_seconds": 7.805000000000001,
+    "wall_seconds": 8.389249739935622
+  },
+  "comparison": {
+    "shared": 66045,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 7.954413592847793e-07,
+    "max_logg_difference": 3.471110204822381e-11,
+    "triangle_payload_identical": true
+  },
+  "relative_reduction": {
+    "accepted": 0.35422483446138187,
+    "rhs": 0.2945958795111745,
+    "wall_seconds": 0.2634106513116764,
+    "trace_wall_seconds": 0.27557081863746047
+  },
+  "cost_scope": "accepted/rejected/RHS sums cover final persistent vertices only; nonpersistent discarded refinement probes are not in v3 map. Do not interpret them as full-render executed RHS totals."
+}
@@ -0,0 +1,242 @@
+OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE /home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky --integrator dp54 --width 3840 --height 2160 --look-ra-deg 262.5 --look-dec-deg -30 --fov-deg 45 --observer-radius 100 --coarse-cell-pixels 16 --refine-max-level 4 --refine-jacobian-min .2 --catalog /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/single_dim_star.csv --exposure 1 --tone-map reinhard --psf-min-y 1e-20 --psf-relative-tail 1e-4 --ode-min-step 1e-12 --ode-max-step 2 --verbose --lens-map-output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.grlens --output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.png
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000040 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+PSF cache ready: 64x64 phases, radius 25 px, relative tail 1e-04, tail abs 1e-06, boundary 1e-07, build 0.250 s
+Frame 0: integrator=dp54 step=0.1 max_steps=65536 threshold=8 atol=(x 1e-09, Pi 1e-09, L 1e-09) rtol=1e-09 bounds=[1e-12, 2] max_rejections=32 lookback=6553.6
+Frame 0: tracing 32776 initial rays from 64800 mesh triangles...
+Frame 0: initial ray trace finished in 2.562 s.
+Frame 0: starting adaptive ray-trace refinement (max level 4)...
+Frame 0: refinement generation 0 tracing 32686 samples from 32776 vertices and 64800 triangles.
+Frame 0: refinement generation 0 finished; added 3014 vertices, now 35790 vertices and 70828 triangles.
+Frame 0: refinement generation 1 tracing 7900 samples from 35790 vertices and 70828 triangles.
+Frame 0: refinement generation 1 finished; added 4852 vertices, now 40642 vertices and 80532 triangles.
+Frame 0: refinement generation 2 tracing 13375 samples from 40642 vertices and 80532 triangles.
+Frame 0: refinement generation 2 finished; added 8889 vertices, now 49531 vertices and 98310 triangles.
+Frame 0: refinement generation 3 tracing 24826 samples from 49531 vertices and 98310 triangles.
+Frame 0: refinement generation 3 finished; added 16055 vertices, now 65586 vertices and 130420 triangles.
+Frame 0: refinement generation 4 tracing 4403 samples from 65586 vertices and 130420 triangles.
+Frame 0: refinement generation 4 finished; added 389 vertices, now 65975 vertices and 131198 triangles.
+Frame 0: refinement generation 5 tracing 261 samples from 65975 vertices and 131198 triangles.
+Frame 0: refinement generation 5 finished; added 58 vertices, now 66033 vertices and 131314 triangles.
+Frame 0: refinement generation 6 tracing 67 samples from 66033 vertices and 131314 triangles.
+Frame 0: refinement generation 6 finished; added 12 vertices, now 66045 vertices and 131338 triangles.
+Frame 0: refinement generation 7 tracing 14 samples from 66045 vertices and 131338 triangles.
+Frame 0: refinement generation 7 finished; added 0 vertices, now 66045 vertices and 131338 triangles.
+Frame 0: adaptive ray-trace refinement finished in 8.212 s; 66045 vertices, 131338 triangles.
+Boundary accounting: EEE=122456 DDD=5624 EED/EDD=3258 UUD/UDD=0 U+E=0 UUU=0 error=0; approx-black=0 (0 px^2), retries=0, budget-incomplete=0.
+Frame 0 trace cost: accepted=15768677 rejected=97176 rhs=130409139 over 66045 vertices (saturated=0).
+Wrote lens map: /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.grlens (66045 vertices, 131338 triangles)
+Frame 0: traced 66045 lens vertices; starting catalog render.
+Frame 0: finding and prefetching catalog tiles...
+Frame 0: catalog prefetch finished (0 candidate tiles).
+Frame 0: splatting 131338 lens triangles...
+Frame 0: splat worker 1/16 started.
+Frame 0: splat worker 1/16 reached 8 local triangles.
+Frame 0: splat worker 1/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 32 local triangles.
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+Frame 0: splat worker 16/16 reached 8 local triangles.
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+Frame 0: splat worker 11/16 reached 8 local triangles.
+Frame 0: splat worker 8/16 reached 128 local triangles.
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+Frame 0: splat worker 6/16 reached 128 local triangles.
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+Frame 0: splat worker 2/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 128 local triangles.
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+Frame 0: splat worker 6/16 reached 512 local triangles.
+Frame 0: splat worker 4/16 reached 256 local triangles.
+Frame 0: splat worker 1/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
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+Frame 0: splat worker 5/16 reached 1024 local triangles.
+Frame 0: splat worker 12/16 reached 512 local triangles.
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+Frame 0: splat worker 13/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 512 local triangles.
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+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 1024 local triangles.
+Frame 0: splat worker 8/16 reached 2048 local triangles.
+Frame 0: splat worker 5/16 reached 2048 local triangles.
+Frame 0: splat worker 13/16 reached 2048 local triangles.
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+Frame 0: splat worker 12/16 reached 2048 local triangles.
+Frame 0: splat worker 2/16 reached 2048 local triangles.
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+Frame 0: splat worker 6/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 4096 local triangles.
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+Frame 0: splat worker 13/16 finished after 8856 local triangles.
+Frame 0: catalog splatting finished in 0.1 s; writing image...
+Rendered 1965 images from 1 catalog stars to /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax2.png (ok)
+PSF splats: cached 0, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 1965
+Warning: --psf-min-y discarded one or more PSF events.
@@ -0,0 +1,233 @@
+OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE /home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky --integrator dp54 --width 3840 --height 2160 --look-ra-deg 262.5 --look-dec-deg -30 --fov-deg 45 --observer-radius 100 --coarse-cell-pixels 16 --refine-max-level 4 --refine-jacobian-min .2 --catalog /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/single_dim_star.csv --exposure 1 --tone-map reinhard --psf-min-y 1e-20 --psf-relative-tail 1e-4 --ode-min-step 1e-12 --ode-max-step 8 --verbose --lens-map-output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.grlens --output /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.png
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000041 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+PSF cache ready: 64x64 phases, radius 25 px, relative tail 1e-04, tail abs 1e-06, boundary 1e-07, build 0.223 s
+Frame 0: integrator=dp54 step=0.1 max_steps=65536 threshold=8 atol=(x 1e-09, Pi 1e-09, L 1e-09) rtol=1e-09 bounds=[1e-12, 8] max_rejections=32 lookback=6553.6
+Frame 0: tracing 32776 initial rays from 64800 mesh triangles...
+Frame 0: initial ray trace finished in 1.735 s.
+Frame 0: starting adaptive ray-trace refinement (max level 4)...
+Frame 0: refinement generation 0 tracing 32686 samples from 32776 vertices and 64800 triangles.
+Frame 0: refinement generation 0 finished; added 3014 vertices, now 35790 vertices and 70828 triangles.
+Frame 0: refinement generation 1 tracing 7900 samples from 35790 vertices and 70828 triangles.
+Frame 0: refinement generation 1 finished; added 4852 vertices, now 40642 vertices and 80532 triangles.
+Frame 0: refinement generation 2 tracing 13375 samples from 40642 vertices and 80532 triangles.
+Frame 0: refinement generation 2 finished; added 8889 vertices, now 49531 vertices and 98310 triangles.
+Frame 0: refinement generation 3 tracing 24826 samples from 49531 vertices and 98310 triangles.
+Frame 0: refinement generation 3 finished; added 16055 vertices, now 65586 vertices and 130420 triangles.
+Frame 0: refinement generation 4 tracing 4403 samples from 65586 vertices and 130420 triangles.
+Frame 0: refinement generation 4 finished; added 389 vertices, now 65975 vertices and 131198 triangles.
+Frame 0: refinement generation 5 tracing 261 samples from 65975 vertices and 131198 triangles.
+Frame 0: refinement generation 5 finished; added 58 vertices, now 66033 vertices and 131314 triangles.
+Frame 0: refinement generation 6 tracing 67 samples from 66033 vertices and 131314 triangles.
+Frame 0: refinement generation 6 finished; added 12 vertices, now 66045 vertices and 131338 triangles.
+Frame 0: refinement generation 7 tracing 14 samples from 66045 vertices and 131338 triangles.
+Frame 0: refinement generation 7 finished; added 0 vertices, now 66045 vertices and 131338 triangles.
+Frame 0: adaptive ray-trace refinement finished in 6.070 s; 66045 vertices, 131338 triangles.
+Boundary accounting: EEE=122456 DDD=5624 EED/EDD=3258 UUD/UDD=0 U+E=0 UUU=0 error=0; approx-black=0 (0 px^2), retries=0, budget-incomplete=0.
+Frame 0 trace cost: accepted=10183020 rejected=194781 rhs=91991144 over 66045 vertices (saturated=0).
+Wrote lens map: /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.grlens (66045 vertices, 131338 triangles)
+Frame 0: traced 66045 lens vertices; starting catalog render.
+Frame 0: finding and prefetching catalog tiles...
+Frame 0: catalog prefetch finished (0 candidate tiles).
+Frame 0: splatting 131338 lens triangles...
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+Frame 0: splat worker 10/16 finished after 10255 local triangles.
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+Frame 0: splat worker 11/16 finished after 8075 local triangles.
+Frame 0: splat worker 8/16 finished after 8168 local triangles.
+Frame 0: catalog splatting finished in 0.1 s; writing image...
+Rendered 1954 images from 1 catalog stars to /home/wyj/Code/C/GR_4d_raytracing/local/step_bounds_4k/r100_4k_hmax8.png (ok)
+PSF splats: cached 0, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 1954
+Warning: --psf-min-y discarded one or more PSF events.
@@ -0,0 +1,13 @@
+{
+  "binary_sha256": "72ba409cd60bc72a7f0ca16f736cab6be6d4ab3f42a11d00647eeb03cc7a7e2a",
+  "utc": "2026-10-05T22:19:23Z",
+  "source_sha256": {
+    "src/main.c": "6cf3f6354b52b5eb029e1f3605c403c4161bb3df5d4202a47b97409318358ff9",
+    "src/geodesic.c": "25f24a2e1c9ce49508fed230dfb3f6d9986e92bb4a5e6347bb2356ac0ee5fffa",
+    "src/frame.c": "317cf2a777be139a2cab6a1b9f00094b7834fbb0382389960526ee3281ca55bf"
+  },
+  "catalog": "one negligible synthetic point; no survey catalog",
+  "scope": "README R100 45-degree 3840x2160 coarse16 refine4 jacobian0.2",
+  "threads": 16,
+  "max_attempts": 2
+}
@@ -0,0 +1,3 @@
+r100_4k_hmax2 {"vertices": 66045, "triangles": 131338, "outcomes": {"0": 62419, "1": 3626}, "reasons": {"0": 62419, "1": 3626}, "accepted": 15768677, "rejected": 97176, "rhs": 130409139, "provenance": {"atol_x": 1e-09, "atol_Pi": 1e-09, "atol_L": 1e-09, "rtol": 1e-09, "min_step": 1e-12, "max_step": 2.0, "max_lookback_time": 6553.6, "retry_lookback_increment": 6553.6, "max_total_lookback_time": 26214.4, "integrator": 1, "initial_step": 0.1, "initial_max_steps": 65536, "threshold": 8.0, "retry_step_increment": 65536, "max_total_steps": 262144}, "accepted_percentiles": {"0": 162, "0.5": 212, "0.9": 328, "0.99": 404, "1": 520}, "rejected_percentiles": {"0": 0, "0.5": 1, "0.9": 3, "0.99": 4, "1": 5}, "rhs_percentiles": {"0": 1421, "0.5": 1799, "0.9": 2597, "0.99": 3129, "1": 3941}, "sha256": "ef7267074338192f8597b1f2a0300fd36da8e25441e064719c7ad586c481ae7a", "unique_film_positions": 66045, "duplicate_film_positions": 0, "wall_seconds": 11.389317202148959}
+r100_4k_hmax8 {"vertices": 66045, "triangles": 131338, "outcomes": {"0": 62419, "1": 3626}, "reasons": {"0": 62419, "1": 3626}, "accepted": 10183020, "rejected": 194781, "rhs": 91991144, "provenance": {"atol_x": 1e-09, "atol_Pi": 1e-09, "atol_L": 1e-09, "rtol": 1e-09, "min_step": 1e-12, "max_step": 8.0, "max_lookback_time": 6553.6, "retry_lookback_increment": 6553.6, "max_total_lookback_time": 26214.4, "integrator": 1, "initial_step": 0.1, "initial_max_steps": 65536, "threshold": 8.0, "retry_step_increment": 65536, "max_total_steps": 262144}, "accepted_percentiles": {"0": 80, "0.5": 127, "0.9": 259, "0.99": 337, "1": 432}, "rejected_percentiles": {"0": 0, "0.5": 3, "0.9": 5, "0.99": 6, "1": 7}, "rhs_percentiles": {"0": 868, "0.5": 1204, "0.9": 2114, "0.99": 2646, "1": 3318}, "sha256": "b1897493b7fa5b88f86872e81d15ac876818a705fa0fefe8b1ee262da9de59bb", "unique_film_positions": 66045, "duplicate_film_positions": 0, "wall_seconds": 8.389249739935622}
+comparison {"shared": 66045, "only_a": 0, "only_b": 0, "terminal_mismatches": 0, "max_sky_angle": 7.954413592847793e-07, "max_logg_difference": 3.471110204822381e-11}
@@ -0,0 +1,37 @@
+camera,dir,theta,cfg,outcome,reason,end_id,stop_t,steps,rejected,rhs,nx,ny,nz,g,thr,L,L0
+r30_inward,0,0.16812279429621627,ref_tol1e-12_h0.25,1,1,4294967295,-142.17574796859728,2081,0,14854,0,0,0,0,8.0000000000000195,8.0658840965825682,0.065884096582549498
+r30_inward,0,0.16812279429621627,ref_tol1e-13_h0.125,1,1,4294967295,-142.17574845681202,3332,0,23611,0,0,0,0,8.0000000000000249,8.0658840965825735,0.065884096582549498
+r30_inward,0,0.16812279429621627,tol1e-11_h2,1,1,4294967295,-142.17574172483768,1304,0,9415,0,0,0,0,8.0000000000000266,8.0658840965825753,0.065884096582549498
+r30_inward,0,0.16812279429621627,tol1e-11_h8,1,1,4294967295,-142.17574172483768,1304,0,9415,0,0,0,0,8.0000000000000266,8.0658840965825753,0.065884096582549498
+r30_inward,1,0.16812289429621627,ref_tol1e-12_h0.25,1,1,4294967295,-225.85293500418322,3746,0,26509,0,0,0,0,8.0000000000000338,8.0658840955358357,0.065884095535802364
+r30_inward,1,0.16812289429621627,ref_tol1e-13_h0.125,1,1,4294967295,-238.90906331559862,6388,0,45003,0,0,0,0,8.000000000000016,8.065884095535818,0.065884095535802364
+r30_inward,1,0.16812289429621627,tol1e-11_h2,1,1,4294967295,-212.59582609170599,2180,0,15547,0,0,0,0,8.0000000000000071,8.0658840955358091,0.065884095535802364
+r30_inward,1,0.16812289429621627,tol1e-11_h8,1,1,4294967295,-212.59582609170599,2180,0,15547,0,0,0,0,8.0000000000000071,8.0658840955358091,0.065884095535802364
+r30_inward,2,0.16812299429621627,ref_tol1e-12_h0.25,0,0,0,-370.18047830118235,2790,1,19831,-0.35873499147611138,-6.5068267720987458e-16,-0.9334394495041628,1.0350983390130453,nan,-0.038385896473527227,0.065884094489054593
+r30_inward,2,0.16812299429621627,ref_tol1e-13_h0.125,0,0,0,-370.1804778092,4857,1,34300,-0.35873507984449715,-6.5068265353608199e-16,-0.93343941554284182,1.035098339013504,nan,-0.038385896473972475,0.065884094489054593
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@@ -0,0 +1,96 @@
+### building critical_ref_check
+ cc -std=c11 -O2 -Wall -Wextra -Wpedantic -I/home/wyj/Code/C/GR_4d_raytracing/src /home/wyj/Code/C/GR_4d_raytracing/benchmarks/adaptive_step_bounds_2026-10-05/critical_ref_check.c /home/wyj/Code/C/GR_4d_raytracing/src/geodesic.c /home/wyj/Code/C/GR_4d_raytracing/src/asymptotic.c /home/wyj/Code/C/GR_4d_raytracing/src/asymptotic_schwarzschild.c /home/wyj/Code/C/GR_4d_raytracing/src/spacetime_common.c /home/wyj/Code/C/GR_4d_raytracing/src/observer.c -lm -o /tmp/opencode/step_bounds/critical_ref_check
+ echo '### command: critical_ref_check'
+### command: critical_ref_check
+ /tmp/opencode/step_bounds/critical_ref_check
+RAW camera=r30_inward dir=0 theta=0.16812279429621627 cfg=ref_tol1e-12_h0.25 outcome=1 reason=1 end=4294967295 stop_t=-142.17574796859728 steps=2081 rejected=0 rhs=14854 g=0 thr=8.0000000000000195 L=8.0658840965825682 L0=0.065884096582549498 nx=0 ny=0 nz=0
+RAW camera=r30_inward dir=0 theta=0.16812279429621627 cfg=ref_tol1e-13_h0.125 outcome=1 reason=1 end=4294967295 stop_t=-142.17574845681202 steps=3332 rejected=0 rhs=23611 g=0 thr=8.0000000000000249 L=8.0658840965825735 L0=0.065884096582549498 nx=0 ny=0 nz=0
+RAW camera=r30_inward dir=0 theta=0.16812279429621627 cfg=tol1e-11_h2 outcome=1 reason=1 end=4294967295 stop_t=-142.17574172483768 steps=1304 rejected=0 rhs=9415 g=0 thr=8.0000000000000266 L=8.0658840965825753 L0=0.065884096582549498 nx=0 ny=0 nz=0
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+RAW camera=r30_inward dir=1 theta=0.16812289429621627 cfg=tol1e-11_h8 outcome=1 reason=1 end=4294967295 stop_t=-212.59582609170599 steps=2180 rejected=0 rhs=15547 g=0 thr=8.0000000000000071 L=8.0658840955358091 L0=0.065884095535802364 nx=0 ny=0 nz=0
+RAW camera=r30_inward dir=2 theta=0.16812299429621627 cfg=ref_tol1e-12_h0.25 outcome=0 reason=0 end=0 stop_t=-370.18047830118235 steps=2790 rejected=1 rhs=19831 g=1.0350983390130453 thr=nan L=-0.038385896473527227 L0=0.065884094489054593 nx=-0.35873499147611138 ny=-6.5068267720987458e-16 nz=-0.9334394495041628
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+RAW camera=r30_inward dir=2 theta=0.16812299429621627 cfg=tol1e-11_h2 outcome=0 reason=0 end=0 stop_t=-370.18048452857704 steps=1299 rejected=1 rhs=9387 g=1.0350983390054869 thr=nan L=-0.038385896466199748 L0=0.065884094489054593 nx=-0.3587338729380895 ny=-6.5068297686427377e-16 nz=-0.93343987937458439
+RAW camera=r30_inward dir=2 theta=0.16812299429621627 cfg=tol1e-11_h8 outcome=0 reason=0 end=0 stop_t=-370.1804845285946 steps=1257 rejected=1 rhs=9100 g=1.035098339005424 thr=nan L=-0.038385896466138665 L0=0.065884094489054593 nx=-0.35873387293809145 ny=-6.5068297686427416e-16 nz=-0.93343987937458361
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+CAPAIR camera=r30_inward dir=0 theta=0.16812279429621627 pair=ref_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-6.2437596000108897e-06 dthr=-7.1054273576010019e-15 end=4294967295/4294967295
+CAPAIR camera=r30_inward dir=1 theta=0.16812289429621627 pair=ref_vs_tighter class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=13.056128311415392 dthr=1.7763568394002505e-14 end=4294967295/4294967295
+CAPAIR camera=r30_inward dir=1 theta=0.16812289429621627 pair=h2_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=0 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r30_inward dir=1 theta=0.16812289429621627 pair=ref_vs_h2 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-13.257108912477236 dthr=2.6645352591003757e-14 end=4294967295/4294967295
+CAPAIR camera=r30_inward dir=1 theta=0.16812289429621627 pair=ref_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-13.257108912477236 dthr=2.6645352591003757e-14 end=4294967295/4294967295
+CAPAIR camera=r30_inward dir=2 theta=0.16812299429621627 pair=ref_vs_tighter class=ESC/ESC same=1 dn_ang=9.4669651562462453e-08 dgrel=4.4320103143036249e-13 dstop_t=-4.9198234819414211e-07 dthr=nan end=0/0
+CAPAIR camera=r30_inward dir=2 theta=0.16812299429621627 pair=h2_vs_h8 class=ESC/ESC same=1 dn_ang=2.0539125955565396e-15 dgrel=6.0618177144533547e-14 dstop_t=1.7564616427989677e-11 dthr=nan end=0/0
+CAPAIR camera=r30_inward dir=2 theta=0.16812299429621627 pair=ref_vs_h2 class=ESC/ESC same=1 dn_ang=1.198297077398556e-06 dgrel=7.3021588775645796e-12 dstop_t=6.2273946923596668e-06 dthr=nan end=0/0
+CAPAIR camera=r30_inward dir=2 theta=0.16812299429621627 pair=ref_vs_h8 class=ESC/ESC same=1 dn_ang=1.1982970752891323e-06 dgrel=7.3627770547091131e-12 dstop_t=6.2274122569760948e-06 dthr=nan end=0/0
+CAPAIR camera=r100_inward dir=0 theta=0.051461896376274734 pair=ref_vs_tighter class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=1.5066669334373728e-07 dthr=1.2434497875801753e-14 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=0 theta=0.051461896376274734 pair=h2_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=0 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=0 theta=0.051461896376274734 pair=ref_vs_h2 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-1.6874740822458989e-06 dthr=-2.6645352591003757e-14 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=0 theta=0.051461896376274734 pair=ref_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-1.6874740822458989e-06 dthr=-2.6645352591003757e-14 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=1 theta=0.051461996376274736 pair=ref_vs_tighter class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=12.699935010939669 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=1 theta=0.051461996376274736 pair=h2_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=0 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=1 theta=0.051461996376274736 pair=ref_vs_h2 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-12.863757176939146 dthr=-6.2172489379008766e-14 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=1 theta=0.051461996376274736 pair=ref_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-12.863757176939146 dthr=-6.2172489379008766e-14 end=4294967295/4294967295
+CAPAIR camera=r100_inward dir=2 theta=0.051462096376274739 pair=ref_vs_tighter class=ESC/ESC same=1 dn_ang=2.7365576305005138e-08 dgrel=4.0134562340199409e-13 dstop_t=-1.4223877542463015e-07 dthr=nan end=0/0
+CAPAIR camera=r100_inward dir=2 theta=0.051462096376274739 pair=h2_vs_h8 class=ESC/ESC same=1 dn_ang=1.6930901125533633e-15 dgrel=5.9729998724833422e-14 dstop_t=1.6143530956469476e-11 dthr=nan end=0/0
+CAPAIR camera=r100_inward dir=2 theta=0.051462096376274739 pair=ref_vs_h2 class=ESC/ESC same=1 dn_ang=3.243722235535319e-07 dgrel=6.5301097862402457e-12 dstop_t=1.6862181837495882e-06 dthr=nan end=0/0
+CAPAIR camera=r100_inward dir=2 theta=0.051462096376274739 pair=ref_vs_h8 class=ESC/ESC same=1 dn_ang=3.2437222186044184e-07 dgrel=6.5900618295700042e-12 dstop_t=1.6862343272805447e-06 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=0 theta=0.57037671003940071 pair=ref_vs_tighter class=ESC/ESC same=1 dn_ang=1.4212247739786624e-07 dgrel=3.9634961979118088e-13 dstop_t=7.4312907827334129e-07 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=0 theta=0.57037671003940071 pair=h2_vs_h8 class=ESC/ESC same=1 dn_ang=4.0093378617100928e-10 dgrel=6.0618177144533547e-14 dstop_t=1.6541434888495132e-11 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=0 theta=0.57037671003940071 pair=ref_vs_h2 class=ESC/ESC same=1 dn_ang=6.9368349486792499e-07 dgrel=7.5597306192776159e-12 dstop_t=-3.6107234677729139e-06 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=0 theta=0.57037671003940071 pair=ref_vs_h8 class=ESC/ESC same=1 dn_ang=6.9408442870960736e-07 dgrel=7.6205708410270745e-12 dstop_t=-3.6107069263380254e-06 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=1 theta=0.57037681003940066 pair=ref_vs_tighter class=ESC/ESC same=1 dn_ang=2.3363758065620761 dgrel=1.0434986208451846e-12 dstop_t=12.140629916198748 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=1 theta=0.57037681003940066 pair=h2_vs_h8 class=ESC/ESC same=1 dn_ang=5.0943830155578499e-05 dgrel=6.106226635438361e-14 dstop_t=1.659827830735594e-11 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=1 theta=0.57037681003940066 pair=ref_vs_h2 class=ESC/ESC same=1 dn_ang=1.7079955663413957 dgrel=1.6635359756378421e-11 dstop_t=-8.8742907176965105 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=1 theta=0.57037681003940066 pair=ref_vs_h8 class=ESC/ESC same=1 dn_ang=1.7080465101715514 dgrel=1.6696422022732804e-11 dstop_t=-8.8742907176799122 dthr=nan end=0/0
+CAPAIR camera=r2p1_outward dir=2 theta=0.57037691003940061 pair=ref_vs_tighter class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=-7.4898969160130946e-07 dthr=3.5527136788005009e-15 end=4294967295/4294967295
+CAPAIR camera=r2p1_outward dir=2 theta=0.57037691003940061 pair=h2_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=0 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r2p1_outward dir=2 theta=0.57037691003940061 pair=ref_vs_h2 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=3.6041923436869183e-06 dthr=0 end=4294967295/4294967295
+CAPAIR camera=r2p1_outward dir=2 theta=0.57037691003940061 pair=ref_vs_h8 class=DARK/DARK same=1 dn_ang=nan dgrel=nan dstop_t=3.6041923436869183e-06 dthr=0 end=4294967295/4294967295
+EXACT_CRITICAL_DIRECTION camera=r30_inward theta=0.16812289429621627 ref0=DARK/1/4294967295 ref1=DARK/1/4294967295 same=1 dn_ang=nan dstop_t=13.056128311415392
+EXACT_CRITICAL_REFERENCE_NOT_CONVERGED camera=r30_inward dn_ang=nan dstop_t=13.056128311415392 class_same=1
+EXACT_CRITICAL_DIRECTION camera=r100_inward theta=0.051461996376274736 ref0=DARK/1/4294967295 ref1=DARK/1/4294967295 same=1 dn_ang=nan dstop_t=12.699935010939669
+EXACT_CRITICAL_REFERENCE_NOT_CONVERGED camera=r100_inward dn_ang=nan dstop_t=12.699935010939669 class_same=1
+EXACT_CRITICAL_DIRECTION camera=r2p1_outward theta=0.57037681003940066 ref0=ESC/0/0 ref1=ESC/0/0 same=1 dn_ang=2.3363758065620761 dstop_t=12.140629916198748
+EXACT_CRITICAL_REFERENCE_NOT_CONVERGED camera=r2p1_outward dn_ang=2.3363758065620761 dstop_t=12.140629916198748 class_same=1
+NEIGHBOR_REFERENCE_CHECK camera=r30_inward dir=0 theta=0.16812279429621627 ref_class0=DARK/1/4294967295 ref_class1=DARK/1/4294967295 same=1 clean=1 stepped=1 dn_ang=nan dgrel=nan dstop_t=4.8821473797033832e-07
+NEIGHBOR_REFERENCE_CHECK camera=r30_inward dir=2 theta=0.16812299429621627 ref_class0=ESC/0/0 ref_class1=ESC/0/0 same=1 clean=1 stepped=1 dn_ang=9.4669651562462453e-08 dgrel=4.4320103143036249e-13 dstop_t=-4.9198234819414211e-07
+NEIGHBOR_REFERENCE_CHECK camera=r100_inward dir=0 theta=0.051461896376274734 ref_class0=DARK/1/4294967295 ref_class1=DARK/1/4294967295 same=1 clean=1 stepped=1 dn_ang=nan dgrel=nan dstop_t=1.5066669334373728e-07
+NEIGHBOR_REFERENCE_CHECK camera=r100_inward dir=2 theta=0.051462096376274739 ref_class0=ESC/0/0 ref_class1=ESC/0/0 same=1 clean=1 stepped=1 dn_ang=2.7365576305005138e-08 dgrel=4.0134562340199409e-13 dstop_t=-1.4223877542463015e-07
+NEIGHBOR_REFERENCE_CHECK camera=r2p1_outward dir=0 theta=0.57037671003940071 ref_class0=ESC/0/0 ref_class1=ESC/0/0 same=1 clean=1 stepped=1 dn_ang=1.4212247739786624e-07 dgrel=3.9634961979118088e-13 dstop_t=7.4312907827334129e-07
+NEIGHBOR_REFERENCE_CHECK camera=r2p1_outward dir=2 theta=0.57037691003940061 ref_class0=DARK/1/4294967295 ref_class1=DARK/1/4294967295 same=1 clean=1 stepped=1 dn_ang=nan dgrel=nan dstop_t=-7.4898969160130946e-07
+CRITICAL_REFERENCE_CHECK status=0
+CRITICAL_REF_DONE
+
+real	0m0.418s
+user	0m0.402s
+sys	0m0.016s
+ set +x
@@ -0,0 +1,271 @@
+### command: a_public schwarzschild
+ /tmp/opencode/step_bounds/a_public schwarzschild
+REF r30_inward dir=0 theta=0 outcome=1 reason=1 stop_t=-69.5728394 steps=531 rejected=0 rhs=4004 g=0 thr=8
+REF r30_inward dir=1 theta=3.14159 outcome=0 reason=0 stop_t=-226 steps=905 rejected=0 rhs=6629 g=1.03509833901 thr=nan
+REF r30_inward dir=2 theta=1.5708 outcome=0 reason=0 stop_t=-256.70592 steps=1028 rejected=0 rhs=7490 g=1.03509833901 thr=nan
+REF r30_inward dir=3 theta=0.168123 outcome=1 reason=1 stop_t=-225.852935 steps=3746 rejected=0 rhs=26509 g=0 thr=8
+REF r30_inward dir=4 theta=0.167123 outcome=1 reason=1 stop_t=-94.2779103 steps=1127 rejected=0 rhs=8176 g=0 thr=8
+REF r30_inward dir=5 theta=0.169123 outcome=0 reason=0 stop_t=-322.366447 steps=1834 rejected=0 rhs=13132 g=1.03509833901 thr=nan
+REF r30_inward dir=6 theta=0.168113 outcome=1 reason=1 stop_t=-118.245807 steps=1606 rejected=0 rhs=11529 g=0 thr=8
+REF r30_inward dir=7 theta=0.168133 outcome=0 reason=0 stop_t=-346.252134 steps=2312 rejected=1 rhs=16485 g=1.03509833901 thr=nan
+REF r30_inward dir=8 theta=0.168123 outcome=1 reason=1 stop_t=-142.175748 steps=2081 rejected=0 rhs=14854 g=0 thr=8
+REF r30_inward dir=9 theta=0.168123 outcome=0 reason=0 stop_t=-370.180478 steps=2790 rejected=1 rhs=19831 g=1.03509833901 thr=nan
+REF r30_inward dir=10 theta=0.218123 outcome=0 reason=0 stop_t=-302.584521 steps=1409 rejected=1 rhs=10164 g=1.03509833901 thr=nan
+REF r30_inward dir=11 theta=0.118123 outcome=1 reason=1 stop_t=-73.7563113 steps=665 rejected=0 rhs=4942 g=0 thr=8
+REF r100_inward dir=0 theta=0 outcome=1 reason=1 stop_t=-144.299101 steps=830 rejected=0 rhs=6097 g=0 thr=8
+REF r100_inward dir=1 theta=3.14159 outcome=0 reason=0 stop_t=-156 steps=625 rejected=0 rhs=4669 g=1.01015254455 thr=nan
+REF r100_inward dir=2 theta=1.5708 outcome=0 reason=0 stop_t=-237.678408 steps=952 rejected=0 rhs=6958 g=1.01015254455 thr=nan
+REF r100_inward dir=3 theta=0.051462 outcome=1 reason=1 stop_t=-301.077405 steps=4045 rejected=0 rhs=28602 g=0 thr=8
+REF r100_inward dir=4 theta=0.050462 outcome=1 reason=1 stop_t=-163.061409 steps=1292 rejected=0 rhs=9331 g=0 thr=8
+REF r100_inward dir=5 theta=0.052462 outcome=0 reason=0 stop_t=-391.57927 steps=2014 rejected=1 rhs=14399 g=1.01015254455 thr=nan
+REF r100_inward dir=6 theta=0.051452 outcome=1 reason=1 stop_t=-187.095903 steps=1773 rejected=0 rhs=12698 g=0 thr=8
+REF r100_inward dir=7 theta=0.051472 outcome=0 reason=0 stop_t=-415.386875 steps=2493 rejected=0 rhs=17745 g=1.01015254455 thr=nan
+REF r100_inward dir=8 theta=0.0514619 outcome=1 reason=1 stop_t=-211.027405 steps=2252 rejected=0 rhs=16051 g=0 thr=8
+REF r100_inward dir=9 theta=0.0514621 outcome=0 reason=0 stop_t=-439.313552 steps=2969 rejected=0 rhs=21077 g=1.01015254455 thr=nan
+REF r100_inward dir=10 theta=0.101462 outcome=0 reason=0 stop_t=-372.348056 steps=1571 rejected=0 rhs=11291 g=1.01015254455 thr=nan
+REF r100_inward dir=11 theta=0.001462 outcome=1 reason=1 stop_t=-144.304446 steps=830 rejected=0 rhs=6097 g=0 thr=8
+REF r2p1_outward dir=0 theta=0 outcome=0 reason=0 stop_t=-253.9 steps=1120 rejected=1 rhs=8141 g=4.58257569496 thr=nan
+REF r2p1_outward dir=1 theta=3.14159 outcome=1 reason=1 stop_t=-32.2468847 steps=186 rejected=0 rhs=1589 g=0 thr=8
+REF r2p1_outward dir=2 theta=1.5708 outcome=1 reason=1 stop_t=-32.7725901 steps=316 rejected=1 rhs=2506 g=0 thr=8
+REF r2p1_outward dir=3 theta=0.570377 outcome=0 reason=0 stop_t=-414.940103 steps=4263 rejected=2 rhs=30149 g=4.58257569495 thr=nan
+REF r2p1_outward dir=4 theta=0.569377 outcome=0 reason=0 stop_t=-285.577403 steps=1686 rejected=1 rhs=12103 g=4.58257569496 thr=nan
+REF r2p1_outward dir=5 theta=0.571377 outcome=1 reason=1 stop_t=-61.5813727 steps=995 rejected=1 rhs=7259 g=0 thr=8
+REF r2p1_outward dir=6 theta=0.570367 outcome=0 reason=0 stop_t=-309.521289 steps=2162 rejected=2 rhs=15442 g=4.58257569495 thr=nan
+REF r2p1_outward dir=7 theta=0.570387 outcome=1 reason=1 stop_t=-85.4867841 steps=1474 rejected=1 rhs=10612 g=0 thr=8
+REF r2p1_outward dir=8 theta=0.570377 outcome=0 reason=0 stop_t=-333.450704 steps=2639 rejected=1 rhs=18774 g=4.58257569495 thr=nan
+REF r2p1_outward dir=9 theta=0.570377 outcome=1 reason=1 stop_t=-109.415611 steps=1950 rejected=1 rhs=13944 g=0 thr=8
+REF r2p1_outward dir=10 theta=0.620377 outcome=1 reason=1 stop_t=-41.9883684 steps=585 rejected=1 rhs=4389 g=0 thr=8
+REF r2p1_outward dir=11 theta=0.520377 outcome=0 reason=0 stop_t=-264.96182 steps=1303 rejected=2 rhs=9429 g=4.58257569496 thr=nan
+REF r1p5_freefall dir=0 theta=0 outcome=1 reason=1 stop_t=-30.6580907 steps=231 rejected=1 rhs=1911 g=0 thr=8
+REF r1p5_freefall dir=1 theta=1.5708 outcome=0 reason=0 stop_t=-255.249558 steps=1130 rejected=1 rhs=8211 g=1 thr=nan
+REF r1p5_freefall dir=2 theta=3.14159 outcome=0 reason=0 stop_t=-254.5 steps=1143 rejected=1 rhs=8302 g=0.464101615138 thr=nan
+REF r1p5_freefall dir=3 theta=2.35619 outcome=0 reason=0 stop_t=-254.612997 steps=1127 rejected=1 rhs=8190 g=0.550510257217 thr=nan
+SUMMARY upper r30_inward upper=0.25 min=1e-12 n=12 mismatch=0 max_dn_ang=8.66705e-05 max_dgrel=2.2616e-09 max_dstopT=35.0811 sum_rhs=76510 esc=6 dark=6 unres=0 inc=0 wall=0.041s
+SUMMARY upper r30_inward upper=0.5 min=1e-12 n=12 mismatch=0 max_dn_ang=0.00018656 max_dgrel=2.26833e-09 max_dstopT=39.0614 sum_rhs=49063 esc=6 dark=6 unres=0 inc=0 wall=0.027s
+SUMMARY upper r30_inward upper=1 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000280143 max_dgrel=2.2658e-09 max_dstopT=41.1726 sum_rhs=36974 esc=6 dark=6 unres=0 inc=0 wall=0.020s
+SUMMARY upper r30_inward upper=2 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY upper r30_inward upper=4 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24952e-09 max_dstopT=41.2044 sum_rhs=29617 esc=6 dark=6 unres=0 inc=0 wall=0.016s
+SUMMARY upper r30_inward upper=8 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.25767e-09 max_dstopT=41.2044 sum_rhs=28714 esc=6 dark=6 unres=0 inc=0 wall=0.016s
+SUMMARY upper r30_inward upper=16 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.26556e-09 max_dstopT=41.2044 sum_rhs=28455 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r30_inward upper=32 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.26605e-09 max_dstopT=41.2044 sum_rhs=28434 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r30_inward upper=64 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.26605e-09 max_dstopT=41.2044 sum_rhs=28434 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r100_inward upper=0.25 min=1e-12 n=12 mismatch=0 max_dn_ang=2.60363e-05 max_dgrel=2.04765e-09 max_dstopT=35.2041 sum_rhs=93464 esc=6 dark=6 unres=0 inc=0 wall=0.050s
+SUMMARY upper r100_inward upper=0.5 min=1e-12 n=12 mismatch=0 max_dn_ang=5.69583e-05 max_dgrel=2.05623e-09 max_dstopT=39.2691 sum_rhs=56595 esc=6 dark=6 unres=0 inc=0 wall=0.030s
+SUMMARY upper r100_inward upper=1 min=1e-12 n=12 mismatch=0 max_dn_ang=8.34774e-05 max_dgrel=2.05088e-09 max_dstopT=41.2546 sum_rhs=39788 esc=6 dark=6 unres=0 inc=0 wall=0.022s
+SUMMARY upper r100_inward upper=2 min=1e-12 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY upper r100_inward upper=4 min=1e-12 n=12 mismatch=0 max_dn_ang=8.08898e-05 max_dgrel=2.02847e-09 max_dstopT=41.091 sum_rhs=29393 esc=6 dark=6 unres=0 inc=0 wall=0.016s
+SUMMARY upper r100_inward upper=8 min=1e-12 n=12 mismatch=0 max_dn_ang=8.03365e-05 max_dgrel=2.03431e-09 max_dstopT=41.0553 sum_rhs=28427 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r100_inward upper=16 min=1e-12 n=12 mismatch=0 max_dn_ang=8.03365e-05 max_dgrel=2.04195e-09 max_dstopT=41.0553 sum_rhs=28189 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r100_inward upper=32 min=1e-12 n=12 mismatch=0 max_dn_ang=8.03365e-05 max_dgrel=2.04297e-09 max_dstopT=41.0553 sum_rhs=28182 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r100_inward upper=64 min=1e-12 n=12 mismatch=0 max_dn_ang=8.03365e-05 max_dgrel=2.04297e-09 max_dstopT=41.0553 sum_rhs=28182 esc=6 dark=6 unres=0 inc=0 wall=0.015s
+SUMMARY upper r2p1_outward upper=0.25 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287223 max_dgrel=2.66126e-09 max_dstopT=263.145 sum_rhs=62258 esc=5 dark=7 unres=0 inc=0 wall=0.034s
+SUMMARY upper r2p1_outward upper=0.5 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.64443e-09 max_dstopT=263.145 sum_rhs=42490 esc=5 dark=7 unres=0 inc=0 wall=0.023s
+SUMMARY upper r2p1_outward upper=1 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.61531e-09 max_dstopT=263.145 sum_rhs=33544 esc=5 dark=7 unres=0 inc=0 wall=0.019s
+SUMMARY upper r2p1_outward upper=2 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY upper r2p1_outward upper=4 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.59774e-09 max_dstopT=263.145 sum_rhs=27580 esc=5 dark=7 unres=0 inc=0 wall=0.015s
+SUMMARY upper r2p1_outward upper=8 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.60591e-09 max_dstopT=263.145 sum_rhs=26831 esc=5 dark=7 unres=0 inc=0 wall=0.015s
+SUMMARY upper r2p1_outward upper=16 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287223 max_dgrel=2.61374e-09 max_dstopT=263.145 sum_rhs=26614 esc=5 dark=7 unres=0 inc=0 wall=0.015s
+SUMMARY upper r2p1_outward upper=32 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.6148e-09 max_dstopT=263.145 sum_rhs=26607 esc=5 dark=7 unres=0 inc=0 wall=0.015s
+SUMMARY upper r2p1_outward upper=64 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287221 max_dgrel=2.6148e-09 max_dstopT=263.145 sum_rhs=26607 esc=5 dark=7 unres=0 inc=0 wall=0.015s
+SUMMARY upper r1p5_freefall upper=0.25 min=1e-12 n=4 mismatch=0 max_dn_ang=1.00222e-10 max_dgrel=3.16466e-10 max_dstopT=2.6078e-08 sum_rhs=23597 esc=3 dark=1 unres=0 inc=0 wall=0.014s
+SUMMARY upper r1p5_freefall upper=0.5 min=1e-12 n=4 mismatch=0 max_dn_ang=8.87544e-11 max_dgrel=3.65847e-10 max_dstopT=3.08873e-08 sum_rhs=12747 esc=3 dark=1 unres=0 inc=0 wall=0.008s
+SUMMARY upper r1p5_freefall upper=1 min=1e-12 n=4 mismatch=0 max_dn_ang=8.18746e-11 max_dgrel=3.81078e-10 max_dstopT=2.81655e-08 sum_rhs=7553 esc=3 dark=1 unres=0 inc=0 wall=0.005s
+SUMMARY upper r1p5_freefall upper=2 min=1e-12 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY upper r1p5_freefall upper=4 min=1e-12 n=4 mismatch=0 max_dn_ang=8.1566e-11 max_dgrel=3.6318e-10 max_dstopT=2.34608e-08 sum_rhs=4039 esc=3 dark=1 unres=0 inc=0 wall=0.002s
+SUMMARY upper r1p5_freefall upper=8 min=1e-12 n=4 mismatch=0 max_dn_ang=8.15091e-11 max_dgrel=3.54659e-10 max_dstopT=2.12507e-08 sum_rhs=3591 esc=3 dark=1 unres=0 inc=0 wall=0.002s
+SUMMARY upper r1p5_freefall upper=16 min=1e-12 n=4 mismatch=0 max_dn_ang=8.14607e-11 max_dgrel=3.46852e-10 max_dstopT=1.92511e-08 sum_rhs=3465 esc=3 dark=1 unres=0 inc=0 wall=0.002s
+SUMMARY upper r1p5_freefall upper=32 min=1e-12 n=4 mismatch=0 max_dn_ang=8.1455e-11 max_dgrel=3.45979e-10 max_dstopT=1.94793e-08 sum_rhs=3458 esc=3 dark=1 unres=0 inc=0 wall=0.002s
+SUMMARY upper r1p5_freefall upper=64 min=1e-12 n=4 mismatch=0 max_dn_ang=8.1455e-11 max_dgrel=3.45979e-10 max_dstopT=1.94793e-08 sum_rhs=3458 esc=3 dark=1 unres=0 inc=0 wall=0.002s
+SUMMARY min r30_inward upper=2 min=0.1 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=0.01 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=0.001 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=0.0001 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-05 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-06 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-08 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-10 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-12 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r30_inward upper=2 min=1e-14 n=12 mismatch=0 max_dn_ang=0.000281866 max_dgrel=2.24374e-09 max_dstopT=41.2044 sum_rhs=31843 esc=6 dark=6 unres=0 inc=0 wall=0.017s
+SUMMARY min r100_inward upper=2 min=0.1 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=0.01 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=0.001 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=0.0001 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-05 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-06 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-08 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-10 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-12 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r100_inward upper=2 min=1e-14 n=12 mismatch=0 max_dn_ang=8.28604e-05 max_dgrel=2.0262e-09 max_dstopT=41.2161 sum_rhs=32389 esc=6 dark=6 unres=0 inc=0 wall=0.018s
+SUMMARY min r2p1_outward upper=2 min=0.1 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=0.01 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=0.001 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.017s
+SUMMARY min r2p1_outward upper=2 min=0.0001 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.017s
+SUMMARY min r2p1_outward upper=2 min=1e-05 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=1e-06 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=1e-08 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=1e-10 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=1e-12 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r2p1_outward upper=2 min=1e-14 n=12 mismatch=1 max_dn_ang=0.000287222 max_dgrel=2.59243e-09 max_dstopT=263.145 sum_rhs=29421 esc=5 dark=7 unres=0 inc=0 wall=0.016s
+SUMMARY min r1p5_freefall upper=2 min=0.1 n=4 mismatch=1 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=254.3 sum_rhs=3654 esc=2 dark=1 unres=0 inc=1 wall=0.002s
+SUMMARY min r1p5_freefall upper=2 min=0.01 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=0.001 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=0.0001 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-05 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-06 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-08 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-10 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-12 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+SUMMARY min r1p5_freefall upper=2 min=1e-14 n=4 mismatch=0 max_dn_ang=8.165e-11 max_dgrel=3.7195e-10 max_dstopT=2.57141e-08 sum_rhs=5131 esc=3 dark=1 unres=0 inc=0 wall=0.003s
+RK4 r30_inward dir=8 theta=0.168123 o01=1/1 o005=1/1 hhalve_dn=nan hhalve_dgrel=nan vsdp_dn=nan vsdp_dgrel=nan vsdp_class=1
+RK4 r30_inward dir=9 theta=0.168123 o01=0/0 o005=0/0 hhalve_dn=1.89584e-07 hhalve_dgrel=7.32747e-15 vsdp_dn=7.95167e-08 vsdp_dgrel=4.66294e-13 vsdp_class=1
+RK4 r30_inward dir=6 theta=0.168113 o01=1/1 o005=1/1 hhalve_dn=nan hhalve_dgrel=nan vsdp_dn=nan vsdp_dgrel=nan vsdp_class=1
+RK4 r30_inward dir=7 theta=0.168133 o01=0/0 o005=0/0 hhalve_dn=1.73965e-09 hhalve_dgrel=7.9492e-14 vsdp_dn=7.86496e-10 vsdp_dgrel=2.6934e-13 vsdp_class=1
+RK4 r2p1_outward dir=8 theta=0.570377 o01=0/0 o005=0/0 hhalve_dn=1.03961e-05 hhalve_dgrel=1.66234e-12 vsdp_dn=8.49321e-07 vsdp_dgrel=5.46896e-13 vsdp_class=1
+RK4 r2p1_outward dir=9 theta=0.570377 o01=1/1 o005=1/1 hhalve_dn=nan hhalve_dgrel=nan vsdp_dn=nan vsdp_dgrel=nan vsdp_class=1
+RK4 r2p1_outward dir=6 theta=0.570367 o01=0/0 o005=0/0 hhalve_dn=1.03971e-07 hhalve_dgrel=1.61182e-12 vsdp_dn=8.47692e-09 vsdp_dgrel=3.02647e-13 vsdp_class=1
+RK4 r2p1_outward dir=7 theta=0.570387 o01=1/1 o005=1/1 hhalve_dn=nan hhalve_dgrel=nan vsdp_dn=nan vsdp_dgrel=nan vsdp_class=1
+TOTAL_RAYS 816
+
+real	0m2.428s
+user	0m2.423s
+sys	0m0.004s
+ set +x
+### command: a_public minkowski
+ /tmp/opencode/step_bounds/a_public minkowski
+SUMMARY mink upper=1 min=0.1 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=4886 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=1 min=1e-06 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=4886 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=1 min=1e-12 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=4886 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=4 min=0.1 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2590 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=4 min=1e-06 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2590 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=4 min=1e-12 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2590 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=16 min=0.1 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2037 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=16 min=1e-06 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2037 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=16 min=1e-12 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=2037 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=64 min=0.1 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=64 min=1e-06 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=64 min=1e-12 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=256 min=0.1 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=256 min=1e-06 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+SUMMARY mink upper=256 min=1e-12 n=6 mismatch=0 max_dn_ang=0 max_dgrel=0 sum_rhs=1932 esc=6 dark=0 unres=0 inc=0
+TOTAL_RAYS 186
+
+real	0m0.013s
+user	0m0.013s
+sys	0m0.000s
+ set +x
+### command: a_public alcubierre
+ /tmp/opencode/step_bounds/a_public alcubierre
+REF alc_v3_s1 dir=0 theta=nan outcome=0 reason=0 stop_t=-16.4338937 steps=347 rejected=1 rhs=2730 g=1.3 thr=nan
+REF alc_v3_s1 dir=1 theta=nan outcome=0 reason=0 stop_t=-29.3767055 steps=597 rejected=1 rhs=4480 g=0.7 thr=nan
+REF alc_v3_s1 dir=2 theta=nan outcome=0 reason=0 stop_t=-20.2190145 steps=414 rejected=0 rhs=3192 g=1 thr=nan
+REF alc_v3_s1 dir=3 theta=nan outcome=0 reason=0 stop_t=-20.2190145 steps=414 rejected=0 rhs=3192 g=1 thr=nan
+REF alc_v3_s1 dir=4 theta=nan outcome=0 reason=0 stop_t=-17.6897755 steps=367 rejected=0 rhs=2863 g=1.17815368048 thr=nan
+REF alc_v3_s1 dir=5 theta=nan outcome=0 reason=0 stop_t=-24.329102 steps=497 rejected=1 rhs=3780 g=0.822613315483 thr=nan
+REF alc_v3_s10 dir=0 theta=nan outcome=0 reason=0 stop_t=-2.53543426 steps=523 rejected=3 rhs=3976 g=1.3 thr=nan
+REF alc_v3_s10 dir=1 theta=nan outcome=0 reason=0 stop_t=-3.84949982 steps=775 rejected=0 rhs=5719 g=0.7 thr=nan
+REF alc_v3_s10 dir=2 theta=nan outcome=0 reason=0 stop_t=-2.94282517 steps=589 rejected=0 rhs=4417 g=1 thr=nan
+REF alc_v3_s10 dir=3 theta=nan outcome=0 reason=0 stop_t=-2.94282517 steps=589 rejected=0 rhs=4417 g=1 thr=nan
+REF alc_v3_s10 dir=4 theta=nan outcome=0 reason=0 stop_t=-2.67090915 steps=543 rejected=2 rhs=4109 g=1.17959135733 thr=nan
+REF alc_v3_s10 dir=5 theta=nan outcome=0 reason=0 stop_t=-3.3698049 steps=677 rejected=0 rhs=5033 g=0.820579506843 thr=nan
+REF alc_v9_s1 dir=0 theta=nan outcome=0 reason=0 stop_t=-11.5627491 steps=283 rejected=1 rhs=2282 g=1.9 thr=nan
+REF alc_v9_s1 dir=1 theta=nan outcome=0 reason=0 stop_t=-189.149503 steps=3825 rejected=1 rhs=27069 g=0.1 thr=nan
+REF alc_v9_s1 dir=2 theta=nan outcome=0 reason=0 stop_t=-16.1619146 steps=351 rejected=4 rhs=2772 g=1 thr=nan
+REF alc_v9_s1 dir=3 theta=nan outcome=0 reason=0 stop_t=-16.1619146 steps=351 rejected=4 rhs=2772 g=1 thr=nan
+REF alc_v9_s1 dir=4 theta=nan outcome=0 reason=0 stop_t=-13.0192142 steps=308 rejected=1 rhs=2457 g=1.5041731473 thr=nan
+REF alc_v9_s1 dir=5 theta=nan outcome=0 reason=0 stop_t=-22.987334 steps=491 rejected=1 rhs=3738 g=0.54079971046 thr=nan
+REF alc_v9_s10 dir=0 theta=nan outcome=0 reason=0 stop_t=-2.03742978 steps=452 rejected=5 rhs=3493 g=1.9 thr=nan
+REF alc_v9_s10 dir=1 theta=nan outcome=0 reason=0 stop_t=-19.9638367 steps=4013 rejected=0 rhs=28385 g=0.1 thr=nan
+REF alc_v9_s10 dir=2 theta=nan outcome=0 reason=0 stop_t=-2.62069451 steps=525 rejected=0 rhs=3969 g=1 thr=nan
+REF alc_v9_s10 dir=3 theta=nan outcome=0 reason=0 stop_t=-2.62069451 steps=525 rejected=0 rhs=3969 g=1 thr=nan
+REF alc_v9_s10 dir=4 theta=nan outcome=0 reason=0 stop_t=-2.20704191 steps=469 rejected=3 rhs=3598 g=1.5316539409 thr=nan
+REF alc_v9_s10 dir=5 theta=nan outcome=0 reason=0 stop_t=-3.67922549 steps=742 rejected=0 rhs=5488 g=0.483265790771 thr=nan
+REF alc_v9_s100 dir=0 theta=nan outcome=0 reason=0 stop_t=-1.10374298 steps=2252 rejected=5 rhs=16093 g=1.9 thr=nan
+REF alc_v9_s100 dir=1 theta=nan outcome=0 reason=0 stop_t=-2.89638367 steps=5813 rejected=0 rhs=40978 g=0.1 thr=nan
+REF alc_v9_s100 dir=2 theta=nan outcome=0 reason=0 stop_t=-1.18800796 steps=2377 rejected=0 rhs=16926 g=1 thr=nan
+REF alc_v9_s100 dir=3 theta=nan outcome=0 reason=0 stop_t=-1.18800796 steps=2377 rejected=0 rhs=16926 g=1 thr=nan
+REF alc_v9_s100 dir=4 theta=nan outcome=0 reason=0 stop_t=-1.12678339 steps=2281 rejected=2 rhs=16275 g=1.53910006629 thr=nan
+REF alc_v9_s100 dir=5 theta=nan outcome=0 reason=0 stop_t=-1.36694611 steps=2740 rejected=0 rhs=19474 g=0.462933441354 thr=nan
+SUMMARY upper alc_v3_s1 upper=0.05 min=0.0001 n=6 mismatch=0 max_dn_ang=7.54397e-14 max_dgrel=7.62723e-13 max_dstopT=1.98952e-13 sum_rhs=19740 esc=6 dark=0 unres=0 inc=0 wall=0.005s
+SUMMARY upper alc_v3_s1 upper=0.05 min=1e-08 n=6 mismatch=0 max_dn_ang=7.54397e-14 max_dgrel=7.62723e-13 max_dstopT=1.98952e-13 sum_rhs=19740 esc=6 dark=0 unres=0 inc=0 wall=0.005s
+SUMMARY upper alc_v3_s1 upper=0.05 min=1e-12 n=6 mismatch=0 max_dn_ang=7.54397e-14 max_dgrel=7.62723e-13 max_dstopT=1.98952e-13 sum_rhs=19740 esc=6 dark=0 unres=0 inc=0 wall=0.005s
+SUMMARY upper alc_v3_s1 upper=0.2 min=0.0001 n=6 mismatch=0 max_dn_ang=1.2079e-10 max_dgrel=3.45157e-10 max_dstopT=4.09095e-10 sum_rhs=6475 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.2 min=1e-08 n=6 mismatch=0 max_dn_ang=1.2079e-10 max_dgrel=3.45157e-10 max_dstopT=4.09095e-10 sum_rhs=6475 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v3_s1 upper=0.2 min=1e-12 n=6 mismatch=0 max_dn_ang=1.2079e-10 max_dgrel=3.45157e-10 max_dstopT=4.09095e-10 sum_rhs=6475 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v3_s1 upper=0.4 min=0.0001 n=6 mismatch=0 max_dn_ang=1.02989e-10 max_dgrel=3.46442e-10 max_dstopT=3.14323e-10 sum_rhs=4613 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.4 min=1e-08 n=6 mismatch=0 max_dn_ang=1.02989e-10 max_dgrel=3.46442e-10 max_dstopT=3.14323e-10 sum_rhs=4613 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.4 min=1e-12 n=6 mismatch=0 max_dn_ang=1.02989e-10 max_dgrel=3.46442e-10 max_dstopT=3.14323e-10 sum_rhs=4613 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.8 min=0.0001 n=6 mismatch=0 max_dn_ang=7.88763e-11 max_dgrel=7.95433e-10 max_dstopT=7.3689e-10 sum_rhs=3794 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.8 min=1e-08 n=6 mismatch=0 max_dn_ang=7.88763e-11 max_dgrel=7.95433e-10 max_dstopT=7.3689e-10 sum_rhs=3794 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=0.8 min=1e-12 n=6 mismatch=0 max_dn_ang=7.88763e-11 max_dgrel=7.95433e-10 max_dstopT=7.3689e-10 sum_rhs=3794 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=1.6 min=0.0001 n=6 mismatch=0 max_dn_ang=1.23935e-10 max_dgrel=1.11826e-09 max_dstopT=1.14768e-09 sum_rhs=3430 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=1.6 min=1e-08 n=6 mismatch=0 max_dn_ang=1.23935e-10 max_dgrel=1.11826e-09 max_dstopT=1.14768e-09 sum_rhs=3430 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=1.6 min=1e-12 n=6 mismatch=0 max_dn_ang=1.23935e-10 max_dgrel=1.11826e-09 max_dstopT=1.14768e-09 sum_rhs=3430 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=3.2 min=0.0001 n=6 mismatch=0 max_dn_ang=1.54539e-10 max_dgrel=1.25996e-09 max_dstopT=1.3457e-09 sum_rhs=3290 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=3.2 min=1e-08 n=6 mismatch=0 max_dn_ang=1.54539e-10 max_dgrel=1.25996e-09 max_dstopT=1.3457e-09 sum_rhs=3290 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s1 upper=3.2 min=1e-12 n=6 mismatch=0 max_dn_ang=1.54539e-10 max_dgrel=1.25996e-09 max_dstopT=1.3457e-09 sum_rhs=3290 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.005 min=0.0001 n=6 mismatch=0 max_dn_ang=5.82867e-15 max_dgrel=3.10862e-14 max_dstopT=4.66294e-14 sum_rhs=27412 esc=6 dark=0 unres=0 inc=0 wall=0.006s
+SUMMARY upper alc_v3_s10 upper=0.005 min=1e-08 n=6 mismatch=0 max_dn_ang=5.82867e-15 max_dgrel=3.10862e-14 max_dstopT=4.66294e-14 sum_rhs=27412 esc=6 dark=0 unres=0 inc=0 wall=0.006s
+SUMMARY upper alc_v3_s10 upper=0.005 min=1e-12 n=6 mismatch=0 max_dn_ang=5.82867e-15 max_dgrel=3.10862e-14 max_dstopT=4.66294e-14 sum_rhs=27412 esc=6 dark=0 unres=0 inc=0 wall=0.006s
+SUMMARY upper alc_v3_s10 upper=0.02 min=0.0001 n=6 mismatch=0 max_dn_ang=6.29929e-12 max_dgrel=2.40162e-10 max_dstopT=1.39897e-11 sum_rhs=8337 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v3_s10 upper=0.02 min=1e-08 n=6 mismatch=0 max_dn_ang=6.29929e-12 max_dgrel=2.40162e-10 max_dstopT=1.39897e-11 sum_rhs=8337 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v3_s10 upper=0.02 min=1e-12 n=6 mismatch=0 max_dn_ang=6.29929e-12 max_dgrel=2.40162e-10 max_dstopT=1.39897e-11 sum_rhs=8337 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v3_s10 upper=0.04 min=0.0001 n=6 mismatch=0 max_dn_ang=3.28758e-11 max_dgrel=3.85361e-10 max_dstopT=6.29403e-11 sum_rhs=5621 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.04 min=1e-08 n=6 mismatch=0 max_dn_ang=3.28758e-11 max_dgrel=3.85361e-10 max_dstopT=6.29403e-11 sum_rhs=5621 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.04 min=1e-12 n=6 mismatch=0 max_dn_ang=3.28758e-11 max_dgrel=3.85361e-10 max_dstopT=6.29403e-11 sum_rhs=5621 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.08 min=0.0001 n=6 mismatch=0 max_dn_ang=1.04151e-11 max_dgrel=2.78111e-10 max_dstopT=8.02363e-11 sum_rhs=4648 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.08 min=1e-08 n=6 mismatch=0 max_dn_ang=1.04151e-11 max_dgrel=2.78111e-10 max_dstopT=8.02363e-11 sum_rhs=4648 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.08 min=1e-12 n=6 mismatch=0 max_dn_ang=1.04151e-11 max_dgrel=2.78111e-10 max_dstopT=8.02363e-11 sum_rhs=4648 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.16 min=0.0001 n=6 mismatch=0 max_dn_ang=1.13121e-11 max_dgrel=7.59968e-10 max_dstopT=9.53793e-11 sum_rhs=4270 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.16 min=1e-08 n=6 mismatch=0 max_dn_ang=1.13121e-11 max_dgrel=7.59968e-10 max_dstopT=9.53793e-11 sum_rhs=4270 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.16 min=1e-12 n=6 mismatch=0 max_dn_ang=1.13121e-11 max_dgrel=7.59968e-10 max_dstopT=9.53793e-11 sum_rhs=4270 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.32 min=0.0001 n=6 mismatch=0 max_dn_ang=3.13081e-11 max_dgrel=9.77839e-10 max_dstopT=1.04124e-10 sum_rhs=4116 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.32 min=1e-08 n=6 mismatch=0 max_dn_ang=3.13081e-11 max_dgrel=9.77839e-10 max_dstopT=1.04124e-10 sum_rhs=4116 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v3_s10 upper=0.32 min=1e-12 n=6 mismatch=0 max_dn_ang=3.13081e-11 max_dgrel=9.77839e-10 max_dstopT=1.04124e-10 sum_rhs=4116 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=0.05 min=0.0001 n=6 mismatch=0 max_dn_ang=6.63192e-13 max_dgrel=2.59086e-11 max_dstopT=1.38662e-11 sum_rhs=39452 esc=6 dark=0 unres=0 inc=0 wall=0.010s
+SUMMARY upper alc_v9_s1 upper=0.05 min=1e-08 n=6 mismatch=0 max_dn_ang=6.63192e-13 max_dgrel=2.59086e-11 max_dstopT=1.38662e-11 sum_rhs=39452 esc=6 dark=0 unres=0 inc=0 wall=0.010s
+SUMMARY upper alc_v9_s1 upper=0.05 min=1e-12 n=6 mismatch=0 max_dn_ang=6.63192e-13 max_dgrel=2.59086e-11 max_dstopT=1.38662e-11 sum_rhs=39452 esc=6 dark=0 unres=0 inc=0 wall=0.010s
+SUMMARY upper alc_v9_s1 upper=0.2 min=0.0001 n=6 mismatch=0 max_dn_ang=1.07764e-10 max_dgrel=2.07282e-09 max_dstopT=6.80462e-10 sum_rhs=11690 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s1 upper=0.2 min=1e-08 n=6 mismatch=0 max_dn_ang=1.07764e-10 max_dgrel=2.07282e-09 max_dstopT=6.80462e-10 sum_rhs=11690 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s1 upper=0.2 min=1e-12 n=6 mismatch=0 max_dn_ang=1.07764e-10 max_dgrel=2.07282e-09 max_dstopT=6.80462e-10 sum_rhs=11690 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s1 upper=0.4 min=0.0001 n=6 mismatch=0 max_dn_ang=6.25e-11 max_dgrel=2.46644e-09 max_dstopT=1.08309e-09 sum_rhs=7413 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s1 upper=0.4 min=1e-08 n=6 mismatch=0 max_dn_ang=6.25e-11 max_dgrel=2.46644e-09 max_dstopT=1.08309e-09 sum_rhs=7413 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s1 upper=0.4 min=1e-12 n=6 mismatch=0 max_dn_ang=6.25e-11 max_dgrel=2.46644e-09 max_dstopT=1.08309e-09 sum_rhs=7413 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s1 upper=0.8 min=0.0001 n=6 mismatch=0 max_dn_ang=5.34924e-11 max_dgrel=2.71772e-09 max_dstopT=1.1859e-09 sum_rhs=5369 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=0.8 min=1e-08 n=6 mismatch=0 max_dn_ang=5.34924e-11 max_dgrel=2.71772e-09 max_dstopT=1.1859e-09 sum_rhs=5369 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=0.8 min=1e-12 n=6 mismatch=0 max_dn_ang=5.34924e-11 max_dgrel=2.71772e-09 max_dstopT=1.1859e-09 sum_rhs=5369 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=1.6 min=0.0001 n=6 mismatch=0 max_dn_ang=1.03537e-10 max_dgrel=2.8194e-09 max_dstopT=9.54927e-10 sum_rhs=4431 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=1.6 min=1e-08 n=6 mismatch=0 max_dn_ang=1.03537e-10 max_dgrel=2.8194e-09 max_dstopT=9.54927e-10 sum_rhs=4431 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=1.6 min=1e-12 n=6 mismatch=0 max_dn_ang=1.03537e-10 max_dgrel=2.8194e-09 max_dstopT=9.54927e-10 sum_rhs=4431 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=3.2 min=0.0001 n=6 mismatch=0 max_dn_ang=1.23927e-10 max_dgrel=2.82251e-09 max_dstopT=3.24928e-09 sum_rhs=3983 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=3.2 min=1e-08 n=6 mismatch=0 max_dn_ang=1.23927e-10 max_dgrel=2.82251e-09 max_dstopT=3.24928e-09 sum_rhs=3983 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s1 upper=3.2 min=1e-12 n=6 mismatch=0 max_dn_ang=1.23927e-10 max_dgrel=2.82251e-09 max_dstopT=3.24928e-09 sum_rhs=3983 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.005 min=0.0001 n=6 mismatch=0 max_dn_ang=8.9373e-14 max_dgrel=1.10281e-11 max_dstopT=3.55271e-13 sum_rhs=48167 esc=6 dark=0 unres=0 inc=0 wall=0.011s
+SUMMARY upper alc_v9_s10 upper=0.005 min=1e-08 n=6 mismatch=0 max_dn_ang=8.9373e-14 max_dgrel=1.10281e-11 max_dstopT=3.55271e-13 sum_rhs=48167 esc=6 dark=0 unres=0 inc=0 wall=0.011s
+SUMMARY upper alc_v9_s10 upper=0.005 min=1e-12 n=6 mismatch=0 max_dn_ang=8.9373e-14 max_dgrel=1.10281e-11 max_dstopT=3.55271e-13 sum_rhs=48167 esc=6 dark=0 unres=0 inc=0 wall=0.011s
+SUMMARY upper alc_v9_s10 upper=0.02 min=0.0001 n=6 mismatch=0 max_dn_ang=5.33142e-11 max_dgrel=6.90633e-10 max_dstopT=1.09151e-10 sum_rhs=13692 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s10 upper=0.02 min=1e-08 n=6 mismatch=0 max_dn_ang=5.33142e-11 max_dgrel=6.90633e-10 max_dstopT=1.09151e-10 sum_rhs=13692 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s10 upper=0.02 min=1e-12 n=6 mismatch=0 max_dn_ang=5.33142e-11 max_dgrel=6.90633e-10 max_dstopT=1.09151e-10 sum_rhs=13692 esc=6 dark=0 unres=0 inc=0 wall=0.003s
+SUMMARY upper alc_v9_s10 upper=0.04 min=0.0001 n=6 mismatch=0 max_dn_ang=1.75204e-10 max_dgrel=9.74943e-10 max_dstopT=3.64615e-10 sum_rhs=8484 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s10 upper=0.04 min=1e-08 n=6 mismatch=0 max_dn_ang=1.75204e-10 max_dgrel=9.74943e-10 max_dstopT=3.64615e-10 sum_rhs=8484 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s10 upper=0.04 min=1e-12 n=6 mismatch=0 max_dn_ang=1.75204e-10 max_dgrel=9.74943e-10 max_dstopT=3.64615e-10 sum_rhs=8484 esc=6 dark=0 unres=0 inc=0 wall=0.002s
+SUMMARY upper alc_v9_s10 upper=0.08 min=0.0001 n=6 mismatch=0 max_dn_ang=1.1957e-10 max_dgrel=1.45708e-09 max_dstopT=2.69508e-10 sum_rhs=6251 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.08 min=1e-08 n=6 mismatch=0 max_dn_ang=1.1957e-10 max_dgrel=1.45708e-09 max_dstopT=2.69508e-10 sum_rhs=6251 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.08 min=1e-12 n=6 mismatch=0 max_dn_ang=1.1957e-10 max_dgrel=1.45708e-09 max_dstopT=2.69508e-10 sum_rhs=6251 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.16 min=0.0001 n=6 mismatch=0 max_dn_ang=1.72733e-11 max_dgrel=1.07679e-09 max_dstopT=1.26013e-10 sum_rhs=5278 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.16 min=1e-08 n=6 mismatch=0 max_dn_ang=1.72733e-11 max_dgrel=1.07679e-09 max_dstopT=1.26013e-10 sum_rhs=5278 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.16 min=1e-12 n=6 mismatch=0 max_dn_ang=1.72733e-11 max_dgrel=1.07679e-09 max_dstopT=1.26013e-10 sum_rhs=5278 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.32 min=0.0001 n=6 mismatch=0 max_dn_ang=5.49931e-11 max_dgrel=8.67977e-10 max_dstopT=2.55501e-10 sum_rhs=4872 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.32 min=1e-08 n=6 mismatch=0 max_dn_ang=5.49931e-11 max_dgrel=8.67977e-10 max_dstopT=2.55501e-10 sum_rhs=4872 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY upper alc_v9_s10 upper=0.32 min=1e-12 n=6 mismatch=0 max_dn_ang=5.49931e-11 max_dgrel=8.67977e-10 max_dstopT=2.55501e-10 sum_rhs=4872 esc=6 dark=0 unres=0 inc=0 wall=0.001s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=0.0001 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=1e-05 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=1e-06 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=1e-08 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=1e-12 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+SUMMARY min_stress alc_v9_s100 upper=0.004 min=1e-14 n=6 mismatch=0 max_dn_ang=1.69451e-11 max_dgrel=1.33161e-09 max_dstopT=1.05733e-11 sum_rhs=18095 esc=6 dark=0 unres=0 inc=0 wall=0.004s
+TOTAL_RAYS 498
+
+real	0m0.264s
+user	0m0.254s
+sys	0m0.010s
+ set +x
@@ -0,0 +1,33 @@
+### command: b_actual
+ /tmp/opencode/step_bounds/b_actual
+B r30_inward dir=0 ref=1 refstop=-69.5728394 span=69.5728 T=20 target=-20 steps=17 reached=1 term=-1 h=[0.1,1.72575] first=0.1 last=0.839319 boundary=1 rhs=119 rej=0 nullmax=3.01e-12 final_t=-20 wall=0.0001s
+B r30_inward dir=1 ref=0 refstop=-226 span=226 T=20 target=-20 steps=13 reached=1 term=-1 h=[0.1,2] first=0.1 last=0.123959 boundary=1 rhs=91 rej=0 nullmax=8.69e-12 final_t=-20 wall=0.0001s
+B r30_inward dir=2 ref=1 refstop=-142.175748 span=142.176 T=20 target=-20 steps=20 reached=1 term=-1 h=[0.1,1.40832] first=0.1 last=0.637699 boundary=1 rhs=140 rej=0 nullmax=1.53e-11 final_t=-20 wall=0.0001s
+B r30_inward dir=3 ref=0 refstop=-370.180478 span=370.18 T=20 target=-20 steps=20 reached=1 term=-1 h=[0.1,1.40832] first=0.1 last=0.6377 boundary=1 rhs=140 rej=0 nullmax=1.53e-11 final_t=-20 wall=0.0001s
+B r30_inward dir=4 ref=1 refstop=-118.245807 span=118.246 T=20 target=-20 steps=20 reached=1 term=-1 h=[0.1,1.40833] first=0.1 last=0.637634 boundary=1 rhs=140 rej=0 nullmax=1.53e-11 final_t=-20 wall=0.0001s
+B r30_inward dir=5 ref=0 refstop=-346.252134 span=346.252 T=20 target=-20 steps=20 reached=1 term=-1 h=[0.1,1.40831] first=0.1 last=0.637765 boundary=1 rhs=140 rej=0 nullmax=1.53e-11 final_t=-20 wall=0.0001s
+B r100_inward dir=0 ref=1 refstop=-144.299101 span=144.299 T=20 target=-20 steps=12 reached=1 term=-1 h=[0.1,2] first=0.1 last=1.4 boundary=1 rhs=84 rej=0 nullmax=1.45e-14 final_t=-20 wall=0.0001s
+B r100_inward dir=1 ref=0 refstop=-156 span=156 T=20 target=-20 steps=12 reached=1 term=-1 h=[0.1,2] first=0.1 last=1.4 boundary=1 rhs=84 rej=0 nullmax=7.66e-15 final_t=-20 wall=0.0001s
+B r100_inward dir=2 ref=1 refstop=-301.077405 span=301.077 T=20 target=-20 steps=12 reached=1 term=-1 h=[0.1,2] first=0.1 last=1.4 boundary=1 rhs=84 rej=0 nullmax=1.4e-14 final_t=-20 wall=0.0001s
+B r100_inward dir=3 ref=1 refstop=-211.027405 span=211.027 T=20 target=-20 steps=12 reached=1 term=-1 h=[0.1,2] first=0.1 last=1.4 boundary=1 rhs=84 rej=0 nullmax=1.32e-14 final_t=-20 wall=0.0001s
+B r2p1_outward dir=0 ref=0 refstop=-253.9 span=253.9 T=20 target=-20 steps=46 reached=1 term=-1 h=[0.1,1.0708] first=0.1 last=1.06594 boundary=1 rhs=322 rej=0 nullmax=6.27e-11 final_t=-20 wall=0.0002s
+B r2p1_outward dir=1 ref=0 refstop=-414.940103 span=414.94 T=20 target=-20 steps=105 reached=1 term=-1 h=[0.1,0.211533] first=0.1 last=0.192781 boundary=1 rhs=735 rej=0 nullmax=4.7e-11 final_t=-20 wall=0.0005s
+B r2p1_outward dir=2 ref=0 refstop=-333.450704 span=333.451 T=20 target=-20 steps=105 reached=1 term=-1 h=[0.1,0.211533] first=0.1 last=0.192739 boundary=1 rhs=735 rej=0 nullmax=4.7e-11 final_t=-20 wall=0.0005s
+B r2p1_outward dir=3 ref=1 refstop=-109.415611 span=109.416 T=20 target=-20 steps=105 reached=1 term=-1 h=[0.1,0.211532] first=0.1 last=0.192823 boundary=1 rhs=735 rej=0 nullmax=4.7e-11 final_t=-20 wall=0.0005s
+B r2p1_outward dir=4 ref=1 refstop=-32.2468847 span=32.2469 T=20 target=-20 steps=37 reached=1 term=-1 h=[0.1,0.899361] first=0.1 last=0.332712 boundary=1 rhs=259 rej=0 nullmax=2.99e-11 final_t=-20 wall=0.0002s
+B r1p5_freefall dir=0 ref=1 refstop=-30.6580907 span=30.6581 T=20 target=-20 steps=49 reached=1 term=-1 h=[0.1,0.695968] first=0.1 last=0.106174 boundary=1 rhs=343 rej=0 nullmax=4.94e-10 final_t=-20 wall=0.0002s
+B r1p5_freefall dir=1 ref=0 refstop=-254.5 span=254.5 T=20 target=-20 steps=52 reached=1 term=-1 h=[0.0920967,1.08419] first=0.1 last=0.22147 boundary=1 rhs=364 rej=0 nullmax=4.03e-11 final_t=-20 wall=0.0002s
+B mink_moving dir=0 ref=0 refstop=-51.2640254 span=51.264 T=20 target=-20 steps=3 reached=1 term=-1 h=[1,14] first=1 last=14 boundary=1 rhs=21 rej=0 nullmax=2.22e-16 final_t=-20 wall=0.0000s
+B mink_moving dir=1 ref=0 refstop=-71.5846741 span=71.5847 T=20 target=-20 steps=3 reached=1 term=-1 h=[1,14] first=1 last=14 boundary=1 rhs=21 rej=0 nullmax=0 final_t=-20 wall=0.0000s
+B alc_v3_s1 dir=0 ref=0 refstop=-16.4338937 span=16.4339 T=16.4339 target=-16.4339 steps=56 reached=1 term=-1 h=[0.05,0.4] first=0.05 last=0.203538 boundary=1 rhs=406 rej=2 nullmax=0 final_t=-16.4338937 wall=0.0001s
+B alc_v3_s1 dir=1 ref=0 refstop=-29.3767055 span=29.3767 T=20 target=-20 steps=62 reached=1 term=-1 h=[0.05,0.4] first=0.05 last=0.27784 boundary=1 rhs=441 rej=1 nullmax=0 final_t=-20 wall=0.0001s
+B alc_v9_s10 dir=0 ref=0 refstop=-2.03742978 span=2.03743 T=2.03743 target=-2.03743 steps=77 reached=1 term=-1 h=[0.005,0.04] first=0.005 last=0.0388523 boundary=1 rhs=588 rej=7 nullmax=0 final_t=-2.03742978 wall=0.0001s
+B alc_v9_s10 dir=1 ref=0 refstop=-19.9638367 span=19.9638 T=19.9638 target=-19.9638 steps=521 reached=1 term=-1 h=[0.005,0.04] first=0.005 last=0.0365282 boundary=1 rhs=3682 rej=5 nullmax=2.22e-16 final_t=-19.9638367 wall=0.0009s
+B alc_v9_s100 dir=0 ref=0 refstop=-1.10374298 span=1.10374 T=1.10374 target=-1.10374 steps=302 reached=1 term=-1 h=[0.0005,0.004] first=0.0005 last=0.00388798 boundary=1 rhs=2163 rej=7 nullmax=0 final_t=-1.10374298 wall=0.0005s
+B alc_v9_s100 dir=1 ref=0 refstop=-2.89638367 span=2.89638 T=2.89638 target=-2.89638 steps=746 reached=1 term=-1 h=[0.0005,0.004] first=0.0005 last=0.00365282 boundary=1 rhs=5257 rej=5 nullmax=2.22e-16 final_t=-2.89638367 wall=0.0012s
+TOTAL_OBSERVED_STEPS 2427
+
+real	0m0.152s
+user	0m0.145s
+sys	0m0.006s
+ set +x
@@ -0,0 +1,142 @@
+{
+  "r100_tight_reference": {
+    "vertices": 3158,
+    "triangles": 6188,
+    "outcomes": {
+      "0": 2906,
+      "1": 252
+    },
+    "reasons": {
+      "0": 2906,
+      "1": 252
+    },
+    "accepted": 2908050,
+    "rejected": 1963,
+    "rhs": 21294763,
+    "accepted_percentiles": {
+      "0": 659,
+      "0.5": 885,
+      "0.9": 1166,
+      "0.99": 1410,
+      "1": 1609
+    },
+    "rejected_percentiles": {
+      "0": 0,
+      "0.5": 0,
+      "0.9": 2,
+      "0.99": 3,
+      "1": 4
+    },
+    "rhs_percentiles": {
+      "0": 4900,
+      "0.5": 6496,
+      "0.9": 8463,
+      "0.99": 10171,
+      "1": 11564
+    },
+    "sha256": "a4f7def4212a7dae2b6290fd8635a5f1b087e11b0f8043e60e48fec71ecdb6e4",
+    "wall_seconds": 2.6278538939077407
+  },
+  "r100_ref_vs_0.5": {
+    "shared": 3158,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 6.236425088081268e-08,
+    "max_logg_difference": 8.506182824080666e-10
+  },
+  "r100_ref_vs_2": {
+    "shared": 3158,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 9.216337364737666e-08,
+    "max_logg_difference": 8.199086565935376e-10
+  },
+  "r100_ref_vs_8": {
+    "shared": 3158,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 8.743723551600822e-08,
+    "max_logg_difference": 8.257244662329688e-10
+  },
+  "r100_ref_vs_32": {
+    "shared": 3158,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 8.743704837242435e-08,
+    "max_logg_difference": 8.34318713074933e-10
+  },
+  "r2p1_tight_reference": {
+    "vertices": 5496,
+    "triangles": 10816,
+    "outcomes": {
+      "1": 1336,
+      "0": 4160
+    },
+    "reasons": {
+      "1": 1336,
+      "0": 4160
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+    "accepted": 4515098,
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+    "rhs": 33269502,
+    "accepted_percentiles": {
+      "0": 419,
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+      "0.99": 1253,
+      "1": 1860
+    },
+    "rejected_percentiles": {
+      "0": 1,
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+      "0.9": 2,
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+    "rhs_percentiles": {
+      "0": 3227,
+      "0.5": 5936,
+      "0.9": 7546,
+      "0.99": 9072,
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+    },
+    "sha256": "a81aac81cff2891627e21c22998ceb51d65ef779bb013922cadeb97140274cba",
+    "wall_seconds": 3.180392162874341
+  },
+  "r2p1_ref_vs_0.5": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
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+    "max_sky_angle": 1.4772143877471049e-05,
+    "max_logg_difference": 2.098608620215714e-09
+  },
+  "r2p1_ref_vs_2": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 1.4772101910544689e-05,
+    "max_logg_difference": 2.0455042104572385e-09
+  },
+  "r2p1_ref_vs_8": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 1.4772018211627154e-05,
+    "max_logg_difference": 2.059625359152051e-09
+  },
+  "r2p1_ref_vs_32": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
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+    "max_sky_angle": 1.4772020763985666e-05,
+    "max_logg_difference": 2.068350379857975e-09
+  }
+}
@@ -0,0 +1,354 @@
+{
+  "r100_hmax0.5": {
+    "vertices": 3158,
+    "triangles": 6188,
+    "outcomes": {
+      "0": 2906,
+      "1": 252
+    },
+    "reasons": {
+      "0": 2906,
+      "1": 252
+    },
+    "accepted": 2269662,
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+    "rhs": 16813349,
+    "accepted_percentiles": {
+      "0": 312,
+      "0.5": 736,
+      "0.9": 786,
+      "0.99": 848,
+      "1": 899
+    },
+    "rejected_percentiles": {
+      "0": 0,
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+      "0.9": 0,
+      "0.99": 1,
+      "1": 1
+    },
+    "rhs_percentiles": {
+      "0": 2471,
+      "0.5": 5446,
+      "0.9": 5803,
+      "0.99": 6223,
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+    },
+    "sha256": "787386a026203d846debf25a6a4f431a131b06bd3ab464f75f3e17a1d379992a",
+    "wall_seconds": 2.0714269301388413
+  },
+  "r100_hmax2": {
+    "vertices": 3158,
+    "triangles": 6188,
+    "outcomes": {
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+      "1": 252
+    },
+    "reasons": {
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+    },
+    "accepted": 723677,
+    "rejected": 5690,
+    "rhs": 6030185,
+    "accepted_percentiles": {
+      "0": 165,
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+      "0.9": 290,
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+      "1": 397
+    },
+    "rejected_percentiles": {
+      "0": 0,
+      "0.5": 2,
+      "0.9": 4,
+      "0.99": 5,
+      "1": 5
+    },
+    "rhs_percentiles": {
+      "0": 1442,
+      "0.5": 1855,
+      "0.9": 2324,
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+    },
+    "sha256": "187c3cbba6a18d88608cd3859da94d88b58ce9d65e0d800d84b3254a6b139151",
+    "wall_seconds": 0.9786226029973477
+  },
+  "r100_hmax8": {
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+    },
+    "reasons": {
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+    },
+    "accepted": 463004,
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+    "accepted_percentiles": {
+      "0": 80,
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+    "rejected_percentiles": {
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+      "0": 868,
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+  },
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+    "only_b": 0,
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+    "max_logg_difference": 2.477072019724247e-11
+  },
+  "r2p1_hmax0.5": {
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+    "outcomes": {
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+    "reasons": {
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+    "accepted": 2646842,
+    "rejected": 830,
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+    "accepted_percentiles": {
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+      "0.9": 618,
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+    },
+    "rejected_percentiles": {
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+    "rhs_percentiles": {
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+    "sha256": "3a77a1e7dee3cd18d3ab8a408826aba932f912dc88749989e0c307013d6e7e81",
+    "wall_seconds": 1.973590083885938
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+  "r2p1_hmax2": {
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+    "accepted": 1131104,
+    "rejected": 4004,
+    "rhs": 9548434,
+    "accepted_percentiles": {
+      "0": 109,
+      "0.5": 202,
+      "0.9": 258,
+      "0.99": 311,
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+    "rejected_percentiles": {
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+    },
+    "rhs_percentiles": {
+      "0": 1050,
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+    "sha256": "899331ea41d1612cf66bc7664b50e866f4f3bc7309e9c206440f801238ca455c",
+    "wall_seconds": 1.177934248931706
+  },
+  "r2p1_hmax8": {
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+    "outcomes": {
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+    "reasons": {
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+    },
+    "accepted": 822680,
+    "rejected": 4004,
+    "rhs": 7389760,
+    "accepted_percentiles": {
+      "0": 87,
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+      "0.9": 212,
+      "0.99": 265,
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+    },
+    "rejected_percentiles": {
+      "0": 0,
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+      "0.9": 1,
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+    },
+    "rhs_percentiles": {
+      "0": 910,
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+    "sha256": "49edfbe9dfb2948d3472e6ef6287bed103332758953756a7e4089316caa0b1b6",
+    "wall_seconds": 0.9704615350347012
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+  "r2p1_hmax32": {
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+    "outcomes": {
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+    },
+    "reasons": {
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+    },
+    "accepted": 795354,
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+    "accepted_percentiles": {
+      "0": 81,
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+      "0.9": 210,
+      "0.99": 261,
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+    },
+    "rejected_percentiles": {
+      "0": 0,
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+    },
+    "rhs_percentiles": {
+      "0": 861,
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+    "sha256": "74bbb1e969644d49b7fdf5a6a7a5930ca8b962ec91628cd91feeb9df039100e7",
+    "wall_seconds": 0.9720155198592693
+  },
+  "r2p1_2_vs_0.5": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 1.046601929593161e-10,
+    "max_logg_difference": 6.900746640781108e-11
+  },
+  "r2p1_2_vs_8": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 8.369894549651799e-11,
+    "max_logg_difference": 1.9082291302652266e-11
+  },
+  "r2p1_2_vs_32": {
+    "shared": 5496,
+    "only_a": 0,
+    "only_b": 0,
+    "terminal_mismatches": 0,
+    "max_sky_angle": 8.114658658759588e-11,
+    "max_logg_difference": 2.823297151621773e-11
+  }
+}
@@ -0,0 +1,54 @@
+# Experiment A/B environment and source identity
+date_utc: 2026-10-05T22:15:50Z
+host: Linux ATRI-gentoo 6.18.48-gentoo #1 SMP PREEMPT_DYNAMIC Mon Aug 31 13:33:24 EDT 2026 x86_64 12th Gen Intel(R) Core(TM) i7-12700K GenuineIntel GNU/Linux
+nproc: 16
+cc:
+cc (Gentoo 16.2.1_p20260926 p1) 16.2.1 20260926
+Copyright (C) 2026 Free Software Foundation, Inc.
+This is free software; see the source for copying conditions.  There is NO
+warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+
+
+git_head: c894fdb11a0845558fdb67b71a9bd019a2d94ed4
+git_status_short:
+ M Makefile
+ M mk/reference_images.mk
+ M nr_spacetime_movie_renderer_design.md
+ M src/asymptotic.c
+ M src/frame.c
+ M src/frame.h
+ M src/geodesic.c
+ M src/geodesic.h
+ M src/lens_map.c
+ M src/lens_map.h
+ M src/main.c
+ M src/ray.c
+ M src/ray.h
+ M tests/test_asymptotic.c
+ M tests/test_camera_cli.py
+ M tests/test_frame.c
+ M usage.md
+?? nmesh_spacetime_output_format.md
+?? tests/test_adaptive_cli.py
+?? tests/test_geodesic_adaptive.c
+
+# sha256 of the sources consumed by the harnesses
+25f24a2e1c9ce49508fed230dfb3f6d9986e92bb4a5e6347bb2356ac0ee5fffa  src/geodesic.c
+1e43b95346f484050354631e8682f9793e618cbbd1de6338bd15e092216ae6fb  src/geodesic.h
+e6c0616461507adb1141ca3caa7e76f30e2497c4d53acfef092597fb60431a4a  src/asymptotic.c
+db029ef837f12800bbf81fc74e7bab6eb9f18e42a53ceb5f205867d8a329321d  src/asymptotic.h
+1792a17f432ceee32ee9c802486ecf9d64d96307c249e0d5cfa563ef4a0fefd5  src/asymptotic_schwarzschild.c
+cc9ad0b04e11bd08bcf238901125e76a26ec332cd7fe72871e7c46fb7a322aec  src/asymptotic_schwarzschild.h
+ea0b5838bc56fbfeedec9110cd20653b892127bfc863db91a3a8cabaad4c520b  src/asymptotic_gl48.h
+359066d78a10f9589a220124147cdbefaff8f97028a9fdd2923b474349599752  src/spacetime.h
+4c7ae6e96fe57e2a2ae2491db924bad56af59abfcc305bbb6ab2609f3b405e0d  src/spacetime_common.c
+690045ed715a951335dc7d654258e0f3b802e0bf6e2815ceb4858fa99cd372d7  src/spacetime_minkowski.c
+e5b5935d16e24b07cedb25d184e8f7029075aec9496f54c23cb1061971914a72  src/spacetime_schwarzschild.c
+75956034303fe3bab9324ecb87533e054458e35a26132a3e885233acad785767  src/spacetime_alcubierre.c
+559f626983c68e06d3223d8381085a0b5ac422529a1ea656f4e24b1b3a50f51a  src/observer.c
+d761aabfbc277b0989bd20302578302d91f8253a9d900943de62ab3edd3f145b  src/observer.h
+
+# sha256 of the harnesses and this script
+853018775c335180199aa3a0046445a5f795f83d18de0ff6a664a6368d835dbd  a_public_endpoints.c
+10a6558815e3ff5fa114aa8ca6dfe3c7db6e860ecb9f7cab20c59145a662d3d2  b_actual_h.c
+1cfd93b0c9f187b4c45d169fbeb8c6fea7f02c3317ac24a32691723b0086548c  run_experiment.sh
@@ -0,0 +1,318 @@
+# Experiment A/B summary tables
+
+## A Schwarzschild references (DP tol=1e-12, max_step=0.25)
+
+| case | dir | theta | outcome | reason | stop_t | steps | rej | rhs | g | thr |
+|---|---|---|---|---|---|---|---|---|---|---|
+| r30_inward | 0 | 0 | DARK | REDSHIFT | -69.57 | 531 | 0 | 4004 | 0 | 8 |
+| r30_inward | 1 | 3.142 | ESC | NONE | -226 | 905 | 0 | 6629 | 1.035 | nan |
+| r30_inward | 2 | 1.571 | ESC | NONE | -256.7 | 1028 | 0 | 7490 | 1.035 | nan |
+| r30_inward | 3 | 0.1681 | DARK | REDSHIFT | -225.9 | 3746 | 0 | 26509 | 0 | 8 |
+| r30_inward | 4 | 0.1671 | DARK | REDSHIFT | -94.28 | 1127 | 0 | 8176 | 0 | 8 |
+| r30_inward | 5 | 0.1691 | ESC | NONE | -322.4 | 1834 | 0 | 13132 | 1.035 | nan |
+| r30_inward | 6 | 0.1681 | DARK | REDSHIFT | -118.2 | 1606 | 0 | 11529 | 0 | 8 |
+| r30_inward | 7 | 0.1681 | ESC | NONE | -346.3 | 2312 | 1 | 16485 | 1.035 | nan |
+| r30_inward | 8 | 0.1681 | DARK | REDSHIFT | -142.2 | 2081 | 0 | 14854 | 0 | 8 |
+| r30_inward | 9 | 0.1681 | ESC | NONE | -370.2 | 2790 | 1 | 19831 | 1.035 | nan |
+| r30_inward | 10 | 0.2181 | ESC | NONE | -302.6 | 1409 | 1 | 10164 | 1.035 | nan |
+| r30_inward | 11 | 0.1181 | DARK | REDSHIFT | -73.76 | 665 | 0 | 4942 | 0 | 8 |
+| r100_inward | 0 | 0 | DARK | REDSHIFT | -144.3 | 830 | 0 | 6097 | 0 | 8 |
+| r100_inward | 1 | 3.142 | ESC | NONE | -156 | 625 | 0 | 4669 | 1.01 | nan |
+| r100_inward | 2 | 1.571 | ESC | NONE | -237.7 | 952 | 0 | 6958 | 1.01 | nan |
+| r100_inward | 3 | 0.05146 | DARK | REDSHIFT | -301.1 | 4045 | 0 | 28602 | 0 | 8 |
+| r100_inward | 4 | 0.05046 | DARK | REDSHIFT | -163.1 | 1292 | 0 | 9331 | 0 | 8 |
+| r100_inward | 5 | 0.05246 | ESC | NONE | -391.6 | 2014 | 1 | 14399 | 1.01 | nan |
+| r100_inward | 6 | 0.05145 | DARK | REDSHIFT | -187.1 | 1773 | 0 | 12698 | 0 | 8 |
+| r100_inward | 7 | 0.05147 | ESC | NONE | -415.4 | 2493 | 0 | 17745 | 1.01 | nan |
+| r100_inward | 8 | 0.05146 | DARK | REDSHIFT | -211 | 2252 | 0 | 16051 | 0 | 8 |
+| r100_inward | 9 | 0.05146 | ESC | NONE | -439.3 | 2969 | 0 | 21077 | 1.01 | nan |
+| r100_inward | 10 | 0.1015 | ESC | NONE | -372.3 | 1571 | 0 | 11291 | 1.01 | nan |
+| r100_inward | 11 | 0.001462 | DARK | REDSHIFT | -144.3 | 830 | 0 | 6097 | 0 | 8 |
+| r2p1_outward | 0 | 0 | ESC | NONE | -253.9 | 1120 | 1 | 8141 | 4.583 | nan |
+| r2p1_outward | 1 | 3.142 | DARK | REDSHIFT | -32.25 | 186 | 0 | 1589 | 0 | 8 |
+| r2p1_outward | 2 | 1.571 | DARK | REDSHIFT | -32.77 | 316 | 1 | 2506 | 0 | 8 |
+| r2p1_outward | 3 | 0.5704 | ESC | NONE | -414.9 | 4263 | 2 | 30149 | 4.583 | nan |
+| r2p1_outward | 4 | 0.5694 | ESC | NONE | -285.6 | 1686 | 1 | 12103 | 4.583 | nan |
+| r2p1_outward | 5 | 0.5714 | DARK | REDSHIFT | -61.58 | 995 | 1 | 7259 | 0 | 8 |
+| r2p1_outward | 6 | 0.5704 | ESC | NONE | -309.5 | 2162 | 2 | 15442 | 4.583 | nan |
+| r2p1_outward | 7 | 0.5704 | DARK | REDSHIFT | -85.49 | 1474 | 1 | 10612 | 0 | 8 |
+| r2p1_outward | 8 | 0.5704 | ESC | NONE | -333.5 | 2639 | 1 | 18774 | 4.583 | nan |
+| r2p1_outward | 9 | 0.5704 | DARK | REDSHIFT | -109.4 | 1950 | 1 | 13944 | 0 | 8 |
+| r2p1_outward | 10 | 0.6204 | DARK | REDSHIFT | -41.99 | 585 | 1 | 4389 | 0 | 8 |
+| r2p1_outward | 11 | 0.5204 | ESC | NONE | -265 | 1303 | 2 | 9429 | 4.583 | nan |
+| r1p5_freefall | 0 | 0 | DARK | REDSHIFT | -30.66 | 231 | 1 | 1911 | 0 | 8 |
+| r1p5_freefall | 1 | 1.571 | ESC | NONE | -255.2 | 1130 | 1 | 8211 | 1 | nan |
+| r1p5_freefall | 2 | 3.142 | ESC | NONE | -254.5 | 1143 | 1 | 8302 | 0.4641 | nan |
+| r1p5_freefall | 3 | 2.356 | ESC | NONE | -254.6 | 1127 | 1 | 8190 | 0.5505 | nan |
+
+## A Schwarzschild upper scan (min_step=1e-12, tol=1e-9)
+
+| case | upper | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| r100_inward | 0.25 | 0 | 2.604e-05 | 2.048e-09 | 35.2 | 93464 | 0 | 6 | 6 | 0 | 0 |
+| r100_inward | 0.5 | 0 | 5.696e-05 | 2.056e-09 | 39.27 | 56595 | 0 | 6 | 6 | 0 | 0 |
+| r100_inward | 1 | 0 | 8.348e-05 | 2.051e-09 | 41.25 | 39788 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 2 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 4 | 0 | 8.089e-05 | 2.028e-09 | 41.09 | 29393 | 2 | 6 | 6 | 0 | 0 |
+| r100_inward | 8 | 0 | 8.034e-05 | 2.034e-09 | 41.06 | 28427 | 3 | 6 | 6 | 0 | 0 |
+| r100_inward | 16 | 0 | 8.034e-05 | 2.042e-09 | 41.06 | 28189 | 3 | 6 | 6 | 0 | 0 |
+| r100_inward | 32 | 0 | 8.034e-05 | 2.043e-09 | 41.06 | 28182 | 3 | 6 | 6 | 0 | 0 |
+| r100_inward | 64 | 0 | 8.034e-05 | 2.043e-09 | 41.06 | 28182 | 3 | 6 | 6 | 0 | 0 |
+| r1p5_freefall | 0.25 | 0 | 1.002e-10 | 3.165e-10 | 2.608e-08 | 23597 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 0.5 | 0 | 8.875e-11 | 3.658e-10 | 3.089e-08 | 12747 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1 | 0 | 8.187e-11 | 3.811e-10 | 2.817e-08 | 7553 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 2 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 4 | 0 | 8.157e-11 | 3.632e-10 | 2.346e-08 | 4039 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 8 | 0 | 8.151e-11 | 3.547e-10 | 2.125e-08 | 3591 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 16 | 0 | 8.146e-11 | 3.469e-10 | 1.925e-08 | 3465 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 32 | 0 | 8.146e-11 | 3.46e-10 | 1.948e-08 | 3458 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 64 | 0 | 8.146e-11 | 3.46e-10 | 1.948e-08 | 3458 | 0 | 3 | 1 | 0 | 0 |
+| r2p1_outward | 0.25 | 1 | 0.0002872 | 2.661e-09 | 263.1 | 62258 | 0 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 0.5 | 1 | 0.0002872 | 2.644e-09 | 263.1 | 42490 | 0 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1 | 1 | 0.0002872 | 2.615e-09 | 263.1 | 33544 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 2 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 4 | 1 | 0.0002872 | 2.598e-09 | 263.1 | 27580 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 8 | 1 | 0.0002872 | 2.606e-09 | 263.1 | 26831 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 16 | 1 | 0.0002872 | 2.614e-09 | 263.1 | 26614 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 32 | 1 | 0.0002872 | 2.615e-09 | 263.1 | 26607 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 64 | 1 | 0.0002872 | 2.615e-09 | 263.1 | 26607 | 1 | 5 | 7 | 0 | 0 |
+| r30_inward | 0.25 | 0 | 8.667e-05 | 2.262e-09 | 35.08 | 76510 | 0 | 6 | 6 | 0 | 0 |
+| r30_inward | 0.5 | 0 | 0.0001866 | 2.268e-09 | 39.06 | 49063 | 1 | 6 | 6 | 0 | 0 |
+| r30_inward | 1 | 0 | 0.0002801 | 2.266e-09 | 41.17 | 36974 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 2 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 4 | 0 | 0.0002819 | 2.25e-09 | 41.2 | 29617 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 8 | 0 | 0.0002819 | 2.258e-09 | 41.2 | 28714 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 16 | 0 | 0.0002819 | 2.266e-09 | 41.2 | 28455 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 32 | 0 | 0.0002819 | 2.266e-09 | 41.2 | 28434 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 64 | 0 | 0.0002819 | 2.266e-09 | 41.2 | 28434 | 2 | 6 | 6 | 0 | 0 |
+
+## A Schwarzschild min scan (max_step=2, tol=1e-9)
+
+| case | min_step | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| r100_inward | 1e-14 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 1e-12 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 1e-10 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 1e-08 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 1e-06 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 1e-05 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 0.0001 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 0.001 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 0.01 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r100_inward | 0.1 | 0 | 8.286e-05 | 2.026e-09 | 41.22 | 32389 | 1 | 6 | 6 | 0 | 0 |
+| r1p5_freefall | 1e-14 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1e-12 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1e-10 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1e-08 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1e-06 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 1e-05 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 0.0001 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 0.001 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 0.01 | 0 | 8.165e-11 | 3.719e-10 | 2.571e-08 | 5131 | 0 | 3 | 1 | 0 | 0 |
+| r1p5_freefall | 0.1 | 1 | 8.165e-11 | 3.719e-10 | 254.3 | 3654 | 0 | 2 | 1 | 0 | 1 |
+| r2p1_outward | 1e-14 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1e-12 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1e-10 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1e-08 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1e-06 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 1e-05 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 0.0001 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 0.001 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 0.01 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r2p1_outward | 0.1 | 1 | 0.0002872 | 2.592e-09 | 263.1 | 29421 | 1 | 5 | 7 | 0 | 0 |
+| r30_inward | 1e-14 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 1e-12 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 1e-10 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 1e-08 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 1e-06 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 1e-05 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 0.0001 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 0.001 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 0.01 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+| r30_inward | 0.1 | 0 | 0.0002819 | 2.244e-09 | 41.2 | 31843 | 2 | 6 | 6 | 0 | 0 |
+
+## A Schwarzschild sensitive RK4 .01 vs .005
+
+| case | dir | theta | out.01 | out.005 | hhalve_dn_ang | |dg| | rhs.01 | rhs.005 |
+|---|---|---|---|---|---|---|---|---|
+| r2p1_outward | 6 | 0.5704 | ESC | ESC | 1.032e-07 | 7.386e-12 | 124072 | 247880 |
+| r2p1_outward | 7 | 0.5704 | DARK | DARK | nan | 0 | 34196 | 68392 |
+| r2p1_outward | 8 | 0.5704 | ESC | ESC | 1.04e-05 | 7.618e-12 | 133644 | 267024 |
+| r2p1_outward | 9 | 0.5704 | DARK | DARK | nan | 0 | 43768 | 87536 |
+| r30_inward | 6 | 0.1681 | DARK | DARK | nan | 0 | 47300 | 94600 |
+| r30_inward | 7 | 0.1681 | ESC | ESC | 0 | 8.238e-14 | 138764 | 277264 |
+| r30_inward | 8 | 0.1681 | DARK | DARK | nan | 0 | 56872 | 113744 |
+| r30_inward | 9 | 0.1681 | ESC | ESC | 1.891e-07 | 7.55e-15 | 148336 | 296408 |
+
+## A Minkowski flat analytic check (n_inf and t)
+
+| upper | min_step | n | max_dn_ang | max_dgrel | max_t_err |
+|---|---|---|---|---|---|
+| 1 | 1e-12 | 6 | 0 | 0 | 5.258e-13 |
+| 1 | 1e-06 | 6 | 0 | 0 | 5.258e-13 |
+| 1 | 0.1 | 6 | 0 | 0 | 5.258e-13 |
+| 4 | 1e-12 | 6 | 0 | 0 | 1.776e-12 |
+| 4 | 1e-06 | 6 | 0 | 0 | 1.776e-12 |
+| 4 | 0.1 | 6 | 0 | 0 | 1.776e-12 |
+| 16 | 1e-12 | 6 | 0 | 0 | 1.3e-11 |
+| 16 | 1e-06 | 6 | 0 | 0 | 1.3e-11 |
+| 16 | 0.1 | 6 | 0 | 0 | 1.3e-11 |
+| 64 | 1e-12 | 6 | 0 | 0 | 3.894e-11 |
+| 64 | 1e-06 | 6 | 0 | 0 | 3.894e-11 |
+| 64 | 0.1 | 6 | 0 | 0 | 3.894e-11 |
+| 256 | 1e-12 | 6 | 0 | 0 | 7.661e-11 |
+| 256 | 1e-06 | 6 | 0 | 0 | 7.661e-11 |
+| 256 | 0.1 | 6 | 0 | 0 | 7.661e-11 |
+
+## A Minkowski flat analytic check (crossing x and t)
+
+| upper | min_step | n | max_x_err | max_t_err |
+|---|---|---|---|---|
+| 1 | 1e-12 | 6 | 4.832e-13 | 5.258e-13 |
+| 1 | 1e-06 | 6 | 4.832e-13 | 5.258e-13 |
+| 1 | 0.1 | 6 | 4.832e-13 | 5.258e-13 |
+| 4 | 1e-12 | 6 | 1.72e-12 | 1.776e-12 |
+| 4 | 1e-06 | 6 | 1.72e-12 | 1.776e-12 |
+| 4 | 0.1 | 6 | 1.72e-12 | 1.776e-12 |
+| 16 | 1e-12 | 6 | 1.268e-11 | 1.3e-11 |
+| 16 | 1e-06 | 6 | 1.268e-11 | 1.3e-11 |
+| 16 | 0.1 | 6 | 1.268e-11 | 1.3e-11 |
+| 64 | 1e-12 | 6 | 3.506e-11 | 3.894e-11 |
+| 64 | 1e-06 | 6 | 3.506e-11 | 3.894e-11 |
+| 64 | 0.1 | 6 | 3.506e-11 | 3.894e-11 |
+| 256 | 1e-12 | 6 | 7.061e-11 | 7.661e-11 |
+| 256 | 1e-06 | 6 | 7.061e-11 | 7.661e-11 |
+| 256 | 0.1 | 6 | 7.061e-11 | 7.661e-11 |
+
+## A Alcubierre alc_v3_s1 upper scan
+
+| case | upper | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| alc_v3_s1 | 0.05 | 0 | 7.544e-14 | 7.627e-13 | 1.99e-13 | 19740 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.05 | 0 | 7.544e-14 | 7.627e-13 | 1.99e-13 | 19740 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.05 | 0 | 7.544e-14 | 7.627e-13 | 1.99e-13 | 19740 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.2 | 0 | 1.208e-10 | 3.452e-10 | 4.091e-10 | 6475 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.2 | 0 | 1.208e-10 | 3.452e-10 | 4.091e-10 | 6475 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.2 | 0 | 1.208e-10 | 3.452e-10 | 4.091e-10 | 6475 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.4 | 0 | 1.03e-10 | 3.464e-10 | 3.143e-10 | 4613 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.4 | 0 | 1.03e-10 | 3.464e-10 | 3.143e-10 | 4613 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.4 | 0 | 1.03e-10 | 3.464e-10 | 3.143e-10 | 4613 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.8 | 0 | 7.888e-11 | 7.954e-10 | 7.369e-10 | 3794 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.8 | 0 | 7.888e-11 | 7.954e-10 | 7.369e-10 | 3794 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 0.8 | 0 | 7.888e-11 | 7.954e-10 | 7.369e-10 | 3794 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 1.6 | 0 | 1.239e-10 | 1.118e-09 | 1.148e-09 | 3430 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 1.6 | 0 | 1.239e-10 | 1.118e-09 | 1.148e-09 | 3430 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 1.6 | 0 | 1.239e-10 | 1.118e-09 | 1.148e-09 | 3430 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 3.2 | 0 | 1.545e-10 | 1.26e-09 | 1.346e-09 | 3290 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 3.2 | 0 | 1.545e-10 | 1.26e-09 | 1.346e-09 | 3290 | 2 | 6 | 0 | 0 | 0 |
+| alc_v3_s1 | 3.2 | 0 | 1.545e-10 | 1.26e-09 | 1.346e-09 | 3290 | 2 | 6 | 0 | 0 | 0 |
+
+## A Alcubierre alc_v3_s10 upper scan
+
+| case | upper | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| alc_v3_s10 | 0.005 | 0 | 5.829e-15 | 3.109e-14 | 4.663e-14 | 27412 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.005 | 0 | 5.829e-15 | 3.109e-14 | 4.663e-14 | 27412 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.005 | 0 | 5.829e-15 | 3.109e-14 | 4.663e-14 | 27412 | 0 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.02 | 0 | 6.299e-12 | 2.402e-10 | 1.399e-11 | 8337 | 4 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.02 | 0 | 6.299e-12 | 2.402e-10 | 1.399e-11 | 8337 | 4 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.02 | 0 | 6.299e-12 | 2.402e-10 | 1.399e-11 | 8337 | 4 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.04 | 0 | 3.288e-11 | 3.854e-10 | 6.294e-11 | 5621 | 6 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.04 | 0 | 3.288e-11 | 3.854e-10 | 6.294e-11 | 5621 | 6 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.04 | 0 | 3.288e-11 | 3.854e-10 | 6.294e-11 | 5621 | 6 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.08 | 0 | 1.042e-11 | 2.781e-10 | 8.024e-11 | 4648 | 12 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.08 | 0 | 1.042e-11 | 2.781e-10 | 8.024e-11 | 4648 | 12 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.08 | 0 | 1.042e-11 | 2.781e-10 | 8.024e-11 | 4648 | 12 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.16 | 0 | 1.131e-11 | 7.6e-10 | 9.538e-11 | 4270 | 13 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.16 | 0 | 1.131e-11 | 7.6e-10 | 9.538e-11 | 4270 | 13 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.16 | 0 | 1.131e-11 | 7.6e-10 | 9.538e-11 | 4270 | 13 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.32 | 0 | 3.131e-11 | 9.778e-10 | 1.041e-10 | 4116 | 13 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.32 | 0 | 3.131e-11 | 9.778e-10 | 1.041e-10 | 4116 | 13 | 6 | 0 | 0 | 0 |
+| alc_v3_s10 | 0.32 | 0 | 3.131e-11 | 9.778e-10 | 1.041e-10 | 4116 | 13 | 6 | 0 | 0 | 0 |
+
+## A Alcubierre alc_v9_s1 upper scan
+
+| case | upper | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| alc_v9_s1 | 0.05 | 0 | 6.632e-13 | 2.591e-11 | 1.387e-11 | 39452 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.05 | 0 | 6.632e-13 | 2.591e-11 | 1.387e-11 | 39452 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.05 | 0 | 6.632e-13 | 2.591e-11 | 1.387e-11 | 39452 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.2 | 0 | 1.078e-10 | 2.073e-09 | 6.805e-10 | 11690 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.2 | 0 | 1.078e-10 | 2.073e-09 | 6.805e-10 | 11690 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.2 | 0 | 1.078e-10 | 2.073e-09 | 6.805e-10 | 11690 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.4 | 0 | 6.25e-11 | 2.466e-09 | 1.083e-09 | 7413 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.4 | 0 | 6.25e-11 | 2.466e-09 | 1.083e-09 | 7413 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.4 | 0 | 6.25e-11 | 2.466e-09 | 1.083e-09 | 7413 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.8 | 0 | 5.349e-11 | 2.718e-09 | 1.186e-09 | 5369 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.8 | 0 | 5.349e-11 | 2.718e-09 | 1.186e-09 | 5369 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 0.8 | 0 | 5.349e-11 | 2.718e-09 | 1.186e-09 | 5369 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 1.6 | 0 | 1.035e-10 | 2.819e-09 | 9.549e-10 | 4431 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 1.6 | 0 | 1.035e-10 | 2.819e-09 | 9.549e-10 | 4431 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 1.6 | 0 | 1.035e-10 | 2.819e-09 | 9.549e-10 | 4431 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 3.2 | 0 | 1.239e-10 | 2.823e-09 | 3.249e-09 | 3983 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 3.2 | 0 | 1.239e-10 | 2.823e-09 | 3.249e-09 | 3983 | 3 | 6 | 0 | 0 | 0 |
+| alc_v9_s1 | 3.2 | 0 | 1.239e-10 | 2.823e-09 | 3.249e-09 | 3983 | 3 | 6 | 0 | 0 | 0 |
+
+## A Alcubierre alc_v9_s10 upper scan
+
+| case | upper | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| alc_v9_s10 | 0.005 | 0 | 8.937e-14 | 1.103e-11 | 3.553e-13 | 48167 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.005 | 0 | 8.937e-14 | 1.103e-11 | 3.553e-13 | 48167 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.005 | 0 | 8.937e-14 | 1.103e-11 | 3.553e-13 | 48167 | 0 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.02 | 0 | 5.331e-11 | 6.906e-10 | 1.092e-10 | 13692 | 6 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.02 | 0 | 5.331e-11 | 6.906e-10 | 1.092e-10 | 13692 | 6 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.02 | 0 | 5.331e-11 | 6.906e-10 | 1.092e-10 | 13692 | 6 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.04 | 0 | 1.752e-10 | 9.749e-10 | 3.646e-10 | 8484 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.04 | 0 | 1.752e-10 | 9.749e-10 | 3.646e-10 | 8484 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.04 | 0 | 1.752e-10 | 9.749e-10 | 3.646e-10 | 8484 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.08 | 0 | 1.196e-10 | 1.457e-09 | 2.695e-10 | 6251 | 12 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.08 | 0 | 1.196e-10 | 1.457e-09 | 2.695e-10 | 6251 | 12 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.08 | 0 | 1.196e-10 | 1.457e-09 | 2.695e-10 | 6251 | 12 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.16 | 0 | 1.727e-11 | 1.077e-09 | 1.26e-10 | 5278 | 15 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.16 | 0 | 1.727e-11 | 1.077e-09 | 1.26e-10 | 5278 | 15 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.16 | 0 | 1.727e-11 | 1.077e-09 | 1.26e-10 | 5278 | 15 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.32 | 0 | 5.499e-11 | 8.68e-10 | 2.555e-10 | 4872 | 14 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.32 | 0 | 5.499e-11 | 8.68e-10 | 2.555e-10 | 4872 | 14 | 6 | 0 | 0 | 0 |
+| alc_v9_s10 | 0.32 | 0 | 5.499e-11 | 8.68e-10 | 2.555e-10 | 4872 | 14 | 6 | 0 | 0 | 0 |
+
+## A Alcubierre v9 s100 lower-bound stress (upper=0.004)
+
+| case | min_step | mismatch | max_dn_ang | max_dgrel | max_dstopT | sum_rhs | max_rej | ESC | DARK | UNRES | INC |
+|---|---|---|---|---|---|---|---|---|---|---|---|
+| alc_v9_s100 | 1e-14 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s100 | 1e-12 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s100 | 1e-08 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s100 | 1e-06 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s100 | 1e-05 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+| alc_v9_s100 | 0.0001 | 0 | 1.695e-11 | 1.332e-09 | 1.057e-11 | 18095 | 7 | 6 | 0 | 0 | 0 |
+
+## B observed accepted step h (finite T=min(20, ref span))
+
+| case | dir | ref | span | target | steps | reached | term | h_min | h_max | h_first | bnd | rhs | rej | null_max |
+|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
+| r30_inward | 0 | DARK | 69.57 | -20 | 17 | 1 | -1 | 0.1 | 1.726 | 0.1 | 1 | 119 | 0 | 3.009e-12 |
+| r30_inward | 1 | ESC | 226 | -20 | 13 | 1 | -1 | 0.1 | 2 | 0.1 | 1 | 91 | 0 | 8.69e-12 |
+| r30_inward | 2 | DARK | 142.2 | -20 | 20 | 1 | -1 | 0.1 | 1.408 | 0.1 | 1 | 140 | 0 | 1.526e-11 |
+| r30_inward | 3 | ESC | 370.2 | -20 | 20 | 1 | -1 | 0.1 | 1.408 | 0.1 | 1 | 140 | 0 | 1.526e-11 |
+| r30_inward | 4 | DARK | 118.2 | -20 | 20 | 1 | -1 | 0.1 | 1.408 | 0.1 | 1 | 140 | 0 | 1.526e-11 |
+| r30_inward | 5 | ESC | 346.3 | -20 | 20 | 1 | -1 | 0.1 | 1.408 | 0.1 | 1 | 140 | 0 | 1.526e-11 |
+| r100_inward | 0 | DARK | 144.3 | -20 | 12 | 1 | -1 | 0.1 | 2 | 0.1 | 1 | 84 | 0 | 1.454e-14 |
+| r100_inward | 1 | ESC | 156 | -20 | 12 | 1 | -1 | 0.1 | 2 | 0.1 | 1 | 84 | 0 | 7.661e-15 |
+| r100_inward | 2 | DARK | 301.1 | -20 | 12 | 1 | -1 | 0.1 | 2 | 0.1 | 1 | 84 | 0 | 1.399e-14 |
+| r100_inward | 3 | DARK | 211 | -20 | 12 | 1 | -1 | 0.1 | 2 | 0.1 | 1 | 84 | 0 | 1.321e-14 |
+| r2p1_outward | 0 | ESC | 253.9 | -20 | 46 | 1 | -1 | 0.1 | 1.071 | 0.1 | 1 | 322 | 0 | 6.274e-11 |
+| r2p1_outward | 1 | ESC | 414.9 | -20 | 105 | 1 | -1 | 0.1 | 0.2115 | 0.1 | 1 | 735 | 0 | 4.698e-11 |
+| r2p1_outward | 2 | ESC | 333.5 | -20 | 105 | 1 | -1 | 0.1 | 0.2115 | 0.1 | 1 | 735 | 0 | 4.698e-11 |
+| r2p1_outward | 3 | DARK | 109.4 | -20 | 105 | 1 | -1 | 0.1 | 0.2115 | 0.1 | 1 | 735 | 0 | 4.698e-11 |
+| r2p1_outward | 4 | DARK | 32.25 | -20 | 37 | 1 | -1 | 0.1 | 0.8994 | 0.1 | 1 | 259 | 0 | 2.991e-11 |
+| r1p5_freefall | 0 | DARK | 30.66 | -20 | 49 | 1 | -1 | 0.1 | 0.696 | 0.1 | 1 | 343 | 0 | 4.938e-10 |
+| r1p5_freefall | 1 | ESC | 254.5 | -20 | 52 | 1 | -1 | 0.0921 | 1.084 | 0.1 | 1 | 364 | 0 | 4.034e-11 |
+| mink_moving | 0 | ESC | 51.26 | -20 | 3 | 1 | -1 | 1 | 14 | 1 | 1 | 21 | 0 | 2.22e-16 |
+| mink_moving | 1 | ESC | 71.58 | -20 | 3 | 1 | -1 | 1 | 14 | 1 | 1 | 21 | 0 | 0 |
+| alc_v3_s1 | 0 | ESC | 16.43 | -16.43 | 56 | 1 | -1 | 0.05 | 0.4 | 0.05 | 1 | 406 | 2 | 0 |
+| alc_v3_s1 | 1 | ESC | 29.38 | -20 | 62 | 1 | -1 | 0.05 | 0.4 | 0.05 | 1 | 441 | 1 | 0 |
+| alc_v9_s10 | 0 | ESC | 2.037 | -2.037 | 77 | 1 | -1 | 0.005 | 0.04 | 0.005 | 1 | 588 | 7 | 0 |
+| alc_v9_s10 | 1 | ESC | 19.96 | -19.96 | 521 | 1 | -1 | 0.005 | 0.04 | 0.005 | 1 | 3682 | 5 | 2.22e-16 |
+| alc_v9_s100 | 0 | ESC | 1.104 | -1.104 | 302 | 1 | -1 | 0.0005 | 0.004 | 0.0005 | 1 | 2163 | 7 | 0 |
+| alc_v9_s100 | 1 | ESC | 2.896 | -2.896 | 746 | 1 | -1 | 0.0005 | 0.004 | 0.0005 | 1 | 5257 | 5 | 2.22e-16 |
@@ -0,0 +1,124 @@
+#!/usr/bin/env python3
+"""One-task, at-most-two-attempt 4K comparison (R100, 3840x2160, FOV45).
+
+This driver does NOT run as part of routine verification.  It refuses to do
+anything unless ``--authorize-two-4k`` is passed explicitly, and an attempt
+ledger makes the task non-repeatable.  Any future execution requires a fresh,
+explicit user authorization for that task; authorization never extends to later
+tasks or routine tests.
+
+Usage:
+    run_4k_pair.py --authorize-two-4k [--out DIR]
+
+OUT defaults to <repo>/local/adaptive_bounds_4k (distinct from any older
+one-off ledger).  The renderer binary is expected at
+build/Release/schwarzschild_sky (see README for the make command).
+"""
+import argparse
+import hashlib
+import json
+import os
+from pathlib import Path
+import shlex
+import subprocess
+import sys
+import time
+
+from mesh_maps import load, compare
+
+ROOT = Path(__file__).resolve().parents[2]
+ENV = dict(os.environ, OMP_NUM_THREADS='16', OMP_DYNAMIC='FALSE')
+BUILD_CMD = 'make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend'
+
+REFUSAL = (
+    'REFUSING TO RUN: the 4K hmax 2-vs-8 pair is a one-task, at-most-two-attempt '
+    'experiment.  Pass --authorize-two-4k only after an explicit fresh user '
+    'authorization for this task.  It is not a routine verification target.')
+
+
+def main():
+    ap = argparse.ArgumentParser(description=__doc__)
+    ap.add_argument('--authorize-two-4k', action='store_true',
+                    help='explicit authorization for the two-attempt 4K pair')
+    ap.add_argument('--out', default=str(ROOT / 'local/adaptive_bounds_4k'),
+                    help='output directory (default: local/adaptive_bounds_4k)')
+    args = ap.parse_args()
+    if not args.authorize_two_4k:
+        print(REFUSAL, file=sys.stderr)
+        return 2
+    out = Path(args.out).resolve()
+    binary = ROOT / 'build/Release/schwarzschild_sky'
+    if not binary.exists():
+        print(f'missing {binary}; build it first:\n    {BUILD_CMD}',
+              file=sys.stderr)
+        return 2
+    out.mkdir(parents=True, exist_ok=True)
+    ledger = out / 'attempts.json'
+    attempts = json.loads(ledger.read_text()) if ledger.exists() else []
+    if attempts:
+        print('This one-task pair has already been attempted; no reruns '
+              'authorized.', file=sys.stderr)
+        return 3
+    catalog = out / 'single_dim_star.csv'
+    catalog.write_text('longitude_deg,latitude_deg,temperature_K,amplitude\n'
+                       '262.5,-30,6000,1e-30\n')
+    with (out / 'cpu.txt').open('w') as f:
+        subprocess.run(['lscpu'], stdout=f, check=True)
+    metadata = {
+        'binary_sha256': hashlib.sha256(binary.read_bytes()).hexdigest(),
+        'utc': time.strftime('%Y-%m-%dT%H:%M:%SZ', time.gmtime()),
+        'source_sha256': {
+            p: hashlib.sha256((ROOT / p).read_bytes()).hexdigest()
+            for p in ('src/main.c', 'src/geodesic.c', 'src/frame.c')},
+        'catalog': 'one negligible synthetic point; no survey catalog',
+        'scope': 'README R100 45-degree 3840x2160 coarse16 refine4 jacobian0.2',
+        'threads': 16, 'max_attempts': 2,
+        'authorization': 'explicit --authorize-two-4k for this task only'}
+    (out / 'metadata.json').write_text(json.dumps(metadata, indent=2) + '\n')
+    maps = {}
+    results = {}
+    for upper in (2, 8):
+        name = f'r100_4k_hmax{upper}'
+        cmd = [str(binary), '--integrator', 'dp54', '--width', '3840',
+               '--height', '2160', '--look-ra-deg', '262.5',
+               '--look-dec-deg', '-30', '--fov-deg', '45',
+               '--observer-radius', '100', '--coarse-cell-pixels', '16',
+               '--refine-max-level', '4', '--refine-jacobian-min', '.2',
+               '--catalog', str(catalog), '--exposure', '1',
+               '--tone-map', 'reinhard', '--psf-min-y', '1e-20',
+               '--psf-relative-tail', '1e-4', '--ode-min-step', '1e-12',
+               '--ode-max-step', str(upper), '--verbose',
+               '--lens-map-output', str(out / (name + '.grlens')),
+               '--output', str(out / (name + '.png'))]
+        attempts.append({'upper': upper, 'command': shlex.join(cmd),
+                         'state': 'attempted'})
+        ledger.write_text(json.dumps(attempts, indent=2) + '\n')
+        start = time.perf_counter()
+        with (out / (name + '.log')).open('w') as log:
+            log.write('OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE ' +
+                      shlex.join(cmd) + '\n')
+            log.flush()
+            result = subprocess.run(cmd, cwd=ROOT, env=ENV, stdout=log,
+                                    stderr=subprocess.STDOUT, timeout=900)
+        attempts[-1].update(returncode=result.returncode,
+                            wall_seconds=time.perf_counter() - start,
+                            state='completed')
+        ledger.write_text(json.dumps(attempts, indent=2) + '\n')
+        if result.returncode:
+            raise SystemExit(f'4K attempt failed: {name}; no automatic retry.')
+        info, maps[upper] = load(out / (name + '.grlens'))
+        info['wall_seconds'] = attempts[-1]['wall_seconds']
+        results[name] = info
+        print(name, json.dumps(info), flush=True)
+    results['comparison'] = compare(maps[2], maps[8])
+    p, q = (results[f'r100_4k_hmax{h}']['provenance'] for h in (2, 8))
+    assert p['max_step'] == 2 and q['max_step'] == 8
+    assert {k: v for k, v in p.items() if k != 'max_step'} == \
+           {k: v for k, v in q.items() if k != 'max_step'}
+    print('comparison', json.dumps(results['comparison']), flush=True)
+    (out / 'summary.json').write_text(json.dumps(results, indent=2) + '\n')
+    return 0
+
+
+if __name__ == '__main__':
+    sys.exit(main())
@@ -0,0 +1,36 @@
+#!/usr/bin/env bash
+# Run the standalone critical-classification reference check
+# (benchmarks/adaptive_step_bounds_2026-10-05/critical_ref_check.c).
+#
+#   benchmarks/adaptive_step_bounds_2026-10-05/run_critical_ref.sh [OUT_DIR]
+#
+# OUT_DIR defaults to <repo>/local/adaptive_step_bounds_2026-10-05.  All output
+# stays under OUT_DIR; the tracked benchmark directory holds only the sources.
+# This is a diagnostic probe (see the C file header); it makes no pass/fail
+# claim about the exactly-critical physical outcome.
+set -euo pipefail
+
+SOURCE=$(cd "$(dirname "$0")" && pwd)
+root=$(cd "$SOURCE/../.." && pwd)
+OUT=${1:-$root/local/adaptive_step_bounds_2026-10-05}
+BIN=/tmp/opencode/step_bounds
+
+mkdir -p "$OUT/raw" "$OUT/logs" "$BIN"
+cd "$OUT"
+OUT=$PWD
+
+{
+  echo "### building critical_ref_check"
+  set -x
+  cc -std=c11 -O2 -Wall -Wextra -Wpedantic -I"$root/src" \
+     "$SOURCE/critical_ref_check.c" "$root/src/geodesic.c" \
+     "$root/src/asymptotic.c" "$root/src/asymptotic_schwarzschild.c" \
+     "$root/src/spacetime_common.c" "$root/src/observer.c" -lm \
+     -o "$BIN/critical_ref_check"
+  echo "### command: critical_ref_check"
+  time "$BIN/critical_ref_check"
+  set +x
+} > logs/critical_ref.log 2>&1
+
+cat logs/critical_ref.log
+echo "outputs under $OUT"
@@ -0,0 +1,36 @@
+#!/usr/bin/env bash
+# Build and run the failure-path floor diagnostic.
+#
+#   benchmarks/adaptive_step_bounds_2026-10-05/run_failure_floor.sh [OUT_DIR]
+#
+# OUT_DIR defaults to <repo>/local/adaptive_bounds_mesh.  All output stays
+# under OUT_DIR; the tracked benchmark directory holds only the sources.
+#
+# failure_floor.c includes ../../tests/test_geodesic_adaptive.c (depth-2 path
+# valid from this directory) and therefore requires -DGEODESIC_EVENT_TESTING
+# and the production RayPool source src/ray.c.  The two analytic backends are
+# textually included by the regression file, so they are not linked here.
+set -euo pipefail
+
+SOURCE=$(cd "$(dirname "$0")" && pwd)
+root=$(cd "$SOURCE/../.." && pwd)
+OUT=${1:-$root/local/adaptive_bounds_mesh}
+BIN=/tmp/opencode/step_bounds
+
+mkdir -p "$OUT/logs" "$BIN"
+cd "$OUT"
+
+{
+  set -x
+  cc -std=c11 -O2 -Wall -Wextra -Wpedantic -fopenmp -DGEODESIC_EVENT_TESTING \
+     -I"$root/src" \
+     "$SOURCE/failure_floor.c" "$root/src/geodesic.c" "$root/src/ray.c" \
+     "$root/src/spacetime_common.c" "$root/src/observer.c" \
+     "$root/src/asymptotic.c" "$root/src/asymptotic_schwarzschild.c" -lm \
+     -o "$BIN/failure_floor"
+  "$BIN/failure_floor"
+  set +x
+} > logs/failure_floor.log 2>&1
+
+cat logs/failure_floor.log
+echo "outputs under $OUT"
@@ -0,0 +1,84 @@
+#!/usr/bin/env bash
+# Long-term reproduction driver for the adaptive step-bound scan (Experiment A/B).
+#
+#   benchmarks/adaptive_step_bounds_2026-10-05/run_limited.sh [OUT_DIR]
+#
+# OUT_DIR defaults to <repo>/local/adaptive_step_bounds_2026-10-05.  All build
+# and run output — env/hash record, build log, stdout logs and per-ray CSV —
+# is written under OUT_DIR, never into this tracked benchmark directory.
+# Scratch binaries go to /tmp/opencode/step_bounds.
+set -euo pipefail
+
+SOURCE=$(cd "$(dirname "$0")" && pwd)
+root=$(cd "$SOURCE/../.." && pwd)
+OUT=${1:-$root/local/adaptive_step_bounds_2026-10-05}
+BIN=/tmp/opencode/step_bounds
+
+mkdir -p "$OUT/raw" "$OUT/logs" "$BIN"
+cd "$OUT"
+OUT=$PWD
+
+SRC_COMMON="$root/src/geodesic.c $root/src/asymptotic.c \
+$root/src/asymptotic_schwarzschild.c $root/src/spacetime_common.c \
+$root/src/observer.c"
+
+# --- environment + source identity (full shell output) --------------------
+{
+  echo "# adaptive_step_bounds_2026-10-05 environment and source identity"
+  echo "date_utc: $(date -u +%Y-%m-%dT%H:%M:%SZ)"
+  echo "host: $(uname -a)"
+  echo "nproc: $(nproc)"
+  echo "cc:"; cc --version
+  echo
+  echo "git_head: $(git -C "$root" rev-parse HEAD 2>/dev/null || echo none)"
+  echo "git_status_short:"; git -C "$root" status --short 2>/dev/null || true
+  echo
+  echo "# sha256 of the production sources consumed by the harnesses"
+  sha256sum $SRC_COMMON
+  echo
+  echo "# sha256 of the benchmark harnesses"
+  sha256sum "$SOURCE/a_public_endpoints.c" "$SOURCE/b_actual_h.c" \
+            "$SOURCE/summarize.py" "$SOURCE/run_limited.sh"
+} > logs/env.txt 2>&1
+cat logs/env.txt
+
+# --- build ----------------------------------------------------------------
+{
+  echo "### building a_public_endpoints"
+  set -x
+  cc -std=c11 -O2 -Wall -Wextra -Wpedantic -I"$root/src" \
+     "$SOURCE/a_public_endpoints.c" $SRC_COMMON -lm -o "$BIN/a_public"
+  echo "### building b_actual_h"
+  cc -std=c11 -O2 -Wall -Wextra -Wpedantic -I"$root/src" \
+     "$SOURCE/b_actual_h.c" "$root/src/asymptotic.c" \
+     "$root/src/asymptotic_schwarzschild.c" "$root/src/spacetime_common.c" \
+     "$root/src/observer.c" -lm -o "$BIN/b_actual"
+  set +x
+} > logs/build.log 2>&1
+cat logs/build.log
+
+# --- Experiment A ---------------------------------------------------------
+{
+  echo "### command: a_public schwarzschild"
+  set -x; time "$BIN/a_public" schwarzschild; set +x
+  echo "### command: a_public minkowski"
+  set -x; time "$BIN/a_public" minkowski; set +x
+  echo "### command: a_public alcubierre"
+  set -x; time "$BIN/a_public" alcubierre; set +x
+} > logs/expA.log 2>&1
+grep -E '^(SUMMARY|TOTAL_RAYS|real|user)' logs/expA.log | tail -20
+
+# --- Experiment B ---------------------------------------------------------
+{
+  echo "### command: b_actual"
+  set -x; time "$BIN/b_actual"; set +x
+} > logs/expB.log 2>&1
+cat logs/expB.log
+
+# --- summary tables -------------------------------------------------------
+python3 "$SOURCE/summarize.py" "$OUT"
+
+echo
+echo "rays A = $(grep '^TOTAL_RAYS' logs/expA.log | awk '{s+=$2} END{print s}')"
+echo "observed steps B = $(grep '^TOTAL_OBSERVED_STEPS' logs/expB.log | awk '{print $2}')"
+echo "outputs under $OUT"
@@ -0,0 +1,84 @@
+#!/usr/bin/env python3
+"""Bounded 320x180 adaptive-mesh candidates (8 cases; no 4K, no references).
+
+Usage:
+    run_mesh.py [OUT_DIR]
+
+OUT_DIR defaults to <repo>/local/adaptive_bounds_mesh.  The renderer binary is
+expected to already exist at build/Release/schwarzschild_sky; build it with
+(make command is also in README.md):
+
+    make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend
+
+No survey catalog is used: the script writes a one-point synthetic dim catalog
+with the required column header (longitude_deg,latitude_deg,temperature_K,
+amplitude) and a 1e-30 amplitude star.  No external CSV is read.
+"""
+import json
+import os
+from pathlib import Path
+import shlex
+import subprocess
+import sys
+import time
+
+from mesh_maps import load, compare  # tracked sibling module (no local/ import)
+
+ROOT = Path(__file__).resolve().parents[2]
+OUT = Path(sys.argv[1]).resolve() if len(sys.argv) > 1 else \
+    ROOT / 'local/adaptive_bounds_mesh'
+BIN = ROOT / 'build/Release/schwarzschild_sky'
+BUILD_CMD = 'make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend'
+ENV = dict(os.environ, OMP_NUM_THREADS='8', OMP_DYNAMIC='FALSE')
+
+
+def scene_args(scene):
+    if scene == 'r100':
+        return ['--observer-radius', '100', '--look-ra-deg', '262.5',
+                '--look-dec-deg', '-30', '--fov-deg', '45',
+                '--refine-jacobian-min', '.2']
+    return ['--observer-position', '2.1', '0', '0', '--observer-velocity',
+            '0', '0', '0', '--look-ra-deg', '0', '--look-dec-deg', '0',
+            '--fov-deg', '90']
+
+
+def main():
+    if not BIN.exists():
+        raise SystemExit(f'missing {BIN}; build it first:\n    {BUILD_CMD}')
+    OUT.mkdir(parents=True, exist_ok=True)
+    catalog = OUT / 'single_dim_star.csv'
+    catalog.write_text('longitude_deg,latitude_deg,temperature_K,amplitude\n'
+                       '262.5,-30,6000,1e-30\n')
+    results = {}
+    for scene in ('r100', 'r2p1'):
+        meshes = {}
+        for upper in (.5, 2, 8, 32):
+            name = f'{scene}_hmax{upper:g}'
+            cmd = [str(BIN), '--integrator', 'dp54',
+                   '--width', '320', '--height', '180',
+                   '--coarse-cell-pixels', '8', '--refine-max-level', '3',
+                   '--catalog', str(catalog), '--exposure', '1',
+                   '--psf-min-y', '1e-20', '--psf-relative-tail', '1e-4',
+                   '--ode-min-step', '1e-12', '--ode-max-step', str(upper),
+                   '--verbose', '--lens-map-output', str(OUT / (name + '.grlens')),
+                   '--output', str(OUT / (name + '.png')), *scene_args(scene)]
+            start = time.perf_counter()
+            with (OUT / (name + '.log')).open('w') as log:
+                log.write('OMP_NUM_THREADS=8 OMP_DYNAMIC=FALSE ' +
+                          shlex.join(cmd) + '\n')
+                log.flush()
+                subprocess.run(cmd, cwd=ROOT, env=ENV, stdout=log,
+                               stderr=subprocess.STDOUT, check=True, timeout=180)
+            info, meshes[upper] = load(OUT / (name + '.grlens'))
+            info['wall_seconds'] = time.perf_counter() - start
+            results[name] = info
+            print(name, json.dumps(info), flush=True)
+        for upper in (.5, 8, 32):
+            comparison = compare(meshes[2], meshes[upper])
+            results[f'{scene}_2_vs_{upper:g}'] = comparison
+            print(f'{scene} 2 vs {upper:g}', json.dumps(comparison), flush=True)
+    (OUT / 'summary.json').write_text(json.dumps(results, indent=2) + '\n')
+
+
+if __name__ == '__main__':
+    main()
@@ -0,0 +1,82 @@
+#!/usr/bin/env python3
+"""Two bounded tight-tolerance mesh references and comparisons (no 4K).
+
+Usage:
+    run_mesh_reference.py [OUT_DIR]
+
+OUT_DIR defaults to <repo>/local/adaptive_bounds_mesh and must already contain
+the eight ``<scene>_hmax<h>.grlens`` maps from ``run_mesh.py``.  The renderer
+binary is expected at build/Release/schwarzschild_sky (see README for the make
+command).  Same one-point synthetic dim catalog, no external CSV.
+"""
+import json
+import os
+from pathlib import Path
+import shlex
+import subprocess
+import sys
+import time
+
+from mesh_maps import load, compare
+
+ROOT = Path(__file__).resolve().parents[2]
+OUT = Path(sys.argv[1]).resolve() if len(sys.argv) > 1 else \
+    ROOT / 'local/adaptive_bounds_mesh'
+BIN = ROOT / 'build/Release/schwarzschild_sky'
+BUILD_CMD = 'make -j4 BUILD_TYPE=Release SPACETIME=schwarzschild backend'
+ENV = dict(os.environ, OMP_NUM_THREADS='8', OMP_DYNAMIC='FALSE')
+
+
+def scene_args(scene):
+    if scene == 'r100':
+        return ['--observer-radius', '100', '--look-ra-deg', '262.5',
+                '--look-dec-deg', '-30', '--fov-deg', '45',
+                '--refine-jacobian-min', '.2']
+    return ['--observer-position', '2.1', '0', '0', '--observer-velocity',
+            '0', '0', '0', '--look-ra-deg', '0', '--look-dec-deg', '0',
+            '--fov-deg', '90']
+
+
+def main():
+    if not BIN.exists():
+        raise SystemExit(f'missing {BIN}; build it first:\n    {BUILD_CMD}')
+    OUT.mkdir(parents=True, exist_ok=True)
+    catalog = OUT / 'single_dim_star.csv'
+    if not catalog.exists():
+        catalog.write_text('longitude_deg,latitude_deg,temperature_K,amplitude\n'
+                           '262.5,-30,6000,1e-30\n')
+    results = {}
+    for scene in ('r100', 'r2p1'):
+        name = scene + '_tight_reference'
+        cmd = [str(BIN), '--integrator', 'dp54', '--width', '320',
+               '--height', '180', '--coarse-cell-pixels', '8',
+               '--refine-max-level', '3', '--catalog', str(catalog),
+               '--exposure', '1', '--psf-min-y', '1e-20',
+               '--psf-relative-tail', '1e-4', '--ode-min-step', '1e-12',
+               '--ode-max-step', '.5', '--ode-rtol', '1e-12',
+               '--ode-atol-x', '1e-12', '--ode-atol-pi', '1e-12',
+               '--ode-atol-l', '1e-12', '--verbose',
+               '--lens-map-output', str(OUT / (name + '.grlens')),
+               '--output', str(OUT / (name + '.png')), *scene_args(scene)]
+        start = time.perf_counter()
+        with (OUT / (name + '.log')).open('w') as log:
+            log.write('OMP_NUM_THREADS=8 OMP_DYNAMIC=FALSE ' +
+                      shlex.join(cmd) + '\n')
+            log.flush()
+            subprocess.run(cmd, cwd=ROOT, env=ENV, stdout=log,
+                           stderr=subprocess.STDOUT, check=True, timeout=180)
+        info, ref = load(OUT / (name + '.grlens'))
+        info['wall_seconds'] = time.perf_counter() - start
+        results[name] = info
+        print(name, json.dumps(info), flush=True)
+        for upper in (.5, 2, 8, 32):
+            _, vertices = load(OUT / f'{scene}_hmax{upper:g}.grlens')
+            result = compare(ref, vertices)
+            results[f'{scene}_ref_vs_{upper:g}'] = result
+            print(scene, 'ref vs', upper, json.dumps(result), flush=True)
+    (OUT / 'reference_summary.json').write_text(
+        json.dumps(results, indent=2) + '\n')
+
+
+if __name__ == '__main__':
+    main()
@@ -0,0 +1,261 @@
+#!/usr/bin/env python3
+"""Summarise the adaptive-step-bounds benchmark raw CSV logs.
+
+Usage:
+    summarize.py [OUT_DIR]
+
+Reads ``OUT_DIR/raw/*.csv`` (written by ``run_limited.sh``) and writes
+``OUT_DIR/logs/summary.txt``.  It has no dependency on any untracked script or
+on older local data.
+
+Defaults: OUT_DIR = <repo>/local/adaptive_step_bounds_2026-10-05, derived from
+this file's location (benchmarks/adaptive_step_bounds_2026-10-05/).
+"""
+import csv
+import math
+import os
+import sys
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+ROOT = os.path.dirname(os.path.dirname(HERE))
+DEFAULT_OUT = os.path.join(ROOT, "local", "adaptive_step_bounds_2026-10-05")
+
+OUTCOME = {0: "ESC", 1: "DARK", 2: "UNRES", 3: "INC"}
+REASON = {
+    0: "NONE",
+    1: "REDSHIFT",
+    2: "BUDGET",
+    3: "TIMERANGE",
+    4: "DOMAIN",
+    5: "INVMETRIC",
+    6: "INTEGERR",
+    7: "UNSUPPORTED",
+    8: "PROTOCOL",
+    9: "IO",
+}
+
+
+def fnum(v):
+    if v is None or v == "" or v == "nan":
+        return math.nan
+    return float(v)
+
+
+def fmt(v):
+    if isinstance(v, float):
+        if math.isnan(v):
+            return "nan"
+        if v == 0:
+            return "0"
+        return f"{v:.4g}"
+    return str(v)
+
+
+def table(title, header, recs):
+    lines = [f"## {title}", ""]
+    lines.append("| " + " | ".join(header) + " |")
+    lines.append("|" + "|".join(["---"] * len(header)) + "|")
+    for r in recs:
+        lines.append("| " + " | ".join(fmt(x) for x in r) + " |")
+    lines.append("")
+    return lines
+
+
+def ang_between(a, b):
+    va = [fnum(a["nx"]), fnum(a["ny"]), fnum(a["nz"])]
+    vb = [fnum(b["nx"]), fnum(b["ny"]), fnum(b["nz"])]
+    na = math.sqrt(sum(x * x for x in va))
+    nb = math.sqrt(sum(x * x for x in vb))
+    if not (na > 0 and nb > 0):
+        return math.nan
+    cross = (va[1]*vb[2]-va[2]*vb[1],
+             va[2]*vb[0]-va[0]*vb[2],
+             va[0]*vb[1]-va[1]*vb[0])
+    dot = sum(x * y for x, y in zip(va, vb))
+    return math.atan2(math.sqrt(sum(x*x for x in cross)), dot)
+
+
+class Raw:
+    def __init__(self, out_dir):
+        self.raw = os.path.join(out_dir, "raw")
+        self.logs = os.path.join(out_dir, "logs")
+
+    def rows(self, name):
+        with open(os.path.join(self.raw, name)) as f:
+            return list(csv.DictReader(f))
+
+
+def summarise_agg(raw, name, title, keycol):
+    recs = raw.rows(name)
+    out = []
+    for r in recs:
+        out.append((r["case"], float(r[keycol]), int(r["class_mismatch"]),
+                    fnum(r["max_dn_ang"]), fnum(r["max_dgrel"]),
+                    fnum(r["max_dstopT"]), int(r["sum_rhs"]),
+                    int(r["max_rejected"]), int(r["escaped"]), int(r["dark"]),
+                    int(r["unresolved"]), int(r["incomplete"])))
+    out.sort(key=lambda x: (x[0], x[1]))
+    return table(title,
+                 ["case", keycol, "mismatch", "max_dn_ang", "max_dgrel",
+                  "max_dstopT", "sum_rhs", "max_rej", "ESC", "DARK", "UNRES",
+                  "INC"], out)
+
+
+def build(raw):
+    lines = ["# Adaptive-step-bounds benchmark summary tables", ""]
+
+    ref = raw.rows("a_sch_reference.csv")
+    recs = []
+    for r in ref:
+        recs.append((r["case"], int(r["dir"]), fnum(r["theta"]),
+                     OUTCOME[int(r["outcome"])], REASON[int(r["reason"])],
+                     fnum(r["stop_t"]), int(r["steps"]), int(r["rejected"]),
+                     int(r["rhs"]), fnum(r["g"]), fnum(r["thr"])))
+    lines += table("A Schwarzschild references (DP tol=1e-12, max_step=0.25)",
+                   ["case", "dir", "theta", "outcome", "reason", "stop_t",
+                    "steps", "rej", "rhs", "g", "thr"], recs)
+
+    lines += summarise_agg(raw, "a_sch_upper_summary.csv",
+                           "A Schwarzschild upper scan (min_step=1e-12, "
+                           "tol=1e-9)", "upper")
+    lines += summarise_agg(raw, "a_sch_min_summary.csv",
+                           "A Schwarzschild min scan (max_step=2, tol=1e-9)",
+                           "min_step")
+
+    rk = raw.rows("a_sch_rk4_sensitive.csv")
+    groups = {}
+    for r in rk:
+        groups.setdefault((r["case"], r["dir"]), {})[r["phase"]] = r
+    recs = []
+    for (case, d), gg in sorted(groups.items()):
+        a = gg.get("rk4_0.01")
+        b = gg.get("rk4_0.005")
+        if not a or not b:
+            continue
+        dn = math.nan if a["outcome"] != b["outcome"] else ang_between(a, b)
+        dg = (math.nan if a["outcome"] != b["outcome"]
+              else abs(fnum(a["g"]) - fnum(b["g"])))
+        recs.append((case, d, fnum(a["theta"]), OUTCOME[int(a["outcome"])],
+                     OUTCOME[int(b["outcome"])], dn, dg, int(a["rhs"]),
+                     int(b["rhs"])))
+    lines += table("A Schwarzschild sensitive RK4 .01 vs .005",
+                   ["case", "dir", "theta", "out.01", "out.005",
+                    "hhalve_dn_ang", "|dg|", "rhs.01", "rhs.005"], recs)
+
+    mk = raw.rows("a_mink_analytic.csv")
+    mkx = raw.rows("a_mink_analytic_x.csv")
+    groups = {}
+    for r in mk:
+        groups.setdefault((r["upper"], r["min_step"]), []).append(r)
+    recs = []
+    for (u, f), g in sorted(groups.items(),
+                            key=lambda kv: (float(kv[0][0]), float(kv[0][1]))):
+        recs.append((u, f, len(g), max(fnum(r["dn_ang"]) for r in g),
+                     max(fnum(r["dgrel"]) for r in g),
+                     max(fnum(r["t_err"]) for r in g)))
+    lines += table("A Minkowski flat analytic check (n_inf and t)",
+                   ["upper", "min_step", "n", "max_dn_ang", "max_dgrel",
+                    "max_t_err"], recs)
+    groups = {}
+    for r in mkx:
+        groups.setdefault((r["upper"], r["min_step"]), []).append(r)
+    recs = []
+    for (u, f), g in sorted(groups.items(),
+                            key=lambda kv: (float(kv[0][0]), float(kv[0][1]))):
+        maxx = max(max(fnum(r["x_err_x"]), fnum(r["x_err_y"]),
+                       fnum(r["x_err_z"])) for r in g)
+        recs.append((u, f, len(g), maxx, max(fnum(r["t_err"]) for r in g)))
+    lines += table("A Minkowski flat analytic check (crossing x and t)",
+                   ["upper", "min_step", "n", "max_x_err", "max_t_err"], recs)
+
+    for case in ["alc_v3_s1", "alc_v3_s10", "alc_v9_s1", "alc_v9_s10"]:
+        lines += summarise_agg(raw, f"a_alc_{case}_upper_summary.csv",
+                               f"A Alcubierre {case} upper scan", "upper")
+    lines += summarise_agg(raw, "a_alc_v9_s100_min_summary.csv",
+                           "A Alcubierre v9 s100 lower-bound stress "
+                           "(upper=0.004)", "min_step")
+
+    b = raw.rows("b_summary.csv")
+    recs = []
+    for r in b:
+        recs.append((r["case"], int(r["dir"]),
+                     OUTCOME[int(r["ref_outcome"])], fnum(r["span"]),
+                     fnum(r["target"]), int(r["observed_steps"]),
+                     int(r["reached_target"]),
+                     REASON.get(int(r["terminated_reason"]),
+                                r["terminated_reason"]),
+                     fnum(r["h_min"]), fnum(r["h_max"]), fnum(r["h_first"]),
+                     int(r["boundary_steps"]), int(r["sum_rhs"]),
+                     int(r["sum_reject"]), fnum(r["null_residual_max"])))
+    lines += table("B observed accepted step h (finite T=min(20, ref span))",
+                   ["case", "dir", "ref", "span", "target", "steps", "reached",
+                    "term", "h_min", "h_max", "h_first", "bnd", "rhs", "rej",
+                    "null_max"], recs)
+
+    if os.path.exists(os.path.join(raw.raw, "critical_ref.csv")):
+        lines += critical_section(raw)
+    return lines
+
+
+def critical_section(raw):
+    rows = raw.rows("critical_ref.csv")
+    key = {}
+    for r in rows:
+        key[(r["camera"], int(r["dir"]), r["cfg"])] = r
+    lines = table("critical reference check (raw rows)",
+                  ["camera", "dir", "theta", "cfg", "outcome", "reason",
+                   "end_id", "stop_t", "steps", "rejected", "rhs", "g", "thr",
+                   "L", "L0"],
+                  [(r["camera"], int(r["dir"]), fnum(r["theta"]), r["cfg"],
+                    OUTCOME[int(r["outcome"])], REASON[int(r["reason"])],
+                    r["end_id"], fnum(r["stop_t"]), int(r["steps"]),
+                    int(r["rejected"]), int(r["rhs"]), fnum(r["g"]),
+                    fnum(r["thr"]), fnum(r.get("L")), fnum(r.get("L0")))
+                   for r in rows])
+    # pair comparisons
+    pairs = [("ref_tol1e-12_h0.25", "ref_tol1e-13_h0.125"),
+             ("tol1e-11_h2", "tol1e-11_h8"),
+             ("ref_tol1e-12_h0.25", "tol1e-11_h2"),
+             ("ref_tol1e-12_h0.25", "tol1e-11_h8")]
+    for a_cfg, b_cfg in pairs:
+        recs = []
+        for (cam, di, cfg), a in sorted(key.items()):
+            if cfg != a_cfg:
+                continue
+            b = key.get((cam, di, b_cfg))
+            if not b:
+                continue
+            same = a["outcome"] == b["outcome"]
+            dn = ang_between(a, b) if same else math.nan
+            dg = (math.nan if not same else
+                  abs(fnum(a["g"]) / fnum(b["g"]) - 1.0)
+                  if fnum(a["g"]) > 0 and fnum(b["g"]) > 0 else math.nan)
+            dstop = (fnum(a["stop_t"]) - fnum(b["stop_t"])
+                     if fnum(a["stop_t"]) == fnum(a["stop_t"]) and
+                     fnum(b["stop_t"]) == fnum(b["stop_t"]) else math.nan)
+            dmar = (fnum(a["thr"]) - fnum(b["thr"])
+                    if fnum(a["thr"]) == fnum(a["thr"]) and
+                    fnum(b["thr"]) == fnum(b["thr"]) else math.nan)
+            recs.append((cam, di, fnum(a["theta"]),
+                         OUTCOME[int(a["outcome"])], OUTCOME[int(b["outcome"])],
+                         same, dn, dg, dstop, dmar))
+        lines += table(f"critical pair {a_cfg} vs {b_cfg}",
+                       ["camera", "dir", "theta", "a", "b", "same",
+                        "dn_ang", "dgrel", "dstop_t", "dthr"], recs)
+    return lines
+
+
+def main(argv):
+    out = argv[1] if len(argv) > 1 else DEFAULT_OUT
+    raw = Raw(out)
+    os.makedirs(raw.logs, exist_ok=True)
+    lines = build(raw)
+    path = os.path.join(raw.logs, "summary.txt")
+    with open(path, "w") as f:
+        f.write("\n".join(lines) + "\n")
+    print(f"wrote {path} ({len(lines)} lines)")
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main(sys.argv))
@@ -0,0 +1,67 @@
+#!/usr/bin/env python3
+"""Postprocess existing 4K/limited maps only; never invokes a renderer.
+
+Usage:
+    summarize_4k.py [OUT_DIR]
+
+OUT_DIR defaults to <repo>/local/adaptive_bounds_4k and must contain
+``r100_4k_hmax2.grlens``, ``r100_4k_hmax8.grlens`` and ``attempts.json``.
+Writes summary.json in OUT_DIR.
+
+Cost scope note: accepted/rejected/RHS sums cover the final persistent map
+vertices only.  Nonpersistent discarded refinement probes are not stored in the
+v3 map, so these sums are not full-render executed RHS totals.
+"""
+import json
+import re
+from pathlib import Path
+import sys
+
+from mesh_maps import load, compare
+
+ROOT = Path(__file__).resolve().parents[2]
+OUT = Path(sys.argv[1]).resolve() if len(sys.argv) > 1 else \
+    ROOT / 'local/adaptive_bounds_4k'
+
+
+def main():
+    summaries = {}
+    meshes = {}
+    for upper in (2, 8):
+        name = f'r100_4k_hmax{upper}'
+        summaries[name], meshes[upper] = load(OUT / (name + '.grlens'))
+        text = (OUT / (name + '.log')).read_text()
+        initial = int(re.search(r'tracing (\d+) initial rays', text).group(1))
+        generations = [int(n) for n in re.findall(
+            r'refinement generation \d+ tracing (\d+) samples', text)]
+        summaries[name]['requested_samples_including_nonpersistent_probes'] = \
+            initial + sum(generations)
+        summaries[name]['initial_samples'] = initial
+        summaries[name]['refinement_samples_per_generation'] = generations
+        summaries[name]['trace_wall_seconds'] = sum(
+            float(x) for x in re.findall(
+                r'(?:initial ray trace|adaptive ray-trace refinement) '
+                r'finished in ([\d.]+) s', text))
+    ledger = OUT / 'attempts.json'
+    if ledger.exists():
+        for entry in json.loads(ledger.read_text()):
+            if entry.get('state') == 'completed':
+                summaries[f'r100_4k_hmax{entry["upper"]}']['wall_seconds'] = \
+                    entry['wall_seconds']
+    summaries['comparison'] = compare(meshes[2], meshes[8])
+    a, b = (summaries[f'r100_4k_hmax{upper}'] for upper in (2, 8))
+    summaries['relative_reduction'] = {
+        key: 1 - b[key] / a[key]
+        for key in ('accepted', 'rhs', 'wall_seconds', 'trace_wall_seconds')}
+    summaries['comparison']['triangle_payload_identical'] = \
+        a['triangle_sha256'] == b['triangle_sha256']
+    summaries['cost_scope'] = (
+        'accepted/rejected/RHS sums cover final persistent vertices only; '
+        'nonpersistent discarded refinement probes are not in the v3 map. '
+        'Do not interpret them as full-render executed RHS totals.')
+    (OUT / 'summary.json').write_text(json.dumps(summaries, indent=2) + '\n')
+    print(json.dumps(summaries, indent=2))
+
+
+if __name__ == '__main__':
+    main()
@@ -0,0 +1 @@
+__pycache__/
@@ -0,0 +1,84 @@
+# Production chunk geometry diagnostic (2026-09-11)
+
+## Scope
+
+This run measures the event stream that the production HIP sink would receive
+for the supplied Schwarzschild Galactic-center render. `PSF_BACKEND=dummy`
+keeps the real imported lens map, all-sky prefetch, OpenMP dynamic triangle
+scheduling, inverse mapping, redshift/color/flux work, PSF cache eligibility,
+and 16,384-event per-worker chunk boundaries. It does not initialize HIP,
+allocate a full HDR framebuffer, splat pixels, or write PNG/FITS output.
+
+The run used repository revision `11e703e33dffb1ff168ba11dd922e68b448116b9`
+plus the uncommitted dummy-backend work. The complete stdout/stderr, executable
+and input hashes, process resource use, and protected-output hashes are in
+[`full_catalog.log`](full_catalog.log). An initial harness-only failure before
+the renderer started is retained as
+[`full_catalog_missing_time.log`](full_catalog_missing_time.log).
+
+## Build and run
+
+```sh
+make -j1 PSF_BACKEND=dummy SPACETIME=schwarzschild ENABLE_HDR=1 backend
+python3 benchmarks/dummy_psf_chunks_2026-09-11/run.py
+```
+
+The runner fixes `OMP_NUM_THREADS=16` and `OMP_DYNAMIC=FALSE`, uses a 600-second
+timeout and a process lock, refuses to overwrite its log, and hashes both the
+named PNG and companion FITS before and after the run. Its renderer arguments
+are exactly the user-supplied command except that the `_hip` executable is
+replaced by `_dummy`; the exact expanded command is the first line of the log.
+
+Inputs and protected outputs:
+
+- lens map SHA-256:
+  `905f960aea2d276f9586c79fba545a72cf742311e9e7e18faea293835c68bf28`
+- existing PNG SHA-256 before/after:
+  `3e01feb911e60acce545a6a86870ca05f96250022e874eb8097bec88a8879bfd`
+- existing FITS SHA-256 before/after:
+  `2408e62dcc22f147da284d87af9a2b0fdd0050eda2dabc23b6ec2554b2f1d38e`
+
+Both protected files retained the same size and nanosecond mtime as well as the
+same hash. No HIP backend was run.
+
+## Result
+
+The catalog prefetch loaded 343,363,141 stars for 130,882 lens triangles. The
+producer classified 598,264,924 cache events, with zero direct fallbacks,
+wing-clipped events, or min-Y discards. Sixteen workers produced 36,524 chunks:
+36,508 full chunks and one final partial chunk per worker.
+
+| full-chunk metric | min | p10 | p25 | p50 | p75 | p90 | p99 | max |
+|---|---:|---:|---:|---:|---:|---:|---:|---:|
+| event-producing triangles | 1 | 1 | 1 | 2 | 3 | 10 | 31 | 59 |
+| occupied 32px center tiles | 1 | 1 | 1 | 1 | 2 | 5 | 30 | 45 |
+| event bbox diagonal (px) | 0.199 | 0.742 | 3.250 | 12.651 | 57.018 | 429.306 | 3759.261 | 3834.557 |
+| triangle-centroid bbox diagonal (px) | 0 | 0 | 0 | 9.618 | 49.477 | 424.149 | 3744.061 | 3824.075 |
+| maximum successive centroid jump (px) | 0 | 0 | 0 | 8.724 | 25.157 | 144.000 | 3744.034 | 3792.034 |
+
+All 36,508 full chunks satisfy the replay prototype's current selector:
+`events >= 8192 && events / occupied_32px_tiles >= 32`.
+
+Catalog prefetch took 55.469 s. Producer classification and chunk accounting
+took 232.340 s; total process wall time was 288.872 s. These are diagnostic CPU
+costs and do not estimate HIP tile-kernel speed.
+
+## Interpretation and limits
+
+The measured production event order strongly supports the hypothesis that a
+full worker chunk is usually filled by very few image-plane triangles: the
+median is two and 75% contain at most three. Center-tile occupancy is even more
+concentrated. This is favorable for a tile16 path because the same output pixels
+receive many contributions that can be reduced before the final double HDR
+write.
+
+The rare tail matters: p99 chunks can contain a few clusters separated by
+nearly the full 4K image width. “Few triangles” therefore does not imply one
+small contiguous bounding rectangle. A production implementation should use a
+sparse occupied-tile list, retain the atomic fallback, and measure the complete
+streaming sink including binning and synchronization.
+
+This is one Schwarzschild Galactic-center frame with one 16-worker dynamic
+schedule. Worker-to-triangle assignment is nondeterministic, so exact quantiles
+may vary between runs. The result establishes event geometry for this input; it
+does not by itself establish single-BH/BBH universality or a HIP speedup.
@@ -0,0 +1,235 @@
+COMMAND OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE /home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky_dummy --verbose --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 --all-sky-catalog assets/2mass/processed/all_sky --exposure 1e13 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --catalog-load-workers 4 --hdr-output --lens-map-input output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens --output output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 c71a843a6064cd730b4694c5fe4e61249a995106526da0fdca97bc625c7db470
+LENS_SHA256 905f960aea2d276f9586c79fba545a72cf742311e9e7e18faea293835c68bf28
+PROTECTED_BEFORE output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png sha256=3e01feb911e60acce545a6a86870ca05f96250022e874eb8097bec88a8879bfd size=13072572 mtime_ns=1788744728751407011
+PROTECTED_BEFORE output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu_HDR.fits sha256=2408e62dcc22f147da284d87af9a2b0fdd0050eda2dabc23b6ec2554b2f1d38e size=99535680 mtime_ns=1788744726380022561
+Dummy PSF backend: --output and --hdr-output are accepted for command parity but no image files will be written.
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.678 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 64440 newly loaded (343363141 stars), 0 unavailable in 55.469 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: splat worker 2/16 started.
+Frame 0: splat worker 1/16 started.
+Frame 0: splat worker 4/16 started.
+Frame 0: splat worker 3/16 started.
+Frame 0: splat worker 5/16 started.
+Frame 0: splat worker 10/16 started.
+Frame 0: splat worker 7/16 started.
+Frame 0: splat worker 8/16 started.
+Frame 0: splat worker 13/16 started.
+Frame 0: splat worker 11/16 started.
+Frame 0: splat worker 6/16 started.
+Frame 0: splat worker 12/16 started.
+Frame 0: splat worker 9/16 started.
+Frame 0: splat worker 14/16 started.
+Frame 0: splat worker 16/16 started.
+Frame 0: splat worker 15/16 started.
+Frame 0: splat worker 1/16 reached 8 local triangles.
+Frame 0: splat worker 6/16 reached 8 local triangles.
+Frame 0: splat worker 10/16 reached 8 local triangles.
+Frame 0: splat worker 14/16 reached 8 local triangles.
+Frame 0: splat worker 12/16 reached 8 local triangles.
+Frame 0: splat worker 2/16 reached 8 local triangles.
+Frame 0: splat worker 5/16 reached 8 local triangles.
+Frame 0: splat worker 3/16 reached 8 local triangles.
+Frame 0: splat worker 7/16 reached 8 local triangles.
+Frame 0: splat worker 15/16 reached 8 local triangles.
+Frame 0: splat worker 8/16 reached 8 local triangles.
+Frame 0: splat worker 4/16 reached 8 local triangles.
+Frame 0: splat worker 11/16 reached 8 local triangles.
+Frame 0: splat worker 13/16 reached 8 local triangles.
+Frame 0: splat worker 9/16 reached 8 local triangles.
+Frame 0: splat worker 16/16 reached 8 local triangles.
+Frame 0: splat worker 12/16 reached 16 local triangles.
+Frame 0: splat worker 4/16 reached 16 local triangles.
+Frame 0: splat worker 14/16 reached 16 local triangles.
+Frame 0: splat worker 6/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 16 local triangles.
+Frame 0: splat worker 8/16 reached 16 local triangles.
+Frame 0: splat worker 3/16 reached 16 local triangles.
+Frame 0: splat worker 7/16 reached 16 local triangles.
+Frame 0: splat worker 2/16 reached 16 local triangles.
+Frame 0: splat worker 15/16 reached 16 local triangles.
+Frame 0: splat worker 5/16 reached 16 local triangles.
+Frame 0: splat worker 11/16 reached 16 local triangles.
+Frame 0: splat worker 13/16 reached 16 local triangles.
+Frame 0: splat worker 9/16 reached 16 local triangles.
+Frame 0: splat worker 16/16 reached 16 local triangles.
+Frame 0: splat worker 12/16 reached 32 local triangles.
+Frame 0: splat worker 4/16 reached 32 local triangles.
+Frame 0: splat worker 7/16 reached 32 local triangles.
+Frame 0: splat worker 6/16 reached 32 local triangles.
+Frame 0: splat worker 8/16 reached 32 local triangles.
+Frame 0: splat worker 2/16 reached 32 local triangles.
+Frame 0: splat worker 3/16 reached 32 local triangles.
+Frame 0: splat worker 11/16 reached 32 local triangles.
+Frame 0: splat worker 9/16 reached 32 local triangles.
+Frame 0: splat worker 1/16 reached 32 local triangles.
+Frame 0: splat worker 15/16 reached 32 local triangles.
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+Frame 0: splat worker 14/16 reached 32 local triangles.
+Frame 0: splat worker 5/16 reached 32 local triangles.
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+Frame 0: splat worker 10/16 reached 16 local triangles.
+Frame 0: splat worker 10/16 reached 32 local triangles.
+Frame 0: splat worker 4/16 reached 64 local triangles.
+Frame 0: splat worker 6/16 reached 64 local triangles.
+Frame 0: splat worker 8/16 reached 64 local triangles.
+Frame 0: splat worker 2/16 reached 64 local triangles.
+Frame 0: splat worker 3/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 64 local triangles.
+Frame 0: splat worker 11/16 reached 64 local triangles.
+Frame 0: splat worker 15/16 reached 64 local triangles.
+Frame 0: splat worker 16/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 64 local triangles.
+Frame 0: splat worker 5/16 reached 64 local triangles.
+Frame 0: splat worker 9/16 reached 64 local triangles.
+Frame 0: splat worker 1/16 reached 64 local triangles.
+Frame 0: splat worker 7/16 reached 64 local triangles.
+Frame 0: splat worker 13/16 reached 64 local triangles.
+Frame 0: splat worker 10/16 reached 64 local triangles.
+Frame 0: splat worker 4/16 reached 128 local triangles.
+Frame 0: splat worker 12/16 reached 128 local triangles.
+Frame 0: splat worker 11/16 reached 128 local triangles.
+Frame 0: splat worker 6/16 reached 128 local triangles.
+Frame 0: splat worker 15/16 reached 128 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
+Frame 0: splat worker 5/16 reached 128 local triangles.
+Frame 0: splat worker 8/16 reached 128 local triangles.
+Frame 0: splat worker 3/16 reached 128 local triangles.
+Frame 0: splat worker 16/16 reached 128 local triangles.
+Frame 0: splat worker 14/16 reached 128 local triangles.
+Frame 0: splat worker 7/16 reached 128 local triangles.
+Frame 0: splat worker 1/16 reached 128 local triangles.
+Frame 0: splat worker 13/16 reached 128 local triangles.
+Frame 0: splat worker 9/16 reached 128 local triangles.
+Frame 0: splat worker 10/16 reached 128 local triangles.
+Frame 0: splat worker 13/16 reached 256 local triangles.
+Frame 0: splat worker 15/16 reached 256 local triangles.
+Frame 0: splat worker 16/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 256 local triangles.
+Frame 0: splat worker 11/16 reached 256 local triangles.
+Frame 0: splat worker 6/16 reached 256 local triangles.
+Frame 0: splat worker 5/16 reached 256 local triangles.
+Frame 0: splat worker 3/16 reached 256 local triangles.
+Frame 0: splat worker 1/16 reached 256 local triangles.
+Frame 0: splat worker 2/16 reached 256 local triangles.
+Frame 0: splat worker 7/16 reached 256 local triangles.
+Frame 0: splat worker 4/16 reached 256 local triangles.
+Frame 0: splat worker 12/16 reached 256 local triangles.
+Frame 0: splat worker 10/16 reached 256 local triangles.
+Frame 0: splat worker 14/16 reached 256 local triangles.
+Frame 0: splat worker 9/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 512 local triangles.
+Frame 0: splat worker 12/16 reached 512 local triangles.
+Frame 0: splat worker 16/16 reached 512 local triangles.
+Frame 0: splat worker 5/16 reached 512 local triangles.
+Frame 0: splat worker 13/16 reached 512 local triangles.
+Frame 0: splat worker 3/16 reached 512 local triangles.
+Frame 0: splat worker 7/16 reached 512 local triangles.
+Frame 0: splat worker 11/16 reached 512 local triangles.
+Frame 0: splat worker 1/16 reached 512 local triangles.
+Frame 0: splat worker 15/16 reached 512 local triangles.
+Frame 0: splat worker 2/16 reached 512 local triangles.
+Frame 0: splat worker 10/16 reached 512 local triangles.
+Frame 0: splat worker 4/16 reached 512 local triangles.
+Frame 0: splat worker 6/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 512 local triangles.
+Frame 0: splat worker 9/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 1024 local triangles.
+Frame 0: splat worker 7/16 reached 1024 local triangles.
+Frame 0: splat worker 12/16 reached 1024 local triangles.
+Frame 0: splat worker 3/16 reached 1024 local triangles.
+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 11/16 reached 1024 local triangles.
+Frame 0: splat worker 5/16 reached 1024 local triangles.
+Frame 0: splat worker 14/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 1024 local triangles.
+Frame 0: splat worker 4/16 reached 1024 local triangles.
+Frame 0: splat worker 9/16 reached 1024 local triangles.
+Frame 0: splat worker 13/16 reached 1024 local triangles.
+Frame 0: splat worker 6/16 reached 1024 local triangles.
+Frame 0: splat worker 1/16 reached 1024 local triangles.
+Frame 0: splat worker 10/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 1024 local triangles.
+Frame 0: splat worker 8/16 reached 2048 local triangles.
+Frame 0: splat worker 12/16 reached 2048 local triangles.
+Frame 0: splat worker 16/16 reached 2048 local triangles.
+Frame 0: splat worker 14/16 reached 2048 local triangles.
+Frame 0: splat worker 7/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 2048 local triangles.
+Frame 0: splat worker 4/16 reached 2048 local triangles.
+Frame 0: splat worker 1/16 reached 2048 local triangles.
+Frame 0: splat worker 11/16 reached 2048 local triangles.
+Frame 0: splat worker 5/16 reached 2048 local triangles.
+Frame 0: splat worker 13/16 reached 2048 local triangles.
+Frame 0: splat worker 15/16 reached 2048 local triangles.
+Frame 0: splat worker 6/16 reached 2048 local triangles.
+Frame 0: splat worker 2/16 reached 2048 local triangles.
+Frame 0: splat worker 9/16 reached 2048 local triangles.
+Frame 0: splat worker 10/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 4096 local triangles.
+Frame 0: splat worker 7/16 reached 4096 local triangles.
+Frame 0: splat worker 16/16 reached 4096 local triangles.
+Frame 0: splat worker 14/16 reached 4096 local triangles.
+Frame 0: splat worker 9/16 reached 4096 local triangles.
+Frame 0: splat worker 4/16 reached 4096 local triangles.
+Frame 0: splat worker 6/16 reached 4096 local triangles.
+Frame 0: splat worker 8/16 reached 4096 local triangles.
+Frame 0: splat worker 13/16 reached 4096 local triangles.
+Frame 0: splat worker 5/16 reached 4096 local triangles.
+Frame 0: splat worker 10/16 reached 4096 local triangles.
+Frame 0: splat worker 15/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 4096 local triangles.
+Frame 0: splat worker 12/16 reached 4096 local triangles.
+Frame 0: splat worker 1/16 reached 4096 local triangles.
+Frame 0: splat worker 2/16 reached 4096 local triangles.
+Frame 0: splat worker 3/16 reached 8192 local triangles.
+Frame 0: splat worker 7/16 reached 8192 local triangles.
+Frame 0: splat worker 16/16 reached 8192 local triangles.
+Frame 0: splat worker 13/16 reached 8192 local triangles.
+Frame 0: splat worker 9/16 reached 8192 local triangles.
+Frame 0: splat worker 4/16 reached 8192 local triangles.
+Frame 0: splat worker 8/16 reached 8192 local triangles.
+Frame 0: splat worker 2/16 finished after 7916 local triangles.
+Frame 0: splat worker 8/16 finished after 8212 local triangles.
+Frame 0: splat worker 6/16 finished after 8150 local triangles.
+Frame 0: splat worker 1/16 finished after 7784 local triangles.
+Frame 0: splat worker 4/16 finished after 8227 local triangles.
+Frame 0: splat worker 15/16 finished after 7878 local triangles.
+Frame 0: splat worker 14/16 finished after 8186 local triangles.
+Frame 0: splat worker 11/16 finished after 7962 local triangles.
+Frame 0: splat worker 9/16 finished after 8276 local triangles.
+Frame 0: splat worker 16/16 finished after 8477 local triangles.
+Frame 0: splat worker 3/16 finished after 8967 local triangles.
+Frame 0: splat worker 7/16 finished after 8576 local triangles.
+Frame 0: splat worker 10/16 finished after 7772 local triangles.
+Frame 0: splat worker 13/16 finished after 8295 local triangles.
+Frame 0: splat worker 12/16 finished after 8013 local triangles.
+Frame 0: splat worker 5/16 finished after 8191 local triangles.
+Dummy PSF diagnostic only: no HDR or image was accumulated/written.
+Dummy PSF chunks: total=36524 full=36508 partial=16 events=598264924 capacity=16384 selector_tile=32px
+Dummy PSF all events: min=263.000 p10=16384.000 p25=16384.000 p50=16384.000 p75=16384.000 p90=16384.000 p99=16384.000 max=16384.000
+Dummy PSF all distinct_triangles: min=1.000 p10=1.000 p25=1.000 p50=2.000 p75=4.000 p90=10.000 p99=31.000 max=59.000
+Dummy PSF all occupied_32px_tiles: min=1.000 p10=1.000 p25=1.000 p50=1.000 p75=2.000 p90=5.000 p99=30.000 max=45.000
+Dummy PSF all event_bbox_diagonal_px: min=0.199 p10=0.743 p25=3.252 p50=12.667 p75=57.123 p90=432.049 p99=3759.261 max=3834.557
+Dummy PSF all triangle_centroid_bbox_diagonal_px: min=0.000 p10=0.000 p25=0.000 p50=9.621 p75=49.817 p90=425.680 p99=3744.061 max=3824.075
+Dummy PSF all maximum_successive_triangle_jump_px: min=0.000 p10=0.000 p25=0.000 p50=8.750 p75=25.157 p90=144.000 p99=3744.034 max=3792.034
+Dummy PSF all adaptive criterion: 36516/36524 chunks tile16-eligible (events>=8192 and events/occupied_32px_tiles>=32)
+Dummy PSF full events: min=16384.000 p10=16384.000 p25=16384.000 p50=16384.000 p75=16384.000 p90=16384.000 p99=16384.000 max=16384.000
+Dummy PSF full distinct_triangles: min=1.000 p10=1.000 p25=1.000 p50=2.000 p75=3.000 p90=10.000 p99=31.000 max=59.000
+Dummy PSF full occupied_32px_tiles: min=1.000 p10=1.000 p25=1.000 p50=1.000 p75=2.000 p90=5.000 p99=30.000 max=45.000
+Dummy PSF full event_bbox_diagonal_px: min=0.199 p10=0.742 p25=3.250 p50=12.651 p75=57.018 p90=429.306 p99=3759.261 max=3834.557
+Dummy PSF full triangle_centroid_bbox_diagonal_px: min=0.000 p10=0.000 p25=0.000 p50=9.618 p75=49.477 p90=424.149 p99=3744.061 max=3824.075
+Dummy PSF full maximum_successive_triangle_jump_px: min=0.000 p10=0.000 p25=0.000 p50=8.724 p75=25.157 p90=144.000 p99=3744.034 max=3792.034
+Dummy PSF full adaptive criterion: 36508/36508 chunks tile16-eligible (events>=8192 and events/occupied_32px_tiles>=32)
+Dummy PSF producers: 16 workers; classification/chunk wall 232.340 s
+Frame 0: catalog classification finished in 232.3 s; reporting chunk statistics...
+Dummy PSF classified 598264924 images from 343363141 catalog stars; no HDR, PNG, or PPM was written.
+PSF splats: cached 598264924, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+PROCESS_WALL 288.871615309 EXIT 0
+PROCESS_USER 3815.986955000 PROCESS_SYSTEM 12.140569000 MAX_RSS_KIB 13769936
+PROTECTED_AFTER output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png sha256=3e01feb911e60acce545a6a86870ca05f96250022e874eb8097bec88a8879bfd size=13072572 mtime_ns=1788744728751407011 unchanged=yes
+PROTECTED_AFTER output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu_HDR.fits sha256=2408e62dcc22f147da284d87af9a2b0fdd0050eda2dabc23b6ec2554b2f1d38e size=99535680 mtime_ns=1788744726380022561 unchanged=yes
@@ -0,0 +1,6 @@
+COMMAND OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE /usr/bin/time -v /home/wyj/Code/C/GR_4d_raytracing/build/Release/schwarzschild_sky_dummy --verbose --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 --all-sky-catalog assets/2mass/processed/all_sky --exposure 1e13 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --catalog-load-workers 4 --hdr-output --lens-map-input output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens --output output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 c71a843a6064cd730b4694c5fe4e61249a995106526da0fdca97bc625c7db470
+LENS_SHA256 905f960aea2d276f9586c79fba545a72cf742311e9e7e18faea293835c68bf28
+PROTECTED_BEFORE output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png sha256=3e01feb911e60acce545a6a86870ca05f96250022e874eb8097bec88a8879bfd size=13072572 mtime_ns=1788744728751407011
+PROTECTED_BEFORE output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu_HDR.fits sha256=2408e62dcc22f147da284d87af9a2b0fdd0050eda2dabc23b6ec2554b2f1d38e size=99535680 mtime_ns=1788744726380022561
@@ -0,0 +1,99 @@
+#!/usr/bin/env python3
+"""Run the fixed full-catalog dummy diagnostic once without touching images."""
+
+import fcntl
+import hashlib
+import os
+from pathlib import Path
+import resource
+import shlex
+import signal
+import subprocess
+import time
+
+ROOT = Path(__file__).resolve().parents[2]
+LOG = Path(__file__).with_name("full_catalog.log")
+BINARY = ROOT / "build/Release/schwarzschild_sky_dummy"
+LENS = ROOT / "output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens"
+PNG = ROOT / "output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png"
+FITS = ROOT / "output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu_HDR.fits"
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def main():
+    if LOG.exists():
+        raise RuntimeError(f"refusing to overwrite {LOG}")
+    for path in (BINARY, LENS, PNG, FITS):
+        if not path.is_file():
+            raise RuntimeError(f"required file is missing: {path}")
+    protected_before = {
+        path: (digest(path), path.stat().st_size, path.stat().st_mtime_ns)
+        for path in (PNG, FITS)
+    }
+    command = [
+        str(BINARY), "--verbose",
+        "--psf-relative-tail", "1e-8", "--psf-min-y", "0",
+        "--max-cache-psf-flux", "1e8",
+        "--all-sky-catalog", "assets/2mass/processed/all_sky",
+        "--exposure", "1e13", "--psf-fwhm-pixels", "2.7",
+        "--psf-moffat-beta", "4.5", "--catalog-load-workers", "4",
+        "--hdr-output", "--lens-map-input",
+        "output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens",
+        "--output",
+        "output/imgs/2mass_galactic_center_schwarzschild_R100_4k_1e13_beta4.5_16_4-full-gpu.png",
+    ]
+    guard = open("/tmp/gr_dummy_psf_chunks.lock", "w")
+    fcntl.flock(guard, fcntl.LOCK_EX | fcntl.LOCK_NB)
+    env = dict(os.environ, OMP_NUM_THREADS="16", OMP_DYNAMIC="FALSE")
+    with LOG.open("x") as out:
+        out.write("COMMAND OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE " +
+                  shlex.join(command) + "\n")
+        out.write("GIT " + subprocess.check_output(
+            ["git", "rev-parse", "HEAD"], cwd=ROOT, text=True))
+        out.write("BINARY_SHA256 " + digest(BINARY) + "\n")
+        out.write("LENS_SHA256 " + digest(LENS) + "\n")
+        for path, state in protected_before.items():
+            out.write(
+                f"PROTECTED_BEFORE {path.relative_to(ROOT)} sha256={state[0]} "
+                f"size={state[1]} mtime_ns={state[2]}\n")
+        out.flush()
+        start = time.monotonic()
+        usage_start = resource.getrusage(resource.RUSAGE_CHILDREN)
+        process = subprocess.Popen(command, cwd=ROOT, env=env, stdout=out,
+                                   stderr=subprocess.STDOUT,
+                                   start_new_session=True)
+        try:
+            returncode = process.wait(timeout=600)
+        except subprocess.TimeoutExpired:
+            os.killpg(process.pid, signal.SIGKILL)
+            process.wait()
+            out.write("TIMEOUT killed and reaped process group\n")
+            raise
+        out.write(
+            f"PROCESS_WALL {time.monotonic() - start:.9f} EXIT {returncode}\n")
+        usage_end = resource.getrusage(resource.RUSAGE_CHILDREN)
+        out.write(
+            f"PROCESS_USER {usage_end.ru_utime - usage_start.ru_utime:.9f} "
+            f"PROCESS_SYSTEM {usage_end.ru_stime - usage_start.ru_stime:.9f} "
+            f"MAX_RSS_KIB {usage_end.ru_maxrss}\n")
+    protected_after = {
+        path: (digest(path), path.stat().st_size, path.stat().st_mtime_ns)
+        for path in (PNG, FITS)
+    }
+    if protected_after != protected_before:
+        raise RuntimeError("a protected render output changed")
+    with LOG.open("a") as out:
+        for path, state in protected_after.items():
+            out.write(
+                f"PROTECTED_AFTER {path.relative_to(ROOT)} sha256={state[0]} "
+                f"size={state[1]} mtime_ns={state[2]} unchanged=yes\n")
+    if returncode:
+        raise RuntimeError(f"dummy diagnostic exited {returncode}")
+    print(LOG)
+
+
+if __name__ == "__main__":
+    main()
@@ -0,0 +1,108 @@
+# Fast-mode CPU benchmark (2026-09-18)
+
+Compares the default per-event phase-cache PSF splat with `--fast-mode` on a
+7.4-degree 2MASS galactic-center field. Commands, raw terminal output, and
+wall-clock totals are preserved below.
+
+## Environment
+
+- Git revision: `7ddc585` plus the uncommitted fast-mode work.
+- Build: `make -j4 PSF_BACKEND=cpu SPACETIME=minkowski backend`
+  (`-O2 -DNDEBUG -fopenmp`, libpng).
+- Host: 12th Gen Intel Core i7-12700K, 16 hardware threads.
+
+## Commands
+
+All runs use the same catalog, geometry, and exposure; only the accumulation
+mode changes. `--all-sky-catalog assets/2mass/processed/all_sky`,
+`--width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29
+--exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0`.
+
+```sh
+./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --output /tmp/fastmode/bench/normal.png
+
+./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --fast-mode --fast-supersample 2 \
+  --output /tmp/fastmode/bench/fast_n2.png
+
+./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --fast-mode --fast-supersample 4 \
+  --output /tmp/fastmode/bench/fast_n4.png
+
+./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --fast-mode --fast-supersample 2 --fast-deposit bilinear \
+  --output /tmp/fastmode/bench/fast_bil_n2.png
+```
+
+## Wall-clock totals
+
+Measured with `date +%s.%N` around each command.
+
+| run | wall time | images |
+| --- | --- | --- |
+| normal (phase cache) | 16.645 s | 5,912,840 |
+| fast nearest N=2 | 1.663 s | 5,912,840 |
+| fast bilinear N=2 | 1.648 s | 5,912,840 |
+| fast nearest N=4 | 12.229 s | 5,912,840 |
+
+Fast nearest N=2 is about 10x faster than the phase-cache path on this
+PSF-dominated field. N=4 increases the supersampled buffer and kernel area by
+4x each and becomes convolution-bound.
+
+## Raw terminal output
+
+```text
+===== normal.log =====
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000056 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.725 s
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.696 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/fastmode/bench/normal.png (ok)
+PSF splats: cached 5912840, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+===== fast_n2.log =====
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000045 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 2x, deposit nearest, kernel radius 93 ss px (46.50 final px), retained flux 1.000000, cached 4-point quadrature
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.708 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/fastmode/bench/fast_n2.png (ok)
+Fast PSF splats: deposited 5912840, wing-clipped 0, discarded below min-Y 0
+===== fast_n4.log =====
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000058 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 4x, deposit nearest, kernel radius 185 ss px (46.25 final px), retained flux 1.000000, cached 4-point quadrature
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.709 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/fastmode/bench/fast_n4.png (ok)
+Fast PSF splats: deposited 5912840, wing-clipped 0, discarded below min-Y 0
+===== fast_bil_n2.log =====
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000047 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 2x, deposit bilinear, kernel radius 93 ss px (46.50 final px), retained flux 1.000000, cached 4-point quadrature
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.712 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/fastmode/bench/fast_bil_n2.png (ok)
+Fast PSF splats: deposited 5912840, wing-clipped 0, discarded below min-Y 0
+```
+
+## Tone-mapped difference vs the normal render
+
+```text
+fast_n2     mean=1.1213 rms=1.7255 max=14 px>16=0/76800
+fast_n4     mean=0.5516 rms=0.9146 max=8 px>16=0/76800
+fast_bil_n2 mean=0.2091 rms=0.4793 max=16 px>16=0/76800
+```
+
+`mean`/`rms` are per-channel 8-bit differences; `px>16` counts pixels with any
+channel more than 16 levels from the normal render. No pixel exceeds 16 in any
+run. These are display-scale differences from the measured deposition tradeoff;
+they are not a bit-exact regression baseline.
@@ -0,0 +1,128 @@
+# Fast-mode deposition error experiment (2026-09-18)
+
+Decision this note settles: whether `--fast-mode` should deposit each point
+source image as a single nearest supersampled pixel or as 4 adjacent
+(bilinear) pixels before the one global PSF convolution and downscale.
+
+## Command
+
+```sh
+python3 scripts/fast_mode_deposit_error.py --phases 12 --grid 48 --tail 1e-6 --max-radius 64
+```
+
+## Model
+
+Reference = pixel-area integral of the normalized circular Moffat
+`M(r; α, β)`, `α = FWHM / (2 sqrt(2^(1/β) - 1))`, on the final grid, using
+8-point Gauss-Legendre quadrature. Fast image with supersample factor `N`:
+
+- deposit the event into the `N x N` supersampled grid (nearest = 1 cell,
+  bilinear = 4 adjacent cells);
+- convolve the whole ss buffer with the single global kernel
+  `k[m] = ∫_ss-cell m M(z; Nα, β) dz` (4-point quadrature);
+- downscale by averaging each `N x N` block, which together with the
+  unnormalised `N`-scaled kernel reproduces the final pixel-area integral.
+
+Metrics: `maxErr`/`rmsErr` are whole-image errors vs the direct image at the
+true position; `coreErr` is the worst central-3x3 pixel error; `FWHMerr`
+compares the fast image with a direct image at the same centroid, so it is a
+pure shape error (0 when deposition is exact at its snapped centre); `centErr`
+is the position quantization vs the true continuous star position; `beterr` is
+the deposition-induced Moffat beta change, isolated from the radial fit's own
+pixel-integration bias by comparing with a reference fit (reported only for
+FWHM >= 2 px). FWHM 1.0 / β 3.5 rows are sub-Nyquist and are not meaningful
+for the shape metrics.
+
+## Raw output
+
+```text
+Fast-mode deposition error experiment
+grid=48 phases=12 tail=1e-06 max_radius=64
+kernel quadrature = 4-point Gauss; reference = 8-point Gauss
+
+ FWHM  beta  N   deposit  R_ss   retain    maxErr    rmsErr   coreErr   centErr   FWHMerr    beterr
+---------------------------------------------------------------------------------------------------
+ 1.00  8.00  2   nearest    10  1.00000 6.333e-01 1.714e-02 6.333e-01 3.043e-01 1.733e-02       nan
+ 1.00  8.00  2  bilinear    10  1.00000 1.805e-01 3.972e-03 1.805e-01 2.722e-03 3.187e-01       nan
+ 1.00  8.00  3   nearest    14  1.00000 3.907e-01 1.061e-02 3.907e-01 1.847e-01 7.491e-03       nan
+ 1.00  8.00  3  bilinear    14  1.00000 7.587e-02 1.676e-03 7.587e-02 5.562e-03 1.816e-01       nan
+ 1.00  8.00  4   nearest    18  1.00000 2.608e-01 7.142e-03 2.608e-01 1.237e-01 3.665e-02       nan
+ 1.00  8.00  4  bilinear    18  1.00000 4.428e-02 9.775e-04 4.428e-02 3.395e-03 3.646e-02       nan
+
+ 2.70  8.00  2   nearest    24  1.00000 1.635e-01 8.693e-03 1.635e-01 2.946e-01 2.325e-08 5.061e-07
+ 2.70  8.00  2  bilinear    24  1.00000 4.339e-02 1.476e-03 4.339e-02 6.018e-09 4.046e-02 8.414e-02
+ 2.70  8.00  3   nearest    35  1.00000 9.597e-02 5.229e-03 9.597e-02 1.768e-01 1.465e-08 1.067e-06
+ 2.70  8.00  3  bilinear    35  1.00000 1.842e-02 6.387e-04 1.842e-02 2.437e-08 1.747e-02 4.029e-02
+ 2.70  8.00  4   nearest    46  1.00000 6.308e-02 3.488e-03 6.308e-02 1.179e-01 1.563e-08 2.905e-05
+ 2.70  8.00  4  bilinear    46  1.00000 1.011e-02 3.418e-04 1.011e-02 1.778e-08 9.355e-03 3.091e-02
+
+ 6.00  8.00  2   nearest    51  1.00000 7.012e-02 7.714e-03 7.012e-02 2.946e-01 1.617e-06 3.132e-06
+ 6.00  8.00  2  bilinear    51  1.00000 9.563e-03 6.146e-04 9.563e-03 8.749e-08 6.686e-03 1.039e-02
+ 6.00  8.00  3   nearest    64  1.00000 4.199e-02 4.631e-03 4.199e-02 1.768e-01 7.456e-10 3.315e-08
+ 6.00  8.00  3  bilinear    64  1.00000 4.090e-03 2.640e-04 4.090e-03 9.147e-06 2.683e-03 4.463e-03
+ 6.00  8.00  4   nearest    64  0.99994 2.795e-02 3.088e-03 2.795e-02 1.179e-01 2.631e-07 9.889e-06
+ 6.00  8.00  4  bilinear    64  0.99994 2.195e-03 1.409e-04 2.195e-03 9.262e-06 1.528e-03 2.354e-03
+
+ 1.00  4.50  2   nearest    19  1.00000 6.006e-01 1.643e-02 6.006e-01 3.041e-01 1.516e-02       nan
+ 1.00  4.50  2  bilinear    19  1.00000 1.745e-01 3.823e-03 1.745e-01 2.673e-03 2.485e-01       nan
+ 1.00  4.50  3   nearest    28  1.00000 3.712e-01 1.016e-02 3.712e-01 1.846e-01 6.881e-03       nan
+ 1.00  4.50  3  bilinear    28  1.00000 7.354e-02 1.616e-03 7.354e-02 5.429e-03 1.432e-01       nan
+ 1.00  4.50  4   nearest    36  1.00000 2.480e-01 6.842e-03 2.480e-01 1.236e-01 3.167e-02       nan
+ 1.00  4.50  4  bilinear    36  1.00000 4.269e-02 9.383e-04 4.269e-02 3.322e-03 3.640e-02       nan
+
+ 2.70  4.50  2   nearest    49  1.00000 1.625e-01 8.537e-03 1.625e-01 2.946e-01 9.993e-07 1.210e-06
+ 2.70  4.50  2  bilinear    49  1.00000 4.413e-02 1.439e-03 4.413e-02 5.868e-07 4.453e-02 4.843e-02
+ 2.70  4.50  3   nearest    64  1.00000 9.571e-02 5.135e-03 9.571e-02 1.768e-01 1.482e-07 2.493e-07
+ 2.70  4.50  3  bilinear    64  1.00000 1.871e-02 6.228e-04 1.871e-02 3.673e-06 1.867e-02 2.057e-02
+ 2.70  4.50  4   nearest    64  0.99999 6.299e-02 3.426e-03 6.299e-02 1.179e-01 1.817e-07 4.228e-07
+ 2.70  4.50  4  bilinear    64  0.99999 1.030e-02 3.333e-04 1.030e-02 3.726e-06 9.995e-03 1.353e-02
+
+ 6.00  4.50  2   nearest    64  0.99998 6.924e-02 7.554e-03 6.924e-02 2.945e-01 1.290e-04 1.735e-04
+ 6.00  4.50  2  bilinear    64  0.99998 9.859e-03 6.016e-04 9.859e-03 2.462e-06 7.468e-03 9.748e-03
+ 6.00  4.50  3   nearest    64  0.99978 4.153e-02 4.535e-03 4.153e-02 1.775e-01 2.110e-08 3.706e-08
+ 6.00  4.50  3  bilinear    64  0.99978 4.214e-03 2.585e-04 4.214e-03 7.436e-04 3.203e-03 4.204e-03
+ 6.00  4.50  4   nearest    64  0.99872 2.767e-02 3.024e-03 2.767e-02 1.185e-01 3.310e-06 1.891e-04
+ 6.00  4.50  4  bilinear    64  0.99872 2.264e-03 1.485e-04 2.264e-03 7.451e-04 1.709e-03 2.399e-03
+
+ 1.00  3.50  2   nearest    35  1.00000 5.809e-01 1.600e-02 5.809e-01 3.038e-01 1.370e-02       nan
+ 1.00  3.50  2  bilinear    35  1.00000 1.708e-01 3.732e-03 1.708e-01 2.601e-03 2.192e-01       nan
+ 1.00  3.50  3   nearest    52  1.00000 3.594e-01 9.895e-03 3.594e-01 1.843e-01 6.403e-03       nan
+ 1.00  3.50  3  bilinear    52  1.00000 7.210e-02 1.579e-03 7.210e-02 5.255e-03 1.252e-01       nan
+ 1.00  3.50  4   nearest    64  1.00000 2.402e-01 6.660e-03 2.402e-01 1.234e-01 2.661e-02       nan
+ 1.00  3.50  4  bilinear    64  1.00000 4.170e-02 9.143e-04 4.170e-02 3.223e-03 3.644e-02       nan
+
+ 2.70  3.50  2   nearest    64  1.00000 1.619e-01 8.440e-03 1.619e-01 2.946e-01 2.790e-05 2.602e-05
+ 2.70  3.50  2  bilinear    64  1.00000 4.461e-02 1.417e-03 4.461e-02 3.036e-07 4.689e-02 3.892e-02
+ 2.70  3.50  3   nearest    64  0.99997 9.553e-02 5.077e-03 9.553e-02 1.769e-01 3.421e-07 3.302e-07
+ 2.70  3.50  3  bilinear    64  0.99997 1.889e-02 6.133e-04 1.889e-02 8.121e-05 2.016e-02 1.646e-02
+ 2.70  3.50  4   nearest    64  0.99989 6.293e-02 3.387e-03 6.293e-02 1.179e-01 8.537e-07 5.529e-06
+ 2.70  3.50  4  bilinear    64  0.99989 1.042e-02 3.282e-04 1.042e-02 8.142e-05 1.066e-02 1.038e-02
+
+Worst case over all tested configurations, by deposit scheme:
+    nearest: maxErr=6.333e-01 rmsErr=1.714e-02 coreErr=6.333e-01 centErr=3.043e-01 FWHMerr=3.665e-02 beterr=1.891e-04
+   bilinear: maxErr=1.805e-01 rmsErr=3.972e-03 coreErr=1.805e-01 centErr=5.562e-03 FWHMerr=3.187e-01 beterr=8.414e-02
+```
+
+## Conclusion
+
+For the production PSF (FWHM 2.7, β 4.5):
+
+| N | deposit | core HDR err | image RMS | centroid err | FWHM err | beta change |
+|---|---|---|---|---|---|---|
+| 2 | nearest | 16.3% | 0.85% | 0.295 px | ~0 | ~1.2e-6 |
+| 2 | bilinear | 4.4% | 0.14% | ~0 | +4.45% | +4.8% |
+| 3 | nearest | 9.6% | 0.51% | 0.177 px | ~0 | ~2.5e-7 |
+| 3 | bilinear | 1.9% | 0.06% | ~0 | +1.87% | +2.1% |
+| 4 | nearest | 6.3% | 0.34% | 0.118 px | ~0 | ~4.2e-7 |
+| 4 | bilinear | 1.0% | 0.03% | ~0 | +1.0% | +1.4% |
+
+- Nearest preserves the specified FWHM/β exactly (kernel-only shape and beta
+  error at the numerical floor); its only error is a bounded position
+  quantization of `0.5/N` output pixels.
+- Bilinear recovers the sub-pixel centroid exactly and roughly quarters the
+  HDR error, but broadens the profile because it interpolates the kernel
+  samples rather than the continuous kernel; it therefore changes the
+  specified FWHM and beta unless separately compensated.
+- A single fixed global convolution cannot provide both. `--fast-mode` default
+  is therefore `nearest`; `--fast-deposit bilinear` is available as an
+  explicit position-over-shape approximation.
@@ -0,0 +1,509 @@
+# Fast-mode FFTW convolution benchmark (2026-09-25)
+
+Replaces the spatial fast-mode global convolution with a reusable FFTW linear
+convolution. This record separates one-time plan/setup from steady-state
+execution and repeats the bounded Galactic-center comparison. Raw resolver and
+end-to-end output is pasted verbatim from the runs below.
+
+The later production-density 4K comparison is recorded separately against the
+first committed FFTW implementation, revision
+`229f50cd864d9768324042c10edbb56bfc120f08`.
+
+## Environment
+
+- Git revision: `3deebfb` plus the uncommitted FFTW work.
+- Host: 12th Gen Intel Core i7-12700K, 16 hardware threads, 128 GB.
+- FFTW: `pkg-config --modversion fftw3_omp` = `3.3.10`;
+  `pkg-config --libs fftw3_omp` = `-lfftw3_omp -lfftw3`.
+- Build:
+  `make -j8 BUILD_TYPE=Release PSF_BACKEND=cpu SPACETIME=minkowski backend`
+  (`-O2 -DNDEBUG -fopenmp -march=native`, libpng, `-DFAST_PSF_FFTW`).
+- Binary SHA-256 (this run):
+  - `build/Release/minkowski_sky`:
+    `ead2a543b8166abe6f82bc1cd41b2e985a6db517aa45a6416d08d188138b8c47`
+  - `build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw`:
+    `8da8bbd532104a0c4f524aabf40b66a50c8c715e44479c7db467669ab5a21215`
+- Timing wrapper: `/usr/bin/time` is not installed on this host. The
+  reproducible wrapper used for the end-to-end runs is zsh's built-in `time`
+  with `TIMEFMT='real=%*E user=%U sys=%S cpu=%P'`, i.e. each command was run as
+  `TIMEFMT='real=%*E user=%U sys=%S cpu=%P'; time <command>`. The `real=...`
+  lines below are the verbatim wrapper output.
+
+## Correctness
+
+```sh
+make -j8 BUILD_TYPE=Debug PSF_BACKEND=cpu SPACETIME=minkowski test
+```
+
+All C tests pass, including the dedicated FFTW-vs-spatial test (258 comparisons
+over sizes `17x13`/`16x16`/`23x31`/`33x17`, `N = 1..4`, nearest and bilinear,
+eight scenes; worst `max_abs = 1.8e-14`), the `test_frame` fast-mode
+regressions, the non-fast FITS references, and both camera CLI checks. HIP and
+dummy renderers compile and link without FFTW; `make PSF_BACKEND=dummy test`
+now fails fast with `make test requires PSF_BACKEND=cpu` instead of reusing a
+stale CPU test binary.
+
+## Resolver-only benchmark
+
+One deterministic sparse impulse buffer, default PSF (FWHM 2.7, beta 4.5,
+relative tail 1e-8), `OMP_NUM_THREADS=16`. `--spatial` additionally runs the
+reference resolver on the identical buffer. Binary:
+`build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw`.
+
+### Default 320x240 N=2, FFTW_ESTIMATE
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 320 --height 240 --supersample 2 --repeats 7 --spatial
+```
+
+```text
+impulse: 320x240 supersample=2 deposit=nearest repeats=7 spatial=1
+plan_mode=estimate
+setup: init=0.039444 s fftw_plan=0.008085 s kernel_fft=0.005237 s
+Fast FFTW: linear min=666x826, fft=672x840, workers=16, plan=estimate, plan=0.008085 s, kernel_fft=0.005237 s, scratch=30.2 MiB
+impulse_hash=5334fa90cfbb1089
+fftw: min=0.005602 s median=0.006455 s max=0.008144 s
+fftw samples: 0.006697 0.005784 0.005602 0.005898 0.006455 0.007675 0.008144
+fftw_hdr_hash=9ad60d92992c9bbd
+spatial: 0.702470 s
+spatial_hdr_hash=9327ac3e8e10d670
+difference: max_abs=7.49e-16 peak=0.359 speedup=108.831x
+rss_max_kb=52908
+```
+
+### Default 320x240 N=4, FFTW_ESTIMATE
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 320 --height 240 --supersample 4 --repeats 7 --spatial
+```
+
+```text
+impulse: 320x240 supersample=4 deposit=nearest repeats=7 spatial=1
+plan_mode=estimate
+setup: init=0.114719 s fftw_plan=0.007169 s kernel_fft=0.011942 s
+Fast FFTW: linear min=1330x1650, fft=1344x1680, workers=16, plan=estimate, plan=0.007169 s, kernel_fft=0.011942 s, scratch=120.7 MiB
+impulse_hash=2639864ea9d3a26a
+fftw: min=0.034756 s median=0.039591 s max=0.042474 s
+fftw samples: 0.041352 0.039591 0.034756 0.040866 0.042474 0.035364 0.036241
+fftw_hdr_hash=1ff070fdaac85f4a
+spatial: 11.054385 s
+spatial_hdr_hash=7682ee8550f88efe
+difference: max_abs=5.38e-15 peak=0.533 speedup=279.214x
+rss_max_kb=161032
+```
+
+### Medium 960x540 N=2, FFTW_ESTIMATE (FFTW only)
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 960 --height 540 --supersample 2 --repeats 7
+```
+
+```text
+impulse: 960x540 supersample=2 deposit=nearest repeats=7 spatial=0
+plan_mode=estimate
+setup: init=0.042270 s fftw_plan=0.006317 s kernel_fft=0.010302 s
+Fast FFTW: linear min=1266x2106, fft=1280x2160, workers=16, plan=estimate, plan=0.006317 s, kernel_fft=0.010302 s, scratch=147.7 MiB
+impulse_hash=6e2de17f6859cd33
+fftw: min=0.038361 s median=0.039872 s max=0.055834 s
+fftw samples: 0.055834 0.038745 0.039872 0.038823 0.038361 0.048436 0.040141
+fftw_hdr_hash=c493dbb793d04706
+rss_max_kb=216272
+```
+
+### 4K 3840x2160 N=2, FFTW_ESTIMATE (FFTW only)
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 3840 --height 2160 --supersample 2 --repeats 5
+```
+
+```text
+impulse: 3840x2160 supersample=2 deposit=nearest repeats=5 spatial=0
+plan_mode=estimate
+setup: init=0.524840 s fftw_plan=0.008154 s kernel_fft=0.482906 s
+Fast FFTW: linear min=4506x7866, fft=4536x7875, workers=16, plan=estimate, plan=0.008154 s, kernel_fft=0.482906 s, scratch=1907.8 MiB
+impulse_hash=e3b6d7f3d621630d
+fftw: min=2.368634 s median=2.481927 s max=2.553895 s
+fftw samples: 2.552212 2.553895 2.481927 2.389895 2.368634
+fftw_hdr_hash=1c5720f72a040e6d
+rss_max_kb=2879596
+```
+
+### 4K 3840x2160 N=4, FFTW_ESTIMATE (FFTW only)
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 3840 --height 2160 --supersample 4 --repeats 5
+```
+
+```text
+impulse: 3840x2160 supersample=4 deposit=nearest repeats=5 spatial=0
+plan_mode=estimate
+setup: init=0.738771 s fftw_plan=0.003636 s kernel_fft=0.599235 s
+Fast FFTW: linear min=9010x15730, fft=9072x15750, workers=16, plan=estimate, plan=0.003636 s, kernel_fft=0.599235 s, scratch=7631.4 MiB
+impulse_hash=e6a528db0fb16c33
+fftw: min=3.276609 s median=3.339285 s max=3.369411 s
+fftw samples: 3.309935 3.369411 3.276609 3.345614 3.339285
+fftw_hdr_hash=e55bed24ef3f5506
+rss_max_kb=10919208
+```
+
+### FFTW_ESTIMATE versus FFTW_MEASURE
+
+`FFTW_MEASURE` cuts steady-state time but costs a large one-time plan. Because
+the plan is created once per process and reused across frames, it only pays off
+for long movie renders; production therefore defaults to `FFTW_ESTIMATE`.
+Wisdom import/export would make `FFTW_MEASURE` the better default and remains a
+follow-up. Measured FFTW_MEASURE plan output is not bit-reproducible (plan
+measurement is timing-dependent), so its `fftw_hdr_hash` may differ run to run;
+the spatial comparison stays at roundoff.
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 320 --height 240 --supersample 2 --repeats 7 --measure --spatial
+```
+
+```text
+impulse: 320x240 supersample=2 deposit=nearest repeats=7 spatial=1
+plan_mode=measure
+setup: init=1.584388 s fftw_plan=1.091687 s kernel_fft=0.467405 s
+Fast FFTW: linear min=666x826, fft=672x840, workers=16, plan=measure, plan=1.091687 s, kernel_fft=0.467405 s, scratch=30.2 MiB
+impulse_hash=5334fa90cfbb1089
+fftw: min=0.003995 s median=0.004702 s max=0.005804 s
+fftw samples: 0.003995 0.004702 0.004330 0.005804 0.004939 0.004986 0.004619
+fftw_hdr_hash=626e386cba92ffa5
+spatial: 0.706244 s
+spatial_hdr_hash=9327ac3e8e10d670
+difference: max_abs=8.05e-16 peak=0.359 speedup=150.198x
+rss_max_kb=51860
+```
+
+```sh
+OMP_NUM_THREADS=16 ./build/Release/obj/minkowski/standard_sink1_cpu/benchmark_fast_psf_fftw \
+  --width 3840 --height 2160 --supersample 2 --repeats 5 --measure
+```
+
+```text
+impulse: 3840x2160 supersample=2 deposit=nearest repeats=5 spatial=0
+plan_mode=measure
+setup: init=41.408673 s fftw_plan=41.239987 s kernel_fft=0.134272 s
+Fast FFTW: linear min=4506x7866, fft=4536x7875, workers=16, plan=measure, plan=41.239987 s, kernel_fft=0.134272 s, scratch=1907.8 MiB
+impulse_hash=e3b6d7f3d621630d
+fftw: min=0.518707 s median=0.522181 s max=0.539465 s
+fftw samples: 0.523380 0.539465 0.518707 0.520357 0.522181
+fftw_hdr_hash=ab90c4b076c775e1
+rss_max_kb=2884132
+```
+
+## End-to-end bounded comparison
+
+Same catalog, geometry, exposure, supersample factors, and worker environment as
+`benchmarks/fast_mode_cpu_2026-09-18.md`. Raw terminal output including the
+timing wrapper:
+
+```sh
+OMP_NUM_THREADS=16 TIMEFMT='real=%*E user=%U sys=%S cpu=%P' \
+  time ./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --output /tmp/opencode/fastmode_fftw_bench/normal.png
+```
+
+```text
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000046 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.776 s
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.729 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/opencode/fastmode_fftw_bench/normal.png (ok)
+PSF splats: cached 5912840, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+real=17.526 user=225.46s sys=2.44s cpu=1300%
+```
+
+```sh
+OMP_NUM_THREADS=16 TIMEFMT='real=%*E user=%U sys=%S cpu=%P' \
+  time ./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --fast-mode --fast-supersample 2 \
+  --output /tmp/opencode/fastmode_fftw_bench/fast_n2.png
+```
+
+```text
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000049 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 2x, deposit nearest, kernel radius 93 ss px (46.50 final px), retained flux 1.000000, cached 4-point quadrature
+Fast FFTW: linear min=666x826, fft=672x840, workers=16, plan=estimate, plan=0.007770 s, kernel_fft=0.005020 s, scratch=30.2 MiB
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.735 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/opencode/fastmode_fftw_bench/fast_n2.png (ok)
+Fast PSF splats: deposited 5912840, wing-clipped 0, discarded below min-Y 0
+real=0.995 user=5.30s sys=0.18s cpu=550%
+```
+
+```sh
+OMP_NUM_THREADS=16 TIMEFMT='real=%*E user=%U sys=%S cpu=%P' \
+  time ./build/Release/minkowski_sky --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 320 --height 240 --fov-deg 10 --look-ra-deg 266 --look-dec-deg -29 \
+  --exposure 1e13 --coarse-cell-pixels 16 --refine-max-level 0 \
+  --fast-mode --fast-supersample 4 \
+  --output /tmp/opencode/fastmode_fftw_bench/fast_n4.png
+```
+
+```text
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000044 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 4x, deposit nearest, kernel radius 185 ss px (46.25 final px), retained flux 1.000000, cached 4-point quadrature
+Fast FFTW: linear min=1330x1650, fft=1344x1680, workers=16, plan=estimate, plan=0.007294 s, kernel_fft=0.012307 s, scratch=120.7 MiB
+Catalog prefetch: 96 requested, 96 newly loaded (6618807 stars), 0 unavailable in 0.722 s; 4 loader workers
+Rendered 5912840 images from 6618807 catalog stars to /tmp/opencode/fastmode_fftw_bench/fast_n4.png (ok)
+Fast PSF splats: deposited 5912840, wing-clipped 0, discarded below min-Y 0
+real=1.033 user=5.56s sys=0.22s cpu=559%
+```
+
+Image counts are identical across normal and both fast runs (5,912,840), so the
+FFTW resolver did not change catalog/deposit behavior. Output SHA-256:
+
+```text
+normal.png   e9f0a98ae7a3c3db546a3f276f400be98c96446fab7bfbc632f388702d4722d1
+fast_n2.png  1f144aefb4a5520d9d76a13ab69026a72580663e5e45f53128a87a0801176ccf
+fast_n4.png  679f14a67a085f76c144ecbe36af51b3b2534c152e8ef59708a7884a3f7c8464
+```
+
+## Production-density 4K Galactic-center comparison
+
+This is the full 3840x2160, 50-degree-field run over the local processed 2MASS
+all-sky catalog, not the bounded 320x240 comparison above.
+
+### Provenance
+
+- Git revision: `229f50cd864d9768324042c10edbb56bfc120f08`
+  (`Feat: Use FFTW linear convolution for CPU fast-mode PSF resolve`).
+- The tracked worktree matched that revision when this record was written; the
+  unrelated untracked `nmesh_spacetime_output_format.md` was not an input.
+- Executable: `build/Release/minkowski_sky`, built at
+  `2026-09-25 23:16:45 -0400`, before the three runs below; size 146,856 bytes;
+  SHA-256
+  `7f6486285b2ff498adb2d4f1acaf62dc96b11125c9cec114f572b9379648962c`.
+  A Make dry-run after the commit requested only the Makefile's unconditional
+  `FORCE` relink and no object recompilation, so the recorded binary used the
+  object set corresponding to the committed tracked sources.
+- Host: 12th Gen Intel Core i7-12700K, 16 hardware threads, 128 GB. The commands
+  did not explicitly set `OMP_NUM_THREADS`; fast-mode initialization reported
+  `workers=16`.
+- Input: `assets/2mass/processed/all_sky`, observed when recording as 64,801
+  regular files and 16,207,861,727 bytes. The renderer selected 1,742 tiles and
+  loaded 54,509,992 stars in each run. No content manifest hash was recorded for
+  this external processed catalog.
+- Timing: zsh built-in `time`; its final timing line is included verbatim for
+  each command.
+
+### Standard cached spatial PSF
+
+```sh
+time ./build/Release/minkowski_sky \
+  --psf-relative-tail 1e-6 --psf-min-y 1e-8 --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 3840 --height 2160 \
+  --look-ra-deg 262.5 --look-dec-deg -30 \
+  --fov-deg 50 \
+  --coarse-cell-pixels 16 \
+  --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 3 \
+  --catalog-load-workers 4 \
+  --hdr-output \
+  --output output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-base.png
+```
+
+```text
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000130 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+PSF cache ready: 64x64 phases, radius 85 px, relative tail 1e-06, tail abs 1e-06, boundary 1e-07, build 2.176 s
+Catalog prefetch: 1742 requested, 1742 newly loaded (54509992 stars), 0 unavailable in 5.886 s; 4 loader workers
+Rendered 52544535 images from 54509992 catalog stars to output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-base.png (ok)
+PSF splats: cached 52477581, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 66954
+Warning: --psf-min-y discarded one or more PSF events.
+./build/Release/minkowski_sky --psf-relative-tail 1e-6 --psf-min-y 1e-8  1e8   938.60s user 15.80s system 1391% cpu 1:08.61 total
+```
+
+### Fast mode, N=2
+
+```sh
+time ./build/Release/minkowski_sky --fast-mode --fast-supersample 2 \
+  --psf-relative-tail 1e-6 --psf-min-y 1e-8 --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 3840 --height 2160 \
+  --look-ra-deg 262.5 --look-dec-deg -30 \
+  --fov-deg 50 \
+  --coarse-cell-pixels 16 \
+  --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 3 \
+  --catalog-load-workers 4 \
+  --hdr-output \
+  --output output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2.png
+```
+
+```text
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000101 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 2x, deposit nearest, kernel radius 169 ss px (84.50 final px), retained flux 0.999999, cached 4-point quadrature
+Fast FFTW: linear min=4658x8018, fft=4704x8064, workers=16, plan=estimate, plan=0.005275 s, kernel_fft=0.141445 s, scratch=2026.1 MiB
+Catalog prefetch: 1742 requested, 1742 newly loaded (54509992 stars), 0 unavailable in 5.873 s; 4 loader workers
+Rendered 52544535 images from 54509992 catalog stars to output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2.png (ok)
+Fast PSF splats: deposited 52477581, wing-clipped 0, discarded below min-Y 66954
+./build/Release/minkowski_sky --fast-mode --fast-supersample 2  1e-6  1e-8     115.74s user 2.08s system 763% cpu 15.439 total
+```
+
+### Fast mode, N=4
+
+```sh
+time ./build/Release/minkowski_sky --fast-mode --fast-supersample 4 \
+  --psf-relative-tail 1e-6 --psf-min-y 1e-8 --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky \
+  --width 3840 --height 2160 \
+  --look-ra-deg 262.5 --look-dec-deg -30 \
+  --fov-deg 50 \
+  --coarse-cell-pixels 16 \
+  --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 3 \
+  --catalog-load-workers 4 \
+  --hdr-output \
+  --output output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4.png
+```
+
+```text
+Fast mode is a preview approximation; --max-cache-psf-flux is ignored and one global kernel is used for every event.
+Blackbody LUT: 1024 CIE 1931 2-deg 1 nm-linear XYZ nodes, T=[670.146556, 101408.88] K, loaded assets/blackbody/cie1931_2deg_xyz_1024.grbblut in 0.000043 s; payload fnv1a64=0e39867b0e70a809
+Blackbody backend: lut
+Fast PSF: supersample 4x, deposit nearest, kernel radius 336 ss px (84.00 final px), retained flux 0.999999, cached 4-point quadrature
+Fast FFTW: linear min=9312x16032, fft=9375x16128, workers=16, plan=estimate, plan=0.005384 s, kernel_fft=0.743673 s, scratch=8075.5 MiB
+Catalog prefetch: 1742 requested, 1742 newly loaded (54509992 stars), 0 unavailable in 5.796 s; 4 loader workers
+Rendered 52544535 images from 54509992 catalog stars to output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4.png (ok)
+Fast PSF splats: deposited 52477581, wing-clipped 0, discarded below min-Y 66954
+./build/Release/minkowski_sky --fast-mode --fast-supersample 4  1e-6  1e-8     135.62s user 5.04s system 722% cpu 19.469 total
+```
+
+### Artifacts and comparison
+
+```text
+05517bde1383327043691ac4b713f638b03ebf6dc72207fe8710a8dce747a03e  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-base.png
+86e9220feac277d77eba87aa8d0febadca5f4eea35cb56164a4eb1578b20fccd  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2.png
+5dfef3b4bd39d9809463594a1065c32c65ad397396514664c8aa22a5da6d780b  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4.png
+1ea508d1ee787c2e5f35ccdf37ca5f4a58e9ff5e9984b50928d66ecf88c44c3d  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-base_HDR.fits
+71de3f1e11cb9f811f5d08ea45b51baf5968e8523873873d6f7c414c1849ba53  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2_HDR.fits
+554848e39fdfb3b4815fb8f2a591b8d356cbdeaaea235a73f19b46017a18e42a  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4_HDR.fits
+```
+
+All three runs produced 52,544,535 images and applied the same event filtering:
+52,477,581 cached/deposited events, no wing clipping or direct fallback, and
+66,954 events (0.12742334% of rendered images) discarded by `--psf-min-y`.
+
+Using the standard HDR buffer as the reference, with
+`relative_L2 = ||fast - base||_2 / ||base||_2`, the existing FITS artifacts give:
+
+| Mode | Wall time | Wall speedup | Approx. speedup after subtracting catalog prefetch | User-CPU speedup | Scratch | HDR relative L2 | HDR total-flux ratio | Tone-mapped PNG normalized RMSE |
+|---|---:|---:|---:|---:|---:|---:|---:|---:|
+| Standard | 68.610 s | 1.000x | 1.000x | 1.000x | n/a | 0 | 1 | 0 |
+| Fast N=2 | 15.439 s | 4.444x | 6.557x | 8.110x | 2026.1 MiB | 10.4384% | 1.000176588 | 0.00678916 |
+| Fast N=4 | 19.469 s | 3.524x | 4.587x | 6.921x | 8075.5 MiB | 4.37249% | 1.000178510 | 0.00365798 |
+
+The post-prefetch figures subtract only the renderer-reported catalog prefetch
+duration from wall time; they are useful context, not isolated PSF timings. N=4
+costs 26.1% more wall time and 3.986x the scratch of N=2, while reducing the HDR
+relative-L2 difference by about 58% and the tone-mapped PNG RMSE by about 46%.
+The nearly identical `+0.0177%` total-flux offset for N=2 and N=4 shows that the
+larger N primarily improves spatial placement rather than global photometry.
+For the intended rapid single-frame exposure/PSF preview, N=2 is therefore the
+default throughput point; N=4 is the higher-fidelity preview option.
+
+### Error distribution across the image
+
+The unweighted relative L2 above is dominated by a small number of very bright
+PSF cores, so it understates how well the dense faint-star texture is
+reproduced in this still frame. `scripts/fast_mode_error_decomposition.py`
+reports the error over the flattened scalar RGB channel samples:
+
+```sh
+python3 scripts/fast_mode_error_decomposition.py \
+  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-base_HDR.fits \
+  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2_HDR.fits \
+  output/imgs/2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4_HDR.fits
+```
+
+```text
+===== 2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-2_HDR.fits =====  relative_L2=10.4384%
+top |d| RGB samples:  sq-error energy   base energy   linear-RGB sum   sample share
+  top   0.0010%:  69.136%     48.948%     2.822%     0.0010%
+  top   0.0100%:  95.732%     87.994%     9.141%     0.0100%
+  top   0.1000%:  99.365%     97.633%    16.396%     0.1000%
+  top   1.0000%:  99.893%     99.224%    25.984%     1.0000%
+  top  10.0000%:  99.988%     99.679%    46.006%    10.0000%
+base-value range (disjoint):  rel_RMS   signed bias   base energy %   linear-RGB sum %   samples
+  [1e-06,0.001):    4.7788%     +0.7665%     0.000%    0.001%  67026
+  [0.001,0.0599):    4.5658%     +0.1902%     0.013%   11.063%  12374574
+  [0.0599,0.1):    4.6294%     +0.1297%     0.027%   10.881%  4486724
+  [0.1,0.229):    4.9079%     +0.0866%     0.124%   25.365%  5466556
+  [0.229,0.769):    6.9340%     +0.0100%     0.301%   24.638%  2239488
+  [0.769,4.62):   11.4421%     -0.0990%     0.615%   10.315%  223948
+  [4.62,inf):   10.4475%     -0.1789%    98.921%   17.738%  24884
+
+===== 2mass_galactic_center_flat_4k_50deg_1e13_beta3-fast-4_HDR.fits =====  relative_L2=4.3725%
+top |d| RGB samples:  sq-error energy   base energy   linear-RGB sum   sample share
+  top   0.0010%:  65.911%     35.557%     2.418%     0.0010%
+  top   0.0100%:  94.540%     86.397%     8.879%     0.0100%
+  top   0.1000%:  99.108%     96.708%    16.179%     0.1000%
+  top   1.0000%:  99.848%     99.208%    25.909%     1.0000%
+  top  10.0000%:  99.982%     99.694%    45.966%    10.0000%
+base-value range (disjoint):  rel_RMS   signed bias   base energy %   linear-RGB sum %   samples
+  [1e-06,0.001):    2.4187%     +0.5689%     0.000%    0.001%  67026
+  [0.001,0.0599):    2.2772%     +0.0729%     0.013%   11.063%  12374574
+  [0.0599,0.1):    2.3129%     +0.0550%     0.027%   10.881%  4486724
+  [0.1,0.229):    2.4542%     +0.0393%     0.124%   25.365%  5466556
+  [0.229,0.769):    3.4700%     +0.0166%     0.301%   24.638%  2239488
+  [0.769,4.62):    5.6752%     -0.0189%     0.615%   10.315%  223948
+  [4.62,inf):    4.3682%     -0.0469%    98.921%   17.738%  24884
+```
+
+The FITS RGB channels are flattened into scalar samples: `sq-error energy` is
+the fraction of `||fast-base||^2`, `linear-RGB sum` is the sum of baseline
+linear-RGB sample values (proportional to total flux, not a per-source
+photometry), and the base-value ranges partition all samples and sum to 100%.
+
+The top 0.01% of RGB channel samples account for 95.7% (`N=2`) or 94.5%
+(`N=4`) of squared-error energy and about 9% of the baseline linear-RGB sum.
+The flux-bearing faint ranges (`[1e-3,0.0599)`, `[0.0599,0.1)`, `[0.1,0.229)`,
+together ~47% of the linear-RGB sum) have 2.3-4.9% local relative RMS and
+signed bias of `+0.04%` to `+0.19%`; the many faint PSFs partially cancel. This
+is consistent with the concentrated bright-core difference being predominantly a
+bounded sub-pixel redistribution rather than a large net linear-RGB loss, and
+explains why this tone-mapped still PNG remains smooth despite the global
+relative L2.
+
+This comparison contains one independent frame only. It does not measure
+temporal coherence: nearest deposition jumps by `1/N` output pixel per axis
+when a moving image crosses a supersampled-cell boundary (`0.5 px` at `N=2`,
+`0.25 px` at `N=4`). Both can produce visible movie flicker and are not
+qualified here as visually faithful movie-output paths.
+
+## Reading
+
+- Steady-state FFTW is ~109x (N=2) and ~279x (N=4) faster than the spatial
+  reference at 320x240, and stays under ~0.06 s per frame at 960x540.
+- 4K N=2 resolves in ~2.5 s (ESTIMATE) or ~0.52 s (MEASURE) on this host; 4K N=4
+  needs ~7.6 GiB scratch and ~3.3 s (ESTIMATE).
+- FFTW-versus-spatial differences are floating-point roundoff (`max_abs` at the
+  `1e-15` level against peaks near `0.5`), not crop, wrap, channel, or
+  normalization errors.
+- At the committed revision, the production-density 4K Galactic-center run
+  completes in 15.439 s at N=2 versus 68.610 s for the standard path (4.444x
+  end-to-end), with identical catalog image/deposit/filter counts. N=4 trades
+  26.1% more wall time for materially lower spatial error.
+- The 4K still-frame error is concentrated: the top 0.01% of RGB channel
+  samples hold ~95% of the squared-error energy but only ~9% of the baseline
+  linear-RGB sum, while the flux-bearing faint-value ranges stay at ~2-5% local
+  relative RMS with signed bias at or below ~0.2%. This does not establish
+  temporal fidelity.
@@ -0,0 +1,204 @@
+# HIP PSF 有界排查与优化（2026-09-07）
+
+后续用户完成了全天空 CPU/HIP 配对运行，并确认 PNG 比特级一致；见
+[完整 4K 记录](2mass_galactic_center_cpu_hip_2026-09-07.md)，其中记录了本次优化提交的实际 hash。
+本页保留提交前有界排查的原始上下文。
+
+## 范围与结论
+
+本次没有运行用户的完整 343,363,141 星 / 598,308,919 星像任务。
+所有 renderer/benchmark 都单进程顺序执行，前一个退出后才启动下一个；单次微基准
+45 秒超时，缩小 renderer 60 秒超时。没有并发性能测试，没有删除原 render 输出。
+
+源码基线为 `265d7b95d5b916ec4768d174d73ad963a43f0088`，优化版是此基线上的未提交改动。
+最初保留了用户现存 HIP binary；另从该 Git commit 的干净源码重建旧版，以复核对照。
+主机 HIP 7.2.53210-9999，AMD Radeon RX 9070 / gfx1201；性能测试设置
+`OMP_NUM_THREADS=16`，catalog loaders 为 4。Release / `-O2`；HIP 显式
+`--offload-arch=gfx1201`。完整元数据见 [metadata.log](hip_psf_2026-09-07/metadata.log)。
+
+已确认的实现问题与处理：
+
+- 旧 HIP 分支将 catalog 查询、逆映射、频移与黑体积分串行化。现在按 triangle 使用
+  OpenMP producer，每 worker 一个 16,384-event 私有块，GPU cache/HDR 只分配一次。
+- 旧 kernel 一线程串行遍历一个 PSF，double atomic 编译为 64-bit CAS 重试循环。
+  现在每个 event 用 32 线程访问相邻像素；保持四点 phase cache、圆形 support 和
+  double RGB 累积。分布实验支持这一改变，不把全部 kernel 时间归因为 atomic 竞争。
+- 旧 host 缓冲是可立即复用的普通 malloc 数组；现在 sink 同步复制进自己拥有的两个
+  pinned slot，重用 host/device slot 前等待上一 kernel 完成，生命周期不依赖 pageable
+  `hipMemcpyAsync` 的运行时暂存行为。GPU copy/kernel 仍在同一 stream 内顺序执行。
+- 旧计时只覆盖前 64 批。现在两个 slot 的计时 event 循环使用，统计全部批次，并约每
+  5 秒在提交时打印进度。完成数是已回收计时的完成数，最多有两个未回收 slot。
+- chunk 提交与整个 CPU direct-fallback 的 download/evaluate/upload 持有同一共享锁。
+  没有 per-star 锁，没有共享可变 CPU scratch，没有改变 backend 错误时立即失败的行为。
+
+未使用分桶规约、float HDR、近似黑体积分或改变 min-Y/tail 参数。
+
+## 受控 kernel 实验
+
+使用 `tests/benchmark_hip_psf.hip` 生成固定 LCG seed 12345 的相同事件。frame 3840×2160，
+FWHM 2.7，beta 4.5，tail 1e-8，cache radius 47；每个事件 56 B。
+每个进程先计算串行 CPU double HDR reference，再执行一个 HIP replay。CPU reference
+耗时不是 production 16-thread CPU render 的性能基线。
+
+| 事件数 | 中心分布范围 | 旧 kernel | 32-thread kernel 原型 | 比值 |
+| ---: | ---: | ---: | ---: | ---: |
+| 4,096 | 16 px | 22.490 ms | 5.702 ms | 3.94× |
+| 16,384 | 1 px | 137.888 ms | 23.976 ms | 5.75× |
+| 16,384 | 3840 px（y 限于2160） | 55.630 ms | 21.492 ms | 2.59× |
+
+原型阶段仅改变 kernel 的线程分工，保留旧上传和计时实现，便于隔离效果。
+原始输出：[旧密集](hip_psf_2026-09-07/baseline_dense.log)、
+[新密集](hip_psf_2026-09-07/wave_dense.log)、
+[旧热点](hip_psf_2026-09-07/baseline_hotspot.log)、
+[新热点](hip_psf_2026-09-07/wave_hotspot.log)、
+[旧分散](hip_psf_2026-09-07/baseline_spread.log)、
+[新分散](hip_psf_2026-09-07/wave_spread.log)。
+
+整合双缓冲后的 65,536-event/16px replay：4/4 批均计时，kernel 78.268 ms，replay wall
+83.762 ms；CPU reference 842.402 ms。double HDR max_abs `1.7053025658242404e-13`，
+max_rel `3.3472443502765663e-15`，总 RGB flux 相对差 `-1.3316774058238102e-17`。
+[原始输出](hip_psf_2026-09-07/final_multibatch.log)。
+
+## 原 4K lens map 的真实 catalog 子集
+
+保留原文件 `output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens`：
+3840×2160、45°、65,817 vertices、130,882 triangles。未重新 tracing/refine。
+
+使用 tile 索引的主对照输入只有三个 tile：RA252/Dec048、RA262/Dec060、RA082/Dec090。
+每个 tile 均匀抽取最多 8192 行，共 21,087 颗星，产生 156,837 个星像。
+准备脚本和源/子集 SHA256：[prepare_inputs.py](hip_psf_2026-09-07/prepare_inputs.py)、
+[input_manifest.log](hip_psf_2026-09-07/input_manifest.log)。
+其余 tile 故意缺失，因此 prefetch 的 64,437 unavailable 是缩小输入条件，不是生产数据错误。
+
+| 实现 | catalog/splat（日志四舍五入） | GPU kernel 合计 | 完整进程 |
+| --- | ---: | ---: | ---: |
+| 原有 HIP binary | 1.9 s | 1.469529 s | 2.971 s |
+| 干净旧源码重建 HIP | 1.9 s | 1.496493 s | 3.016 s |
+| 优化 HIP | 0.4 s | 0.168641 s | 1.487 s |
+| CPU 16 workers | 0.6 s | — | 1.674 s |
+
+所有实现均 cached=156837、wing-clipped=0、direct=0、discarded=0。
+优化版 GPU 16 批全部计时；producer wall=0.326 s，worker generation 总和=2.053 s，
+submission/fallback 总和=1.157 s。worker wall 总和包含并发时间，不能加到 GPU 时间上。
+
+原始日志：[旧 HIP](hip_psf_2026-09-07/baseline_multi.log)、
+[优化 HIP](hip_psf_2026-09-07/final_multi.log)、[CPU](hip_psf_2026-09-07/cpu_multi.log)。
+干净源码旧版复核另见 [clean_baseline_multi.log](hip_psf_2026-09-07/clean_baseline_multi.log)。
+
+旧 HIP 与优化 HIP 的 kernel 时间相差约 8.7 倍、完整进程约 2 倍；这些是小规模单次测量，
+不是完整全天空的加速比。相较 CPU，本子集的完整进程收益较小，cache 初始化和 4K 输出
+占比较高。没有依此预测用户完整任务的完成时间。
+
+辅助诊断保留了同一 lens map 的单 CSV 模式：256 星及 8192 星。
+8192 星时旧/新 splat 为 4.4/0.6 秒，完整进程 5.489/1.706 秒。
+但单 CSV 会放大逐 triangle 扫描成本，不能用它代表生产 tile 索引的 CPU 占比。
+同 8192 星改用 tile 索引后，旧 kernel=0.171626 秒，新 kernel=0.028882 秒。
+日志：[256](hip_psf_2026-09-07/baseline_lens256.log)、
+[CSV旧](hip_psf_2026-09-07/baseline_lens8192.log)、
+[CSV新](hip_psf_2026-09-07/final_lens8192.log)、
+[索引旧](hip_psf_2026-09-07/baseline_indexed.log)、
+[索引新](hip_psf_2026-09-07/final_indexed.log)。
+
+## 验证
+
+- `make -j1 test`：通过；固定 HDR、camera、geodesic、frame、Schwarzschild、observer track、
+  catalog prefetch、CLI 和多线程 movie/lens map 回归均通过。
+  [完整日志](hip_psf_2026-09-07/cpu_regression.log)。
+- `test_hip_psf`：213 事件、71 次 submit，全部计时；覆盖 host 数组立即覆写、slot 复用、
+  画面边缘、wing clipping 和中途 CPU HDR 修改后继续 GPU。
+  [初次日志](hip_psf_2026-09-07/streaming_test.log)、
+  [最终重建后日志](hip_psf_2026-09-07/streaming_test_final.log)。
+- `tests/test_hip_renderer.py`：96×64、4 workers，先 CPU 后 HIP；验证 cached=2/direct=1
+  的混合场和 discarded=3 的 min-Y 场。统计一致、FITS float32 HDR payload 完全一致。
+  [完整日志](hip_psf_2026-09-07/renderer_regression.log)。
+- 4K 子集的旧/新 HIP 以及 CPU/新 HIP：24,883,200 个 FITS float32 样本完全一致；PNG
+  也一致。double 精度由上述 sink/replay tests 单独验证，未将 FITS 当作 double 文件。
+  [比较日志](hip_psf_2026-09-07/hdr_comparison.log)。
+- 在单个子进程设置 `ROCR_VISIBLE_DEVICES=''`，32×24 的显式 HIP render 报设备不可用、
+  非零退出且没有写图。[原始输出](hip_psf_2026-09-07/fail_fast.log)。
+- 初次 mixed fixture 使用 exposure=2 未越过 support 阈值，测试断言正确拒绝了无 fallback
+  的输入；依据源码改为 exposure=1000 后才通过。这是测试输入校正，非 production 修复。
+  [初次输出](hip_psf_2026-09-07/fixture_calibration_failed.log)。
+
+## 可复制命令
+
+以下使用 zsh 默认 `time`，不设置 GNU 风格 `TIMEFMT`。命令必须顺序执行；任何失败或
+超时后先确认前一个进程已退出。原始输出保存在上述链接，未只保留汇总值。
+
+```zsh
+# 从本仓库根目录执行；准备固定样本，输出源与子集哈希。
+python3 benchmarks/hip_psf_2026-09-07/prepare_inputs.py
+
+# 独立重建旧源码，不改变当前 checkout。
+mkdir -p /tmp/gr-hip-baseline-src
+git archive 265d7b95d5b916ec4768d174d73ad963a43f0088 Makefile src mk | tar -x -C /tmp/gr-hip-baseline-src
+make -j4 -C /tmp/gr-hip-baseline-src PSF_BACKEND=hip SPACETIME=schwarzschild ENABLE_HDR=1 \
+  HIP_CXXFLAGS='--offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic' backend
+
+# 当前实现与 CPU reference。
+make -j4 PSF_BACKEND=hip SPACETIME=schwarzschild ENABLE_HDR=1 \
+  HIP_CXXFLAGS='--offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic' backend hip-psf-test hip-psf-bench
+make -j4 PSF_BACKEND=cpu SPACETIME=schwarzschild ENABLE_HDR=1 backend
+
+render_args=(
+  --all-sky-catalog /tmp/gr-hip-catalog-multi --catalog-load-workers 4
+  --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8
+  --exposure 1e13 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --hdr-output
+  --lens-map-input output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens
+  --verbose
+)
+time OMP_NUM_THREADS=16 timeout --kill-after=5s 60s /tmp/gr-hip-baseline-src/build/Release/schwarzschild_sky_hip \
+  "${render_args[@]}" --output /tmp/gr-hip-clean-baseline-multi.png
+time OMP_NUM_THREADS=16 timeout --kill-after=5s 60s ./build/Release/schwarzschild_sky_hip \
+  "${render_args[@]}" --output /tmp/gr-hip-final-multi.png
+time OMP_NUM_THREADS=16 timeout --kill-after=5s 60s ./build/Release/schwarzschild_sky \
+  "${render_args[@]}" --output /tmp/gr-cpu-multi.png
+
+# 原有 binary 的初始记录使用 /tmp/gr-schwarzschild-hip-baseline，其他参数完全相同。
+# 单 tile 索引测试仅将 root 换为 /tmp/gr-hip-catalog-subset。
+# 单 CSV 诊断改用 --catalog benchmarks/hip_psf_2026-09-07/catalog_8192.csv
+# （或 catalog_256.csv），不用 --all-sky-catalog，输出到单独的 /tmp PNG。
+
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s ./build/Release/benchmark_hip_psf 65536 16
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s ./build/Release/test_hip_psf
+make -j1 test
+
+# 小尺寸 renderer 回归；先分别构建带 HDR 的 Minkowski CPU/HIP。
+make PSF_BACKEND=cpu SPACETIME=minkowski ENABLE_HDR=1 backend
+make PSF_BACKEND=hip SPACETIME=minkowski ENABLE_HDR=1 \
+  HIP_CXXFLAGS='--offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic' backend
+python3 tests/test_hip_renderer.py build/Release/minkowski_sky build/Release/minkowski_sky_hip
+python3 scripts/fits_floatdiff.py /tmp/gr-cpu-multi_HDR.fits /tmp/gr-hip-final-multi_HDR.fits
+```
+
+旧/新原型微基准可使用同一 `tests/benchmark_hip_psf.hip` 与基线 sink 源码编译：
+
+```zsh
+cp /tmp/gr-hip-baseline-src/src/hip_psf.hip /tmp/gr-hip-psf-baseline.hip
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -fopenmp -Isrc -x hip \
+  tests/benchmark_hip_psf.hip /tmp/gr-hip-psf-baseline.hip -x none \
+  build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o \
+  -lm -lpng -lcfitsio -o /tmp/hip_psf_bench_baseline
+python3 - <<'PY'
+from pathlib import Path
+s = Path('/tmp/gr-hip-psf-baseline.hip').read_text()
+s = s.replace('const size_t index = (size_t)blockIdx.x * blockDim.x + threadIdx.x;',
+              'const size_t thread = (size_t)blockIdx.x * blockDim.x + threadIdx.x;\n'
+              '  const size_t index = thread / 32;\n  const int lane = thread % 32;')
+s = s.replace('int offset_x = first; offset_x <= last; ++offset_x',
+              'int offset_x = first + lane; offset_x <= last; offset_x += 32')
+s = s.replace('(event_count + threads - 1) / threads',
+              '(event_count * 32 + threads - 1) / threads')
+Path('/tmp/gr-hip-psf-wave.hip').write_text(s)
+PY
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -fopenmp -Isrc -x hip \
+  tests/benchmark_hip_psf.hip /tmp/gr-hip-psf-wave.hip -x none \
+  build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o \
+  -lm -lpng -lcfitsio -o /tmp/hip_psf_bench_wave
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_baseline 4096 16
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_wave 4096 16
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_baseline 16384 1
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_wave 16384 1
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_baseline 16384 3840
+OMP_NUM_THREADS=16 timeout --kill-after=5s 45s /tmp/hip_psf_bench_wave 16384 3840
+```
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.661 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=4096 spread=16 frame=3840x2160 event_bytes=56 CPU_reference=0.051952 s
+HIP create=0.027773 replay_wall=0.027614 upload=0.000021 kernel=0.022490 download=0.004796 batches=1 timed=1 max_abs=4.7073456244106637e-14 max_rel=1.1345618109894268e-14 flux_rel=1.138425198954238e-16
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.681 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=16384 spread=1 frame=3840x2160 event_bytes=56 CPU_reference=0.210148 s
+HIP create=0.025685 replay_wall=0.143944 upload=0.000049 kernel=0.137888 download=0.005726 batches=1 timed=1 max_abs=2.6147972675971687e-12 max_rel=1.6347773919004679e-14 flux_rel=-2.3341330284619701e-16
@@ -0,0 +1,10 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.836 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 1 newly loaded (8192 stars), 64439 unavailable in 0.033 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: catalog splatting finished in 0.3 s; writing image...
+Rendered 12765 images from 8192 catalog stars to /tmp/gr-hip-baseline-indexed.png (ok; imported lens map)
+PSF splats: cached 12765, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 12765 events in 1 batches (1 timed); upload 0.000042 s, kernel 0.171626 s, download 0.025845 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    11.23s user 0.26s system 721% cpu 1.592 total
@@ -0,0 +1,9 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.709 s
+Frame 0: finding and prefetching catalog tiles...
+Frame 0: catalog prefetch finished (0 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: catalog splatting finished in 0.3 s; writing image...
+Rendered 411 images from 256 catalog stars to /tmp/gr-hip-baseline-256.png (ok; imported lens map)
+PSF splats: cached 411, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 411 events in 1 batches (1 timed); upload 0.000014 s, kernel 0.122597 s, download 0.021485 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --catalog  --psf-relative-tai  10.69s user 0.17s system 774% cpu 1.403 total
@@ -0,0 +1,9 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.694 s
+Frame 0: finding and prefetching catalog tiles...
+Frame 0: catalog prefetch finished (0 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: catalog splatting finished in 4.4 s; writing image...
+Rendered 12765 images from 8192 catalog stars to /tmp/gr-hip-baseline-8192.png (ok; imported lens map)
+PSF splats: cached 12765, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 12765 events in 1 batches (1 timed); upload 0.000041 s, kernel 0.171573 s, download 0.025041 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --catalog  --psf-relative-tai  14.92s user 0.17s system 274% cpu 5.489 total
@@ -0,0 +1,10 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.674 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 3 newly loaded (21087 stars), 64437 unavailable in 0.033 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: catalog splatting finished in 1.9 s; writing image...
+Rendered 156837 images from 21087 catalog stars to /tmp/gr-hip-baseline-multi.png (ok; imported lens map)
+PSF splats: cached 156837, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 156837 events in 10 batches (10 timed); upload 0.000312 s, kernel 1.469529 s, download 0.025304 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    12.51s user 0.24s system 429% cpu 2.971 total
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.677 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=16384 spread=3840 frame=3840x2160 event_bytes=56 CPU_reference=0.419966 s
+HIP create=0.023973 replay_wall=0.060952 upload=0.000049 kernel=0.055630 download=0.004973 batches=1 timed=1 max_abs=5.5511151231257827e-17 max_rel=1.0443479008602178e-15 flux_rel=-5.9614463770241093e-20
@@ -0,0 +1,16 @@
+make: Entering directory '/tmp/gr-hip-baseline-src'
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/catalog.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/catalog.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/frame.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/frame.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/geodesic.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/geodesic.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/lens_map.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/lens_map.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/movie.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/movie.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/observer.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/observer_track.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer_track.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/optics.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/ray.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/ray.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/spacetime_common.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_common.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/spacetime_schwarzschild.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_schwarzschild.o
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/main.c -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/main.o
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -Isrc -c src/hip_psf.hip -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o
+hipcc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_hip/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/main.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky_hip
+make: Leaving directory '/tmp/gr-hip-baseline-src'
@@ -0,0 +1,2 @@
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DSPACETIME_SCHWARZSCHILD -DENABLE_HDR_OUTPUT  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/frame.c -o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/frame.o
+cc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_cpu/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/main.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky
@@ -0,0 +1,3 @@
+hipcc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_hip/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/main.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky_hip
+make: Nothing to be done for 'hip-psf-test'.
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -fopenmp -Isrc -x hip tests/benchmark_hip_psf.hip -x none build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o -lm -lpng -lcfitsio -o build/Release/benchmark_hip_psf
@@ -0,0 +1,4 @@
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -Isrc -c src/hip_psf.hip -o build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o
+hipcc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_hip/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/main.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky_hip
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -fopenmp -Isrc -x hip tests/test_hip_psf.hip -x none build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o -lm -lpng -lcfitsio -o build/Release/test_hip_psf
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -fopenmp -Isrc -x hip tests/benchmark_hip_psf.hip -x none build/Release/obj/schwarzschild/hdr_sink1_hip/src/hip_psf.o build/Release/obj/schwarzschild/hdr_sink1_hip/src/optics.o -lm -lpng -lcfitsio -o build/Release/benchmark_hip_psf
@@ -0,0 +1,257 @@
+ra_deg,dec_deg,temperature_K,amplitude_sr
+252.995803,-41.503754,2122.6076,8.520470492e-21
+252.993551,-41.543816,2114.6385,9.967579356e-21
+252.918388,-41.510990,2208.128,1.446557073e-19
+252.900742,-41.506279,2279.2582,1.973490936e-18
+252.884436,-41.488571,2138.1302,1.410128710e-20
+252.986092,-41.597309,2129.5884,3.136569365e-20
+252.984711,-41.606659,2114.2229,9.627036994e-21
+252.924427,-41.399944,3134.4748,2.266711014e-21
+252.938142,-41.386372,5574.2493,7.758286100e-21
+252.958086,-41.625877,1617.2207,3.144977882e-19
+252.970634,-41.365410,2202.8994,1.648245643e-20
+252.810573,-41.475826,3941.0552,1.524175586e-21
+252.854571,-41.396477,2408.7178,2.646847276e-20
+252.974001,-41.655529,2217.0089,4.616359171e-20
+252.783806,-41.501965,2321.7548,7.149940580e-21
+252.782782,-41.459801,2703.1671,4.949843960e-20
+252.880635,-41.648254,2158.5784,8.959667114e-21
+252.832964,-41.372025,2223.318,6.324985653e-20
+252.781331,-41.583836,4289.9357,3.687496634e-21
+252.774616,-41.415287,2503.0345,3.528731590e-20
+252.781981,-41.604404,4481.0767,4.210660307e-21
+252.835709,-41.344860,2471.4445,7.859657597e-20
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+Frame 0: catalog prefetch finished (64440 candidate tiles).
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+Frame 0: catalog splatting finished in 1.9 s; writing image...
+Rendered 156837 images from 21087 catalog stars to /tmp/gr-hip-clean-baseline-multi.png (ok; imported lens map)
+PSF splats: cached 156837, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
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+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    12.48s user 0.25s system 421% cpu 3.016 total
@@ -0,0 +1,209 @@
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+Frame 0: splat worker 15/16 reached 256 local triangles.
+Frame 0: splat worker 16/16 reached 128 local triangles.
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+Frame 0: splat worker 11/16 reached 512 local triangles.
+Frame 0: splat worker 6/16 reached 1024 local triangles.
+Frame 0: splat worker 3/16 reached 1024 local triangles.
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+Frame 0: splat worker 10/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 1024 local triangles.
+Frame 0: splat worker 13/16 reached 2048 local triangles.
+Frame 0: splat worker 12/16 reached 1024 local triangles.
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+Frame 0: splat worker 15/16 reached 1024 local triangles.
+Frame 0: splat worker 9/16 reached 1024 local triangles.
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+Frame 0: splat worker 11/16 reached 1024 local triangles.
+Frame 0: splat worker 3/16 reached 2048 local triangles.
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+Frame 0: splat worker 5/16 reached 2048 local triangles.
+Frame 0: splat worker 9/16 reached 2048 local triangles.
+Frame 0: splat worker 6/16 reached 2048 local triangles.
+Frame 0: splat worker 13/16 reached 4096 local triangles.
+Frame 0: splat worker 12/16 reached 2048 local triangles.
+Frame 0: splat worker 7/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 4096 local triangles.
+Frame 0: splat worker 4/16 reached 4096 local triangles.
+Frame 0: splat worker 8/16 reached 4096 local triangles.
+Frame 0: splat worker 14/16 reached 4096 local triangles.
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+Frame 0: splat worker 15/16 reached 4096 local triangles.
+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 5/16 reached 4096 local triangles.
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+Frame 0: splat worker 13/16 reached 8192 local triangles.
+Frame 0: splat worker 7/16 reached 4096 local triangles.
+Frame 0: splat worker 16/16 reached 2048 local triangles.
+Frame 0: splat worker 9/16 reached 4096 local triangles.
+Frame 0: splat worker 12/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 4096 local triangles.
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+Frame 0: splat worker 15/16 reached 8192 local triangles.
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+Frame 0: splat worker 4/16 reached 8192 local triangles.
+Frame 0: splat worker 1/16 reached 8192 local triangles.
+Frame 0: splat worker 16/16 reached 4096 local triangles.
+Frame 0: splat worker 10/16 reached 4096 local triangles.
+Frame 0: splat worker 8/16 reached 8192 local triangles.
+Frame 0: splat worker 3/16 finished after 10458 local triangles.
+Frame 0: splat worker 16/16 finished after 4920 local triangles.
+Frame 0: splat worker 11/16 finished after 6992 local triangles.
+Frame 0: splat worker 10/16 finished after 4986 local triangles.
+Frame 0: splat worker 15/16 finished after 9498 local triangles.
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+Frame 0: splat worker 4/16 finished after 9108 local triangles.
+Frame 0: splat worker 12/16 finished after 7689 local triangles.
+Frame 0: splat worker 5/16 finished after 7943 local triangles.
+Frame 0: splat worker 14/16 finished after 9623 local triangles.
+Frame 0: splat worker 8/16 finished after 8856 local triangles.
+Frame 0: splat worker 1/16 finished after 9031 local triangles.
+Frame 0: splat worker 2/16 finished after 7194 local triangles.
+Frame 0: splat worker 9/16 finished after 7002 local triangles.
+Frame 0: splat worker 13/16 finished after 11036 local triangles.
+Frame 0: splat worker 7/16 finished after 7616 local triangles.
+Frame 0: catalog splatting finished in 0.6 s; writing image...
+Rendered 156837 images from 21087 catalog stars to /tmp/gr-cpu-multi.png (ok; imported lens map)
+PSF splats: cached 156837, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    17.59s user 1.25s system 1125% cpu 1.674 total
@@ -0,0 +1,41 @@
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_observer.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_minkowski.c -lm -lpng -o build/Release/test_observer_minkowski
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -DSPACETIME_SCHWARZSCHILD -Isrc tests/test_observer.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_schwarzschild.c -lm -lpng -o build/Release/test_observer_schwarzschild
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_geodesic.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_minkowski.c -lm -lpng -o build/Release/test_geodesic
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_frame.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_minkowski.c -lm -lpng -o build/Release/test_frame
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_schwarzschild.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_schwarzschild.c -lm -lpng -o build/Release/test_schwarzschild
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_observer_track.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c -lm -lpng -o build/Release/test_observer_track
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc tests/test_catalog_prefetch.c src/catalog.c src/frame.c src/geodesic.c src/lens_map.c src/movie.c src/observer.c src/observer_track.c src/optics.c src/ray.c src/spacetime_common.c src/spacetime_minkowski.c -lm -lpng -o build/Release/test_catalog_prefetch
+make SPACETIME=minkowski ENABLE_HDR=1 backend
+make[1]: Entering directory '/home/wyj/Code/C/GR_4d_raytracing'
+cc -O2 -DNDEBUG -fopenmp build/Release/obj/minkowski/hdr_sink1_cpu/src/catalog.o build/Release/obj/minkowski/hdr_sink1_cpu/src/frame.o build/Release/obj/minkowski/hdr_sink1_cpu/src/geodesic.o build/Release/obj/minkowski/hdr_sink1_cpu/src/lens_map.o build/Release/obj/minkowski/hdr_sink1_cpu/src/movie.o build/Release/obj/minkowski/hdr_sink1_cpu/src/observer.o build/Release/obj/minkowski/hdr_sink1_cpu/src/observer_track.o build/Release/obj/minkowski/hdr_sink1_cpu/src/optics.o build/Release/obj/minkowski/hdr_sink1_cpu/src/ray.o build/Release/obj/minkowski/hdr_sink1_cpu/src/spacetime_common.o build/Release/obj/minkowski/hdr_sink1_cpu/src/spacetime_minkowski.o build/Release/obj/minkowski/hdr_sink1_cpu/src/main.o -lm -lpng -lcfitsio -o build/Release/minkowski_sky
+make[1]: Leaving directory '/home/wyj/Code/C/GR_4d_raytracing'
+mkdir -p /tmp/gr_psf_event_sink_reference
+OMP_NUM_THREADS=16 build/Release/minkowski_sky --catalog assets/sky_grid_5deg.csv --output /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360.png --hdr-output --width 640 --height 360 --fov-deg 30 --look-ra-deg 1 --look-dec-deg 1 --exposure 0.1 --observer-radius 30 --observer-velocity 0 0 0 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --max-magnification 1e300 --max-cache-psf-flux 1 --psf-relative-tail 1e-8 --psf-min-y 0 --coarse-cell-pixels 16 --refine-max-level 0 --refine-angle-abs-deg 0.001 --refine-angle-rel 0.1 --refine-jacobian-min 1e-3 --refine-min-edge-pixels 0.5 --refine-min-area-pixels2 0.25 --catalog-load-workers 4
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.677 s
+Rendered 35 images from 5654 catalog stars to /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360.png (ok)
+PSF splats: cached 35, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+python3 scripts/fits_floatdiff.py tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits
+floatdiff: shape=(640, 360, 3) samples=691200 mismatches=0 max_abs=0 max_rel=0 worst_sample=0
+make SPACETIME=schwarzschild ENABLE_HDR=1 backend
+make[1]: Entering directory '/home/wyj/Code/C/GR_4d_raytracing'
+cc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_cpu/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/main.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky
+make[1]: Leaving directory '/home/wyj/Code/C/GR_4d_raytracing'
+OMP_NUM_THREADS=16 build/Release/schwarzschild_sky --catalog assets/sky_grid_5deg.csv --output /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360.png --hdr-output --width 640 --height 360 --fov-deg 60 --look-ra-deg 1 --look-dec-deg 1 --exposure 0.1 --observer-radius 30 --observer-velocity 0 0 0 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --max-magnification 1e300 --max-cache-psf-flux 1 --psf-relative-tail 1e-8 --psf-min-y 0 --coarse-cell-pixels 16 --refine-max-level 0 --refine-angle-abs-deg 0.001 --refine-angle-rel 0.1 --refine-jacobian-min 1e-3 --refine-min-edge-pixels 0.5 --refine-min-area-pixels2 0.25 --catalog-load-workers 4
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.670 s
+Rendered 5206 images from 5654 catalog stars to /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360.png (ok)
+PSF splats: cached 5206, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+python3 scripts/fits_floatdiff.py tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits
+floatdiff: shape=(640, 360, 3) samples=691200 mismatches=0 max_abs=0 max_rel=0 worst_sample=0
+./build/Release/test_observer_minkowski
+coordinate-camera regression passed
+./build/Release/test_observer_schwarzschild
+coordinate-camera regression passed
+./build/Release/test_geodesic
+./build/Release/test_frame
+./build/Release/test_schwarzschild
+./build/Release/test_observer_track
+./build/Release/test_catalog_prefetch
+python3 tests/test_camera_cli.py build/Release
+minkowski: CLI checks passed; single/movie PNG identical, map max error 0
+schwarzschild: movie lens map identical with 1, 4 and 16 threads
+schwarzschild: CLI checks passed; single/movie PNG identical, map max error 4.44e-16
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.636 s
+HIP PSF backend failed during initialization: no ROCm-capable device is detected
+exit_code=1
@@ -0,0 +1,208 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.674 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 1 newly loaded (8192 stars), 64439 unavailable in 0.034 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
+Frame 0: splat worker 13/16 started.
+Frame 0: splat worker 1/16 started.
+Frame 0: splat worker 9/16 started.
+Frame 0: splat worker 13/16 reached 8 local triangles.
+Frame 0: splat worker 4/16 started.
+Frame 0: splat worker 16/16 started.
+Frame 0: splat worker 15/16 started.
+Frame 0: splat worker 16/16 reached 8 local triangles.
+Frame 0: splat worker 11/16 started.
+Frame 0: splat worker 3/16 started.
+Frame 0: splat worker 7/16 started.
+Frame 0: splat worker 1/16 reached 8 local triangles.
+Frame 0: splat worker 3/16 reached 8 local triangles.
+Frame 0: splat worker 1/16 reached 16 local triangles.
+Frame 0: splat worker 12/16 started.
+Frame 0: splat worker 5/16 started.
+Frame 0: splat worker 9/16 reached 8 local triangles.
+Frame 0: splat worker 12/16 reached 8 local triangles.
+Frame 0: splat worker 9/16 reached 16 local triangles.
+Frame 0: splat worker 12/16 reached 16 local triangles.
+Frame 0: splat worker 4/16 reached 8 local triangles.
+Frame 0: splat worker 2/16 started.
+Frame 0: splat worker 16/16 reached 16 local triangles.
+Frame 0: splat worker 15/16 reached 8 local triangles.
+Frame 0: splat worker 11/16 reached 8 local triangles.
+Frame 0: splat worker 15/16 reached 16 local triangles.
+Frame 0: splat worker 8/16 started.
+Frame 0: splat worker 11/16 reached 16 local triangles.
+Frame 0: splat worker 7/16 reached 8 local triangles.
+Frame 0: splat worker 15/16 reached 32 local triangles.
+Frame 0: splat worker 8/16 reached 8 local triangles.
+Frame 0: splat worker 7/16 reached 16 local triangles.
+Frame 0: splat worker 13/16 reached 16 local triangles.
+Frame 0: splat worker 10/16 started.
+Frame 0: splat worker 4/16 reached 16 local triangles.
+Frame 0: splat worker 2/16 reached 8 local triangles.
+Frame 0: splat worker 10/16 reached 8 local triangles.
+Frame 0: splat worker 2/16 reached 16 local triangles.
+Frame 0: splat worker 10/16 reached 16 local triangles.
+Frame 0: splat worker 16/16 reached 32 local triangles.
+Frame 0: splat worker 3/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 32 local triangles.
+Frame 0: splat worker 11/16 reached 32 local triangles.
+Frame 0: splat worker 5/16 reached 8 local triangles.
+Frame 0: splat worker 8/16 reached 16 local triangles.
+Frame 0: splat worker 5/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 64 local triangles.
+Frame 0: splat worker 11/16 reached 64 local triangles.
+Frame 0: splat worker 8/16 reached 32 local triangles.
+Frame 0: splat worker 9/16 reached 32 local triangles.
+Frame 0: splat worker 12/16 reached 32 local triangles.
+Frame 0: splat worker 4/16 reached 32 local triangles.
+Frame 0: splat worker 6/16 started.
+Frame 0: splat worker 2/16 reached 32 local triangles.
+Frame 0: splat worker 1/16 reached 128 local triangles.
+Frame 0: splat worker 9/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 started.
+Frame 0: splat worker 16/16 reached 64 local triangles.
+Frame 0: splat worker 7/16 reached 32 local triangles.
+Frame 0: splat worker 13/16 reached 32 local triangles.
+Frame 0: splat worker 10/16 reached 32 local triangles.
+Frame 0: splat worker 7/16 reached 64 local triangles.
+Frame 0: splat worker 6/16 reached 8 local triangles.
+Frame 0: splat worker 3/16 reached 32 local triangles.
+Frame 0: splat worker 6/16 reached 16 local triangles.
+Frame 0: splat worker 4/16 reached 64 local triangles.
+Frame 0: splat worker 13/16 reached 64 local triangles.
+Frame 0: splat worker 10/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 8 local triangles.
+Frame 0: splat worker 15/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 16 local triangles.
+Frame 0: splat worker 1/16 reached 256 local triangles.
+Frame 0: splat worker 16/16 reached 128 local triangles.
+Frame 0: splat worker 9/16 reached 128 local triangles.
+Frame 0: splat worker 2/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 128 local triangles.
+Frame 0: splat worker 6/16 reached 32 local triangles.
+Frame 0: splat worker 5/16 reached 32 local triangles.
+Frame 0: splat worker 3/16 reached 64 local triangles.
+Frame 0: splat worker 15/16 reached 128 local triangles.
+Frame 0: splat worker 11/16 reached 128 local triangles.
+Frame 0: splat worker 7/16 reached 128 local triangles.
+Frame 0: splat worker 14/16 reached 32 local triangles.
+Frame 0: splat worker 4/16 reached 128 local triangles.
+Frame 0: splat worker 13/16 reached 128 local triangles.
+Frame 0: splat worker 10/16 reached 128 local triangles.
+Frame 0: splat worker 8/16 reached 64 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
+Frame 0: splat worker 14/16 reached 64 local triangles.
+Frame 0: splat worker 16/16 reached 256 local triangles.
+Frame 0: splat worker 3/16 reached 128 local triangles.
+Frame 0: splat worker 5/16 reached 64 local triangles.
+Frame 0: splat worker 9/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 128 local triangles.
+Frame 0: splat worker 12/16 reached 256 local triangles.
+Frame 0: splat worker 15/16 reached 256 local triangles.
+Frame 0: splat worker 14/16 reached 128 local triangles.
+Frame 0: splat worker 11/16 reached 256 local triangles.
+Frame 0: splat worker 7/16 reached 256 local triangles.
+Frame 0: splat worker 2/16 reached 256 local triangles.
+Frame 0: splat worker 5/16 reached 128 local triangles.
+Frame 0: splat worker 13/16 reached 256 local triangles.
+Frame 0: splat worker 4/16 reached 256 local triangles.
+Frame 0: splat worker 10/16 reached 256 local triangles.
+Frame 0: splat worker 1/16 reached 512 local triangles.
+Frame 0: splat worker 3/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 256 local triangles.
+Frame 0: splat worker 14/16 reached 256 local triangles.
+Frame 0: splat worker 5/16 reached 256 local triangles.
+Frame 0: splat worker 16/16 reached 512 local triangles.
+Frame 0: splat worker 9/16 reached 512 local triangles.
+Frame 0: splat worker 12/16 reached 512 local triangles.
+Frame 0: splat worker 15/16 reached 512 local triangles.
+Frame 0: splat worker 7/16 reached 512 local triangles.
+Frame 0: splat worker 13/16 reached 512 local triangles.
+Frame 0: splat worker 11/16 reached 512 local triangles.
+Frame 0: splat worker 2/16 reached 512 local triangles.
+Frame 0: splat worker 4/16 reached 512 local triangles.
+Frame 0: splat worker 10/16 reached 512 local triangles.
+Frame 0: splat worker 3/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 512 local triangles.
+Frame 0: splat worker 5/16 reached 512 local triangles.
+Frame 0: splat worker 1/16 reached 1024 local triangles.
+Frame 0: splat worker 13/16 reached 1024 local triangles.
+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 9/16 reached 1024 local triangles.
+Frame 0: splat worker 12/16 reached 1024 local triangles.
+Frame 0: splat worker 7/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 1024 local triangles.
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+Frame 0: splat worker 6/16 reached 256 local triangles.
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+Frame 0: splat worker 6/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 2048 local triangles.
+Frame 0: splat worker 6/16 reached 1024 local triangles.
+Frame 0: splat worker 4/16 reached 2048 local triangles.
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+Frame 0: splat worker 10/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 2048 local triangles.
+Frame 0: splat worker 1/16 reached 4096 local triangles.
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+Frame 0: splat worker 8/16 reached 4096 local triangles.
+Frame 0: splat worker 5/16 reached 4096 local triangles.
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+Frame 0: splat worker 10/16 reached 4096 local triangles.
+Frame 0: splat worker 16/16 reached 8192 local triangles.
+Frame 0: splat worker 3/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 8192 local triangles.
+Frame 0: splat worker 6/16 reached 2048 local triangles.
+Frame 0: splat worker 14/16 reached 4096 local triangles.
+Frame 0: splat worker 9/16 reached 8192 local triangles.
+Frame 0: splat worker 7/16 reached 4096 local triangles.
+Frame 0: splat worker 15/16 reached 2048 local triangles.
+Frame 0: splat worker 12/16 reached 8192 local triangles.
+Frame 0: splat worker 1/16 reached 8192 local triangles.
+Frame 0: splat worker 8/16 reached 8192 local triangles.
+Frame 0: splat worker 10/16 finished after 7675 local triangles.
+Frame 0: splat worker 15/16 finished after 3525 local triangles.
+Frame 0: splat worker 8/16 finished after 8466 local triangles.
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+Frame 0: splat worker 11/16 finished after 11275 local triangles.
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+Frame 0: splat worker 9/16 finished after 10796 local triangles.
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+Frame 0: splat worker 6/16 finished after 3431 local triangles.
+Frame 0: splat worker 16/16 finished after 8447 local triangles.
+HIP producers: 16 workers; summed generation 0.218 s, submission/fallback 0.205 s; wall 0.066 s
+Frame 0: catalog splatting finished in 0.1 s; writing image...
+Rendered 12765 images from 8192 catalog stars to /tmp/gr-hip-final-indexed.png (ok; imported lens map)
+PSF splats: cached 12765, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 12765 events in 15 batches (15 timed); upload 0.000218 s, kernel 0.028882 s, download 0.023217 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    11.10s user 0.26s system 940% cpu 1.208 total
@@ -0,0 +1,210 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.728 s
+Frame 0: finding and prefetching catalog tiles...
+Frame 0: catalog prefetch finished (0 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
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+Frame 0: splat worker 12/16 reached 16 local triangles.
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+Frame 0: splat worker 6/16 reached 64 local triangles.
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+Frame 0: splat worker 8/16 reached 128 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
+Frame 0: splat worker 10/16 reached 128 local triangles.
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+Frame 0: splat worker 7/16 reached 128 local triangles.
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+Frame 0: splat worker 6/16 reached 4096 local triangles.
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+Frame 0: splat worker 16/16 reached 4096 local triangles.
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+Frame 0: splat worker 5/16 reached 8192 local triangles.
+Frame 0: splat worker 6/16 reached 8192 local triangles.
+Frame 0: splat worker 15/16 reached 8192 local triangles.
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+Frame 0: splat worker 1/16 reached 8192 local triangles.
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+Frame 0: splat worker 1/16 finished after 8417 local triangles.
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+Frame 0: splat worker 12/16 finished after 8377 local triangles.
+Frame 0: catalog splatting finished in 0.6 s; writing image...
+Rendered 12765 images from 8192 catalog stars to /tmp/gr-hip-final-8192.png (ok; imported lens map)
+PSF splats: cached 12765, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 12765 events in 14 batches (14 timed); upload 0.000188 s, kernel 0.023472 s, download 0.025256 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --catalog  --psf-relative-tai  18.45s user 0.19s system 1092% cpu 1.706 total
@@ -0,0 +1,210 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.674 s
+Frame 0: finding and prefetching catalog tiles...
+Catalog prefetch: 64440 requested, 3 newly loaded (21087 stars), 64437 unavailable in 0.033 s; 4 loader workers
+Frame 0: catalog prefetch finished (64440 candidate tiles).
+Frame 0: splatting 130882 lens triangles...
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+Frame 0: splat worker 6/16 reached 32 local triangles.
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+Frame 0: splat worker 5/16 started.
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+Frame 0: splat worker 5/16 reached 32 local triangles.
+Frame 0: splat worker 5/16 reached 64 local triangles.
+Frame 0: splat worker 5/16 reached 128 local triangles.
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+Frame 0: splat worker 12/16 reached 8 local triangles.
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+Frame 0: splat worker 11/16 reached 8 local triangles.
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+Frame 0: splat worker 11/16 reached 32 local triangles.
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+Frame 0: splat worker 4/16 reached 64 local triangles.
+Frame 0: splat worker 2/16 reached 32 local triangles.
+Frame 0: splat worker 16/16 reached 128 local triangles.
+Frame 0: splat worker 3/16 reached 8 local triangles.
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+Frame 0: splat worker 11/16 reached 64 local triangles.
+Frame 0: splat worker 14/16 reached 64 local triangles.
+Frame 0: splat worker 1/16 reached 64 local triangles.
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+Frame 0: splat worker 13/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 32 local triangles.
+Frame 0: splat worker 14/16 reached 128 local triangles.
+Frame 0: splat worker 4/16 reached 128 local triangles.
+Frame 0: splat worker 7/16 reached 64 local triangles.
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+Frame 0: splat worker 3/16 reached 32 local triangles.
+Frame 0: splat worker 1/16 reached 128 local triangles.
+Frame 0: splat worker 3/16 reached 64 local triangles.
+Frame 0: splat worker 12/16 reached 64 local triangles.
+Frame 0: splat worker 9/16 reached 256 local triangles.
+Frame 0: splat worker 10/16 reached 16 local triangles.
+Frame 0: splat worker 15/16 reached 64 local triangles.
+Frame 0: splat worker 10/16 reached 32 local triangles.
+Frame 0: splat worker 3/16 reached 128 local triangles.
+Frame 0: splat worker 8/16 reached 32 local triangles.
+Frame 0: splat worker 2/16 reached 64 local triangles.
+Frame 0: splat worker 11/16 reached 128 local triangles.
+Frame 0: splat worker 10/16 reached 64 local triangles.
+Frame 0: splat worker 1/16 reached 256 local triangles.
+Frame 0: splat worker 12/16 reached 128 local triangles.
+Frame 0: splat worker 4/16 reached 256 local triangles.
+Frame 0: splat worker 8/16 reached 64 local triangles.
+Frame 0: splat worker 7/16 reached 128 local triangles.
+Frame 0: splat worker 16/16 reached 256 local triangles.
+Frame 0: splat worker 13/16 reached 128 local triangles.
+Frame 0: splat worker 3/16 reached 256 local triangles.
+Frame 0: splat worker 6/16 reached 256 local triangles.
+Frame 0: splat worker 13/16 reached 256 local triangles.
+Frame 0: splat worker 15/16 reached 128 local triangles.
+Frame 0: splat worker 2/16 reached 128 local triangles.
+Frame 0: splat worker 11/16 reached 256 local triangles.
+Frame 0: splat worker 7/16 reached 256 local triangles.
+Frame 0: splat worker 9/16 reached 512 local triangles.
+Frame 0: splat worker 5/16 reached 512 local triangles.
+Frame 0: splat worker 1/16 reached 512 local triangles.
+Frame 0: splat worker 10/16 reached 128 local triangles.
+Frame 0: splat worker 8/16 reached 128 local triangles.
+Frame 0: splat worker 14/16 reached 256 local triangles.
+Frame 0: splat worker 3/16 reached 512 local triangles.
+Frame 0: splat worker 10/16 reached 256 local triangles.
+Frame 0: splat worker 15/16 reached 256 local triangles.
+Frame 0: splat worker 12/16 reached 256 local triangles.
+Frame 0: splat worker 4/16 reached 512 local triangles.
+Frame 0: splat worker 2/16 reached 256 local triangles.
+Frame 0: splat worker 6/16 reached 512 local triangles.
+Frame 0: splat worker 11/16 reached 512 local triangles.
+Frame 0: splat worker 16/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 512 local triangles.
+Frame 0: splat worker 12/16 reached 512 local triangles.
+Frame 0: splat worker 8/16 reached 256 local triangles.
+Frame 0: splat worker 10/16 reached 512 local triangles.
+Frame 0: splat worker 3/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 512 local triangles.
+Frame 0: splat worker 7/16 reached 512 local triangles.
+Frame 0: splat worker 13/16 reached 512 local triangles.
+Frame 0: splat worker 5/16 reached 1024 local triangles.
+Frame 0: splat worker 9/16 reached 1024 local triangles.
+Frame 0: splat worker 4/16 reached 1024 local triangles.
+Frame 0: splat worker 1/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 512 local triangles.
+Frame 0: splat worker 16/16 reached 1024 local triangles.
+Frame 0: splat worker 6/16 reached 1024 local triangles.
+Frame 0: splat worker 11/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 1024 local triangles.
+Frame 0: splat worker 8/16 reached 512 local triangles.
+Frame 0: splat worker 14/16 reached 1024 local triangles.
+Frame 0: splat worker 12/16 reached 1024 local triangles.
+Frame 0: splat worker 3/16 reached 2048 local triangles.
+Frame 0: splat worker 10/16 reached 1024 local triangles.
+Frame 0: splat worker 7/16 reached 1024 local triangles.
+Frame 0: splat worker 2/16 reached 1024 local triangles.
+Frame 0: splat worker 5/16 reached 2048 local triangles.
+Frame 0: splat worker 16/16 reached 2048 local triangles.
+Frame 0: splat worker 4/16 reached 2048 local triangles.
+Frame 0: splat worker 11/16 reached 2048 local triangles.
+Frame 0: splat worker 6/16 reached 2048 local triangles.
+Frame 0: splat worker 14/16 reached 2048 local triangles.
+Frame 0: splat worker 3/16 reached 4096 local triangles.
+Frame 0: splat worker 12/16 reached 2048 local triangles.
+Frame 0: splat worker 8/16 reached 1024 local triangles.
+Frame 0: splat worker 15/16 reached 2048 local triangles.
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+Frame 0: splat worker 10/16 reached 2048 local triangles.
+Frame 0: splat worker 2/16 reached 2048 local triangles.
+Frame 0: splat worker 13/16 reached 1024 local triangles.
+Frame 0: splat worker 1/16 reached 2048 local triangles.
+Frame 0: splat worker 15/16 reached 4096 local triangles.
+Frame 0: splat worker 5/16 reached 4096 local triangles.
+Frame 0: splat worker 4/16 reached 4096 local triangles.
+Frame 0: splat worker 6/16 reached 4096 local triangles.
+Frame 0: splat worker 7/16 reached 2048 local triangles.
+Frame 0: splat worker 11/16 reached 4096 local triangles.
+Frame 0: splat worker 16/16 reached 4096 local triangles.
+Frame 0: splat worker 3/16 reached 8192 local triangles.
+Frame 0: splat worker 12/16 reached 4096 local triangles.
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+Frame 0: splat worker 13/16 reached 2048 local triangles.
+Frame 0: splat worker 10/16 reached 4096 local triangles.
+Frame 0: splat worker 8/16 reached 2048 local triangles.
+Frame 0: splat worker 9/16 reached 4096 local triangles.
+Frame 0: splat worker 1/16 reached 4096 local triangles.
+Frame 0: splat worker 7/16 reached 4096 local triangles.
+Frame 0: splat worker 15/16 reached 8192 local triangles.
+Frame 0: splat worker 4/16 reached 8192 local triangles.
+Frame 0: splat worker 10/16 reached 8192 local triangles.
+Frame 0: splat worker 2/16 reached 8192 local triangles.
+Frame 0: splat worker 8/16 reached 4096 local triangles.
+Frame 0: splat worker 13/16 reached 4096 local triangles.
+Frame 0: splat worker 11/16 reached 8192 local triangles.
+Frame 0: splat worker 16/16 reached 8192 local triangles.
+Frame 0: splat worker 1/16 finished after 7660 local triangles.
+Frame 0: splat worker 10/16 finished after 9346 local triangles.
+Frame 0: splat worker 4/16 finished after 9445 local triangles.
+Frame 0: splat worker 13/16 finished after 4644 local triangles.
+Frame 0: splat worker 11/16 finished after 8415 local triangles.
+Frame 0: splat worker 12/16 finished after 7133 local triangles.
+Frame 0: splat worker 14/16 finished after 7809 local triangles.
+Frame 0: splat worker 16/16 finished after 8215 local triangles.
+Frame 0: splat worker 15/16 finished after 10883 local triangles.
+Frame 0: splat worker 9/16 finished after 6522 local triangles.
+Frame 0: splat worker 5/16 finished after 8082 local triangles.
+Frame 0: splat worker 7/16 finished after 6345 local triangles.
+Frame 0: splat worker 2/16 finished after 8812 local triangles.
+Frame 0: splat worker 3/16 finished after 14980 local triangles.
+Frame 0: splat worker 6/16 finished after 7718 local triangles.
+Frame 0: splat worker 8/16 finished after 4873 local triangles.
+HIP producers: 16 workers; summed generation 2.053 s, submission/fallback 1.157 s; wall 0.326 s
+Frame 0: catalog splatting finished in 0.4 s; writing image...
+Rendered 156837 images from 21087 catalog stars to /tmp/gr-hip-final-multi.png (ok; imported lens map)
+PSF splats: cached 156837, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+HIP PSF: 156837 events in 16 batches (16 timed); upload 0.000565 s, kernel 0.168641 s, download 0.027545 s
+OMP_NUM_THREADS=16 timeout --kill-after=5s 60s  --all-sky-catalog   4  1e-8    13.75s user 0.26s system 941% cpu 1.487 total
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.671 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 spread=16 frame=3840x2160 event_bytes=56 CPU_reference=0.842402 s
+HIP create=0.031723 replay_wall=0.083762 upload=0.000203 kernel=0.078268 download=0.005152 batches=4 timed=4 max_abs=1.7053025658242404e-13 max_rel=3.3472443502765663e-15 flux_rel=-1.3316774058238102e-17
@@ -0,0 +1,13 @@
+RUN ['/home/wyj/Code/C/GR_4d_raytracing/build/Release/minkowski_sky', '--catalog', '/home/wyj/Code/C/GR_4d_raytracing/tests/data/hip_psf_mixed_catalog.csv', '--width', '96', '--height', '64', '--fov-deg', '30', '--look-ra-deg', '2', '--look-dec-deg', '1', '--coarse-cell-pixels', '16', '--refine-max-level', '0', '--exposure', '2', '--psf-fwhm-pixels', '2.7', '--psf-moffat-beta', '4.5', '--psf-relative-tail', '1e-8', '--max-cache-psf-flux', '1', '--psf-min-y', '0', '--hdr-output', '--output', '/tmp/gr-hip-renderer-test-z25me3rh/cpu-0.png']
+ PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.641 s
+Rendered 3 images from 3 catalog stars to /tmp/gr-hip-renderer-test-z25me3rh/cpu-0.png (ok)
+PSF splats: cached 3, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+
+Traceback (most recent call last):
+  File "/home/wyj/Code/C/GR_4d_raytracing/tests/test_hip_renderer.py", line 61, in <module>
+    main()
+    ~~~~^^
+  File "/home/wyj/Code/C/GR_4d_raytracing/tests/test_hip_renderer.py", line 47, in main
+    assert (stats[0], stats[2], stats[3]) == expected, stats
+           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+AssertionError: (3, 0, 0, 0)
@@ -0,0 +1,9 @@
+gr-hip-baseline-8192 gr-hip-final-8192 shape (3840, 2160, 3) samples 24883200 HDR_payload_exact True candidate_payload_sha256 423da7b025bf4815a5044e5d81c2f2330138cb8536b8058c19c9cba2d50f2f65
+PNG_exact True
+gr-hip-baseline-indexed gr-hip-final-indexed shape (3840, 2160, 3) samples 24883200 HDR_payload_exact True candidate_payload_sha256 423da7b025bf4815a5044e5d81c2f2330138cb8536b8058c19c9cba2d50f2f65
+PNG_exact True
+gr-hip-baseline-multi gr-hip-final-multi shape (3840, 2160, 3) samples 24883200 HDR_payload_exact True candidate_payload_sha256 a935becded15185af9e680aee9923ba51ecfee451a6bba34634a7e8be9a22ab8
+PNG_exact True
+gr-cpu-multi gr-hip-final-multi shape (3840, 2160, 3) samples 24883200 HDR_payload_exact True candidate_payload_sha256 a935becded15185af9e680aee9923ba51ecfee451a6bba34634a7e8be9a22ab8
+PNG_exact True
+clean baseline vs final: HDR_payload_exact True
@@ -0,0 +1,3 @@
+tile_ra252_dec048.csv source_stars 54160 sampled 8192 source_sha256 6ece2dc86b09709f3292a9d20f49d04cb53d520bd1b7d949f3a81306229ab48d sample_sha256 7c5516ff9ae92d0cfc8acfd67f578139a1ea2d3e2ca260cf9a382c38730d5095
+tile_ra262_dec060.csv source_stars 76933 sampled 8192 source_sha256 9cc74db30205fe63fe8feb5581abc892efad44a079499f9185c2b162861b0bd7 sample_sha256 f6c9b4b0db950a660102497376778981322ce95187b1311ae515070fd6a5b88f
+tile_ra082_dec090.csv source_stars 4703 sampled 4703 source_sha256 36f0713ac3c3d7cd849b5886a40228d1c535864e390cc5c055c80534aeef7b65 sample_sha256 36f0713ac3c3d7cd849b5886a40228d1c535864e390cc5c055c80534aeef7b65
@@ -0,0 +1,31 @@
+{
+  "base_commit": "265d7b95d5b916ec4768d174d73ad963a43f0088",
+  "optimized_source": "uncommitted worktree changes",
+  "compiler": "HIP version: 7.2.53210-9999\nclang version 22.1.8\nTarget: x86_64-pc-linux-gnu\nThread model: posix\nInstalledDir: /usr/lib/llvm/22/bin\nConfiguration file: /etc/clang/22/x86_64-pc-linux-gnu-clang++.cfg",
+  "hip_config_version": "7.2.53210-9999",
+  "kernel": "Linux 6.18.41-gentoo",
+  "cpu": [
+    "CPU(s):                                  16",
+    "Model name:                              12th Gen Intel(R) Core(TM) i7-12700K",
+    "Thread(s) per core:                      2",
+    "Core(s) per socket:                      8",
+    "NUMA node0 CPU(s):                       0-15"
+  ],
+  "OMP_NUM_THREADS": 16,
+  "catalog_workers": 4,
+  "hip_flags": "--offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic",
+  "cpu_flags": "-std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp",
+  "event_bytes": 56,
+  "event_capacity": 16384,
+  "device_staging_slots": 2,
+  "sha256": {
+    "src/frame.c": "338d24eaa89d2d4c1e5a7f34d08ca827db13bb79ac3a6caeb155a731390ab023",
+    "src/hip_psf.hip": "b93fed04034a97e1eb25f3fc234da995287bf0c3fcde50609f95b0b3f4052a75",
+    "src/hip_psf.h": "00502f3d95c30d4c3d346e49dcf0e3cb846b5d461c2bfd5b3f24c7257791fad0",
+    "tests/benchmark_hip_psf.hip": "56cccf515b66762acb824556681c9f6986c0ffe3e3346eeadac23bc6d5926aa4",
+    "build/Release/schwarzschild_sky_hip": "1c340e1d8ab008e892101b46132069255ab92eb0d200bd91b2b300a4f4dacf6e",
+    "/tmp/gr-schwarzschild-hip-baseline": "de945e3dc826d559e1f8218a56d24f524c06e5382c8aa43667f9ac1fe5d2d719",
+    "/tmp/gr-hip-baseline-src/build/Release/schwarzschild_sky_hip": "de945e3dc826d559e1f8218a56d24f524c06e5382c8aa43667f9ac1fe5d2d719",
+    "output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens": "905f960aea2d276f9586c79fba545a72cf742311e9e7e18faea293835c68bf28"
+  }
+}
@@ -0,0 +1,27 @@
+#!/usr/bin/env python3
+"""Recreate the bounded 2MASS samples used in this investigation."""
+import hashlib
+from pathlib import Path
+
+repo = Path(__file__).resolve().parents[2]
+source = repo / "assets/2mass/processed/all_sky"
+multi = Path("/tmp/gr-hip-catalog-multi")
+single = Path("/tmp/gr-hip-catalog-subset")
+multi.mkdir(exist_ok=True)
+single.mkdir(exist_ok=True)
+for name in ["tile_ra252_dec048.csv", "tile_ra262_dec060.csv", "tile_ra082_dec090.csv"]:
+    raw = (source / name).read_bytes()
+    rows = raw.decode().splitlines()
+    n = min(8192, len(rows) - 1)
+    sample = ("\n".join([rows[0]] + [rows[1 + i * (len(rows) - 1) // n]
+                                      for i in range(n)]) + "\n").encode()
+    (multi / name).write_bytes(sample)
+    if name == "tile_ra252_dec048.csv":
+        (single / name).write_bytes(sample)
+        (Path(__file__).parent / "catalog_8192.csv").write_bytes(sample)
+        small = "\n".join([rows[0]] + [rows[1 + i * (len(rows) - 1) // 256]
+                                        for i in range(256)]) + "\n"
+        (Path(__file__).parent / "catalog_256.csv").write_text(small)
+    print(name, "source_stars", len(rows) - 1, "sampled", n,
+          "source_sha256", hashlib.sha256(raw).hexdigest(),
+          "sample_sha256", hashlib.sha256(sample).hexdigest())
@@ -0,0 +1,27 @@
+RUN ['/home/wyj/Code/C/GR_4d_raytracing/build/Release/minkowski_sky', '--catalog', '/home/wyj/Code/C/GR_4d_raytracing/tests/data/hip_psf_mixed_catalog.csv', '--width', '96', '--height', '64', '--fov-deg', '30', '--look-ra-deg', '2', '--look-dec-deg', '1', '--coarse-cell-pixels', '16', '--refine-max-level', '0', '--exposure', '1000', '--psf-fwhm-pixels', '2.7', '--psf-moffat-beta', '4.5', '--psf-relative-tail', '1e-8', '--max-cache-psf-flux', '1', '--psf-min-y', '0', '--hdr-output', '--output', '/tmp/gr-hip-renderer-test-s9nk0w12/cpu-0.png']
+ PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.667 s
+Rendered 3 images from 3 catalog stars to /tmp/gr-hip-renderer-test-s9nk0w12/cpu-0.png (ok)
+PSF splats: cached 2, cached wing-clipped 0, direct fallbacks 1, discarded below min-Y 0
+
+RUN ['/home/wyj/Code/C/GR_4d_raytracing/build/Release/minkowski_sky_hip', '--catalog', '/home/wyj/Code/C/GR_4d_raytracing/tests/data/hip_psf_mixed_catalog.csv', '--width', '96', '--height', '64', '--fov-deg', '30', '--look-ra-deg', '2', '--look-dec-deg', '1', '--coarse-cell-pixels', '16', '--refine-max-level', '0', '--exposure', '1000', '--psf-fwhm-pixels', '2.7', '--psf-moffat-beta', '4.5', '--psf-relative-tail', '1e-8', '--max-cache-psf-flux', '1', '--psf-min-y', '0', '--hdr-output', '--output', '/tmp/gr-hip-renderer-test-s9nk0w12/hip-0.png']
+ PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.700 s
+HIP producers: 4 workers; summed generation 0.000 s, submission/fallback 0.020 s; wall 0.007 s
+Rendered 3 images from 3 catalog stars to /tmp/gr-hip-renderer-test-s9nk0w12/hip-0.png (ok)
+PSF splats: cached 2, cached wing-clipped 0, direct fallbacks 1, discarded below min-Y 0
+HIP PSF: 2 events in 2 batches (2 timed); upload 0.000029 s, kernel 0.000887 s, download 0.000107 s
+
+min_y=0: statistics match; HDR max_abs=0.0; exact=True
+RUN ['/home/wyj/Code/C/GR_4d_raytracing/build/Release/minkowski_sky', '--catalog', '/home/wyj/Code/C/GR_4d_raytracing/tests/data/hip_psf_mixed_catalog.csv', '--width', '96', '--height', '64', '--fov-deg', '30', '--look-ra-deg', '2', '--look-dec-deg', '1', '--coarse-cell-pixels', '16', '--refine-max-level', '0', '--exposure', '1000', '--psf-fwhm-pixels', '2.7', '--psf-moffat-beta', '4.5', '--psf-relative-tail', '1e-8', '--max-cache-psf-flux', '1', '--psf-min-y', '1e30', '--hdr-output', '--output', '/tmp/gr-hip-renderer-test-s9nk0w12/cpu-1e30.png']
+ PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.655 s
+Rendered 3 images from 3 catalog stars to /tmp/gr-hip-renderer-test-s9nk0w12/cpu-1e30.png (ok)
+PSF splats: cached 0, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 3
+Warning: --psf-min-y discarded one or more PSF events.
+
+RUN ['/home/wyj/Code/C/GR_4d_raytracing/build/Release/minkowski_sky_hip', '--catalog', '/home/wyj/Code/C/GR_4d_raytracing/tests/data/hip_psf_mixed_catalog.csv', '--width', '96', '--height', '64', '--fov-deg', '30', '--look-ra-deg', '2', '--look-dec-deg', '1', '--coarse-cell-pixels', '16', '--refine-max-level', '0', '--exposure', '1000', '--psf-fwhm-pixels', '2.7', '--psf-moffat-beta', '4.5', '--psf-relative-tail', '1e-8', '--max-cache-psf-flux', '1', '--psf-min-y', '1e30', '--hdr-output', '--output', '/tmp/gr-hip-renderer-test-s9nk0w12/hip-1e30.png']
+ PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 1.664 s
+HIP producers: 4 workers; summed generation 0.000 s, submission/fallback 0.000 s; wall 0.002 s
+Rendered 3 images from 3 catalog stars to /tmp/gr-hip-renderer-test-s9nk0w12/hip-1e30.png (ok)
+PSF splats: cached 0, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 3
+Warning: --psf-min-y discarded one or more PSF events.
+
+min_y=1e30: statistics match; HDR max_abs=0.0; exact=True
@@ -0,0 +1 @@
+HIP PSF cache comparison: max_abs=2.8421709430404007e-14 max_rel=7.5319184269262976e-16
@@ -0,0 +1 @@
+HIP PSF cache comparison: max_abs=2.8421709430404007e-14 max_rel=7.5319184269262976e-16
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.691 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=4096 spread=16 frame=3840x2160 event_bytes=56 CPU_reference=0.051886 s
+HIP create=0.023212 replay_wall=0.010834 upload=0.000021 kernel=0.005702 download=0.004809 batches=1 timed=1 max_abs=7.9936057773011271e-15 max_rel=2.9244848757288279e-15 flux_rel=3.55416413758235e-17
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.671 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=16384 spread=1 frame=3840x2160 event_bytes=56 CPU_reference=0.208507 s
+HIP create=0.024260 replay_wall=0.029202 upload=0.000050 kernel=0.023976 download=0.004869 batches=1 timed=1 max_abs=5.1159076974727213e-13 max_rel=4.4106699745012541e-15 flux_rel=3.1370299104282862e-18
@@ -0,0 +1,3 @@
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.703 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=16384 spread=3840 frame=3840x2160 event_bytes=56 CPU_reference=0.422135 s
+HIP create=0.025980 replay_wall=0.026740 upload=0.000047 kernel=0.021492 download=0.004899 batches=1 timed=1 max_abs=2.7755575615628914e-17 max_rel=5.6947355265748357e-16 flux_rel=4.0906184864912441e-20
@@ -0,0 +1,500 @@
+# HIP PSF 有界真实事件回放与像素归约实验（2026-09-07）
+
+## 结论与交付
+
+**当前方向（2026-09-13）：搁置旧串行 adaptive 的慢因追溯，在新版 worker 私有预分桶
+adaptive 上优化生产管线。以下各日期记录保留历史结论；当前结果和下一步目标以
+“2026-09-13 全天复测与下一步目标”一节为准。**
+
+已实施原计划的有界捕获/回放、16×16 和 32×32 按像素归约原型、独立 CPU producer
+诊断及正确性回归。**原型保留在测试程序中，未替换生产 HIP 路径。**
+实现于 2026-09-11 提交为 `7f5ec1a`；以下日志和 hash 保留 2026-09-07 测量时的状态。
+
+RX 9070 上，65,536 个真实银心视场事件的累积回放中位数从 104.107 ms 降至
+69.823 ms（16×16，约 1.49×）。含公共 GPU 初始化为 137.111 → 102.323 ms（约 1.34×）。
+但同等贡献的分散对照中，16×16 从 85.302 ms 退化至 104.389 ms；32×32 为 79.899 ms。
+强放大样本的 32×32 结果波动区间与 atomic 重叠，不能确认稳定收益。因此尚不足以选择
+一个通用生产默认算法；后续集成应先考虑分布选择及生产流式 producer 的端到端对照。
+没有运行完整全天渲染，也没有推断新的全天加速比。
+
+## 2026-09-11 自适应选择后续实验
+
+在提交 `11e703e33dffb1ff168ba11dd922e68b448116b9` 之上增加了仅用于回放的
+`adaptive` 模式，production sink 仍未改变。选择器逐个 16,384-event chunk 扫描
+32×32 中心 tile 占用；chunk 至少有 8,192 events、且平均每个占用中心 tile 至少
+32 events 时选择 tile16，否则选择现有 atomic。该阈值是基于本页固定输入提出的实验
+假设，不是跨场景或跨设备参数。
+
+选择扫描不构建 support 引用，四个样本的中位成本为 0.037--0.455 ms。tile 路径使用
+独立的有界 event device buffer，不复用 production 双 staging slot，因此同一 stream 内
+可以按 chunk 混合 atomic/tile；mixed fixture 实际覆盖 2 个 tile chunk、1 个 atomic chunk
+和中途 direct fallback。所有额外 scratch 仍在 replay sink 创建时一次分配，未进入 renderer。
+
+同一新 binary（SHA256
+`121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151`）串行运行，
+每项三次；表中为包含选择、分桶、上传、kernel、合并、下载和清理的 `replay_wall`
+中位数：
+
+| 65,536-event 输入 | paired atomic | paired tile16 | adaptive | adaptive 选择 |
+| --- | ---: | ---: | ---: | ---: |
+| 银心密集 | 95.018 ms | 67.354 ms | 67.834 ms | 0.177 ms |
+| 同贡献分散 | 78.203 ms | 99.693 ms | 80.092 ms | 0.455 ms |
+
+自适应路径在密集输入相对 paired atomic 快约 1.40×，距固定 tile16 中位数 0.7%；在分散
+输入保留 atomic，距其 paired 中位数 2.4%。另外两个真实输入的自适应中位数为强放大
+21.617 ms、普通区域 18.347 ms，分别选择 1/1 tile chunk。银心选择 4/4 tile chunks，
+分散对照选择 4/4 atomic chunks。此结果支持继续研究 production 流式集成，但尚未包含
+OpenMP producer 与 sink 锁竞争，也没有授权用本回放结果宣称完整全天加速。
+
+全部 adaptive/mixed 检查通过原有 finite、double HDR 和 RGB/Y 通量阈值；最坏
+`max_abs=5.96856e-11`、`max_rel=5.95958e-13`、RGB 通量相对差
+`<=2.83233e-14`、Y `<=1.15036e-14`。`make -j1 test` 与 production HIP primitive
+也通过。第一次在受限沙箱内运行明确失败为 `no ROCm-capable device is detected`，随后只在
+获准的主机 GPU 环境执行；失败记录保留，没有删除或覆盖。
+
+原始证据：
+
+- 构建：[adaptive_build_host.log](hip_psf_replay_2026-09-07/adaptive_build_host.log)；
+- adaptive 三次：`adaptive_{center_65536,dispersed_65536,lensed_16384,ordinary_12765}_host_{0,1,2}.log`；
+- paired 基线：`paired_{center,dispersed}_{atomic,16}_{0,1,2}.log`；
+- mixed、CPU 与 HIP 回归：`adaptive_boundary_mixed_host_0.log`、
+  `adaptive_cpu_regression.log`、`adaptive_hip_primitive_host.log`；
+- 受限环境失败：`adaptive_center_65536_0.log`。
+
+每份日志均保留完整命令、45/90 s timeout、Git hash、binary hash（适用时）、程序原始输出、
+process wall 和 exit status。所有性能进程均由现有独占 runner 串行执行，未与其他 renderer
+或 profiler 并发。
+
+## 2026-09-12 持续回放与 production 集成
+
+在提交 `2d01c2c101ccea8193a64bb46ceafca3009f0ef5` 之上的未提交实现中，回放器增加了
+1--512 轮有界重复模式，用同一真实事件流测试持续负载。重复模式不把累计 128/256 轮的
+GPU HDR 与单轮 CPU reference 比较，因而输出明确标记 `validation=skipped-for-sustained-timing`；
+单轮真实输入与 mixed boundary 仍执行原有 double HDR、RGB/Y 通量和 finite 检查。
+
+原 replay tile16 在密集输入的 256 轮完整 wall 为 12.968 s，atomic 为 14.326 s，只有
+1.10×--1.18× 的持续收益；tile accumulation 本身仍约快 1.4×，CPU 的整屏嵌套列表分桶
+约占 1.8--1.9 s。不同运行顺序下的 128 轮 adaptive 为 6.372--6.880 s，对应 atomic
+7.149--7.165 s，证明短回放的 1.40× 完整收益不能直接外推。
+
+production sink 随后接入稀疏 touched-tile 分桶和可复用有界 scratch。默认保持 atomic；
+`HIP_PSF_ACCUMULATION=adaptive` 启用与 replay 相同的中心密度选择规则。32 MiB references、
+2 MiB tasks 或 128 MiB partials 超限时按 chunk 回退 atomic，不改变 double RGB、四点 phase
+cache、圆形 support、wing clipping 或 direct fallback 顺序。
+
+最终同 binary（SHA-256
+`c560c193e1dc2104030ed804ea68e16ab7576592191dbf147b917a6e097a66b6`）连续回放
+65,536 个真实银心事件 128 轮：
+
+| production sink | 完整 replay wall | GPU 阶段 | selector | CPU bin | upload | batches |
+| --- | ---: | ---: | ---: | ---: | ---: | ---: |
+| atomic | 7.164 s | 7.132 s | 0 | 0 | 0.023 s | 512 atomic |
+| adaptive | 4.631 s | 3.875 s | 0.018 s | 0.607 s | 0.091 s | 512 tile16 |
+
+完整 replay 为 **1.55×**，记录的 GPU 阶段为 **1.84×**。同 binary 的 64 轮同贡献分散
+输入中，adaptive 选择 256/256 atomic chunks，完整 wall 为 3.167 s，直接 atomic 为
+3.169 s，差异在 0.1% 内。最终 dense 单轮检查的
+`max_abs=2.71051e-19`、`max_rel=1.96115e-14`。最终 mixed boundary
+覆盖 2 个 tile16、1 个 atomic chunk 和中途 direct fallback，最坏 `max_abs=5.96856e-11`、
+`max_rel=5.95958e-13`，RGB/Y 通量阈值均通过。production primitive 在 adaptive 环境下也
+通过，`max_abs=2.84217e-14`、`max_rel=7.53192e-16`。
+
+三 tile、21,087-star renderer 配对使用同一 4K lens map 和同一 production binary
+（SHA-256 `f51cbccac135502440f005c5d61d95d6004be7d4ec5cd09bfe04bab53053143d`）。
+atomic/adaptive 均产生 156,837 events；adaptive 选择 14 tile16 + 2 atomic batches，kernel
+为 0.118894 s，对照 0.169212 s，splat wall 为 0.236/0.285 s。两张 PNG 的 SHA-256 都是
+`99a971fac7f5e66f0a1aafd0921b61f16fcb933c9488320f95e423542d3b6a6d`。约 1.4 s 的完整
+进程受 cache build 等固定成本波动支配，不能用 process wall 判断这项优化。
+
+随后使用同一 4K lens map、598,264,924 events 和 36,530 batches 运行了完整全天
+adaptive 渲染。它推翻了上述有界样本的外推：
+
+| 完整全天 | splat wall | kernel | CPU bin | selector | upload | process wall |
+| --- | ---: | ---: | ---: | ---: | ---: | ---: |
+| atomic | 480.500 s | 477.302449 s | 0 | 0 | 1.411367 s | 533.62 s |
+| adaptive | 586.763 s | 416.265471 s | 155.302 s | 2.212 s | 7.506981 s | 640.35 s |
+
+adaptive 的 GPU kernel 只减少 61.037 s（12.79%），而串行关键路径上的 CPU 分桶增加
+155.302 s，splat wall 因而增加 106.263 s（22.12%），完整进程增加 106.73 s（20.00%）。
+36,515/36,530 batches 被选为 tile16，说明中心 32px tile 密度无法预测完整 47px PSF
+support 扩张后的 references、tasks、列表长度和分桶成本。atomic 从有界回放的
+13.93 ms/batch 到全天的 13.07 ms/batch 没有恶化；tile kernel 则从有界样本的
+7.57 ms/batch 变为全天的 11.40 ms/batch，CPU 分桶另需 4.25 ms/batch。串行分桶是已确认的额外成本；GPU 阶段变慢的具体原因未定位，
+不能仅凭这些时间排除时钟或其他系统因素。
+
+正确性仍成立：atomic/adaptive PNG 的 SHA-256 都是
+`c63df730c7f927fc6b6ae17df5ffbad1d2bb44631a5821557150d00d6269a3e4`。两个 HDR FITS
+共有 24,883,200 个 float，113 个因累积顺序不同；`max_abs=2.38418579e-07`、
+`max_rel=1.18905923e-07`。这项旧串行分桶 adaptive 实现是历史负结果，不能外推为新版并行预分桶的结论；
+默认继续保持 atomic。当时提出的下一轮实验是直接度量 support-expanded 引用工作量，并在
+重新跑完整全天前用真实流式 producer 验证并行预分桶或 GPU 分桶能否把成本移出串行关键路径。
+
+完整 adaptive 原始输出保存在 `full_production_adaptive_user.log`（SHA-256
+`ec7b41d56a76cb93383737c30c6c6055bdb53b9b0cff54034333d96a841b1f36`）；该用户命令未嵌入
+Git/binary hash，运行后工作区 binary 的 SHA-256 为
+`f51cbccac135502440f005c5d61d95d6004be7d4ec5cd09bfe04bab53053143d`，不可仅凭事后 hash
+证明执行期间 binary。atomic 数字来自同一任务先前保留的终端输出。
+
+### 2026-09-12 producer 私有并行预分桶原型
+
+在上述完整全天负结果之后，将 adaptive 选择与 support-expanded CPU 分桶移到每个 OpenMP
+producer 私有的 `HipPsfPreparedChunk`，在获取 sink 共享锁前完成；单个 sink 仍独占 GPU
+HDR、stream、device scratch 和稳定的上传 staging。direct fallback 先准备本 worker 的待提交
+chunk，再在同一锁内完成提交、HDR 下载、CPU splat、HDR 上传。原 `hip_psf_sink_submit` 仍用于
+单线程回放兼容，正常生产默认 atomic 未变。新日志记录 tile references、tasks、merges 和
+单 chunk 峰值，以便下一次评估完整 support 工作量。
+
+同一 65,536-event 银心固定输入重复 128 轮，均为 512 个 tile16 batches。新 binary 的配对
+回放结果如下（两者均通过 `128 × CPU double reference`，`max_rel=2.14616e-14`）：
+
+| 生产 sink 回放 | replay wall | 累计 CPU bin | GPU 阶段 | process wall |
+| --- | ---: | ---: | ---: | ---: |
+| sink 内串行分桶 | 3.886 s | 0.549 s | 3.659 s | 5.778 s |
+| 16 worker 私有预分桶 | 3.958 s | 0.709 s（各 worker 求和） | 3.670 s | 5.873 s |
+
+此输入上并行预分桶没有端到端收益，且累计 CPU 工作与 RSS 上升（约 716→770 MiB）。由于这
+份输入已被全天结果证明低估真实分桶与 tile kernel 成本，此试验仍不能判断全天会否受益，
+更不能宣称 61 s 的 kernel 收益已被回收。**不据此再跑完整全天。**需要先取得代表实际
+36,530 chunks 的 support-expanded references/tasks 分布和并行分桶 wall，再决定是否继续此方向。
+
+真实小型 4K lens-map renderer 中，16 workers 处理 156,837 events，13 tile +3 atomic
+batches；13 个 tile chunk 共 6,145,194 references、64,056 tasks、5,465 merges，单 chunk
+最多 561,449 references。PNG SHA-256 与先前 atomic 输出同为
+`99a971fac7f5e66f0a1aafd0921b61f16fcb933c9488320f95e423542d3b6a6d`。另一个
+32,771-event mixed boundary 回放包含 2 tile +1 atomic chunk 和 direct fallback，通过 CPU
+double reference，`max_abs=5.96856e-11`、`max_rel=5.95958e-13`。HIP primitive 与
+`make -j4 ENABLE_PNG=1 test` 均通过。
+
+新原始日志：`parallel_prebin_{serial_128_validated,16workers_128_validated}.log`、
+`parallel_prebin_renderer_workload.log`、`parallel_prebin_mixed_boundary.log`、
+`parallel_prebin_hip_primitive.log`。先前 `parallel_prebin_16workers_128.log` 因 OpenMP
+`reduction(max:failed)` 的私有初值而没有提交事件；原始失败保留，修正为 `reduction(+:failed)`
+后的 `*_v2.log` 才是首次有效回放，最终数字以上述带 scaled reference 校验的日志为准。
+
+为获取不经 GPU 的真实全天 support 分布，dummy 后端增加显式
+`DUMMY_PSF_SUPPORT_STATS=1` 诊断：每 worker 保存最多 16,384 个事件，在 chunk flush 时按
+production 的 cache-limited 矩形 support 统计 16px references、touched tiles、按 256
+references 切分的 tasks、最大单 tile 列表和第一遍计数耗时。它不生成 HDR、不 materialize
+references、不上传 GPU，不能把第一遍耗时等同于完整两遍分桶成本。21,087-star 小样通过，
+原始记录为 `parallel_prebin_dummy_support_small.log`；该样的 chunk 边界受 OpenMP 动态调度
+影响，不与 HIP renderer 的逐 chunk 列表配对。完整全天诊断结果见下文。
+
+下一次完整全天诊断使用与已跑的 dummy 任务相同的参数，只额外设置环境变量；输出路径仅
+满足 CLI，dummy 不写图像：
+
+```sh
+OMP_NUM_THREADS=16 OMP_DYNAMIC=FALSE DUMMY_PSF_SUPPORT_STATS=1 \
+  ./build/Release/schwarzschild_sky_dummy --verbose \
+  --psf-relative-tail 1e-8 --psf-min-y 0 --max-cache-psf-flux 1e8 \
+  --all-sky-catalog assets/2mass/processed/all_sky --exposure 1e13 \
+  --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --catalog-load-workers 4 \
+  --lens-map-input output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens \
+  --output /tmp/2mass_dummy_support_diagnostic.png
+```
+
+用户随后运行了上述完整全天 dummy 诊断；原始终端输出为
+[`full_dummy_support_user.log`](hip_psf_replay_2026-09-07/full_dummy_support_user.log)，
+SHA-256 `992a3109de28a338c53af229b6a3b4083659a835f78929c36d36178358a6d5e0`。
+日志未嵌入执行时 Git/binary hash；运行后本地 dummy binary 的 SHA-256 为
+`2550fbdc7367ec4d56bdf87894e1322d7f4af5165e93a17af3e6a37806c0649a`。
+同一 343,363,141 stars 产生 598,264,924 cached events，0 direct/wing/discard；
+64,440 catalog tiles 全部加载，49.020 s；16 worker 分类/chunk wall 81.760 s。zsh `time`
+给出总时间 2:11.91；zsh 对 pipeline 中的 `tee` 另列一行，不能把两个 2:11.91 相加。
+该次动态调度产生 36,508 个满 chunk、16 个 partial；与 HIP 的 36,530 batches 不作逐批
+配对，但总事件数一致。
+
+| 全天满 chunk support 统计 | p50 | p90 | p99 | max |
+| --- | ---: | ---: | ---: | ---: |
+| 16px references | 746,748.5 | 802,816 | 802,816 | 802,816 |
+| touched 16px tiles | 49 | 168 | 1,036 | 1,521 |
+| tile tasks | 2,975 | 3,136 | 3,435.93 | 3,733 |
+| 最大 tile 列表 | 16,384 | 16,384 | 16,384 | 16,384 |
+| 第一遍计数 | 0.807 ms | 0.919 ms | 1.049 ms | 7.969 ms |
+
+全部 chunk 合计 27,216,790,943 references、107,847,441 tasks，worker 第一遍计数时间之和
+29.347 s。这是并行 worker 时间之和，**不是**额外 wall time，也不包括第二遍写 references、
+任务构造、锁内 staging 或 GPU 上传。全天 HIP 串行完整分桶为 155.302 s，不能拿 29.347 s
+直接替换它。第一遍显示每个事件平均覆盖约 45.5 个 16px tile；满 chunk 的 p90 已到
+`16,384 × 49`，且最大列表从中位数起就是整批事件。
+
+对旧真实 `center_65536.events` 逐 chunk 用相同 support 矩形计算，四批 references 为
+745,430 / 725,200 / 753,474 / 749,671，接近全天 p50；但 touched tiles 为
+96 / 162 / 203 / 222，最大列表仅 14,637 / 9,099 / 11,188 / 9,220。因此先前有界
+样本只匹配了引用总量，没匹配热点集中度。为区分这两个量，`make_hotspot_fixture.py` 把
+原事件平移到相同整数像素，或保留约 8×8px 位置散布；颜色、flux、support 原样保留，
+亚像素余数仅受 double 舍入影响。这两份**明确是反事实 GPU workload，不是物理星像**。
+固定热点每批恰好 802,816 references、49 tiles、3,136 tasks、最大列表 16,384；
+输入 SHA-256 分别为 `de39e07d420f70aaa2f7309d209e58a1091d2bea4ca6d8332366e6944f19347b`
+与 `87f90c2e43845962702e1643f9b7a635108b75b6e21a30080650442745cadcf6`。
+
+| 128 轮、512 批回放 | atomic wall | tile 串行 wall | tile 并行 wall | atomic GPU 阶段 | tile GPU 阶段 |
+| --- | ---: | ---: | ---: | ---: | ---: |
+| 同一整数像素 | 7.711 s | 4.001 s | 4.071 s | 7.677 s | 3.760 s |
+| 8×8px 散布 | 6.482 s | 3.949 s | 4.046 s | 6.447 s | 3.714 s |
+
+全部回放通过按轮数缩放的 CPU double reference，tile 的最大相对误差不超过
+`3.30e-14`。此对照说明 refs/tile/list 聚合量不足以重现全天 tile GPU 阶段
+`416.265/36,530 = 11.40 ms/batch`：即使强制匹配 p90 热点，回放仍约
+`7.3 ms/batch`。另外在 `center_65536.events` 的同一回放进程内放入 15 个 CPU 忙等线程，
+atomic/tile GPU 阶段为 7.126/3.669 s（512 批），几乎仍是无忙等线程的
+7.13/3.66 s；简单主机抢占也未重现全天差距。上述 workload 与争用实验均为诊断性
+反事实，不能改变真实全天 adaptive 慢 20% 的结论。
+
+原始配对日志：`hotspot_{atomic,adaptive_serial,adaptive_parallel}_128.log`、
+`hotspot_jitter8_{atomic,adaptive_serial,adaptive_parallel}_128.log`、
+`busy_center_{atomic,adaptive}_128.log`。全天 adaptive 原始进度每隔约 5 秒报告累计 HIP
+阶段：首尾约 7–8 ms/batch，中间约 12–13 ms/batch 持续数万批。这提示当前固定 65,536
+events 输入未覆盖真实流中的长期困难区段，但也不能排除其他随时间变化的系统因素；
+原因仍未定位。当时提出从该区段捕获真实 events 和逐批 GPU/CPU 明细；
+2026-09-13 已搁置这项旧版追溯，不再作为新版推进的前置条件。
+
+其余原始证据为 `final_production_{atomic,adaptive}_128.log`、
+`final_production_adaptive_dense.log`、
+`final_production_dispersed_{atomic,adaptive}_64.log`、
+`final_production_adaptive_mixed.log`、`final_hip_test_adaptive.log` 和
+`final_renderer_{atomic,adaptive}.log`。每份日志包含完整命令、timeout、Git hash、binary hash
+及原始输出。production 默认值没有改变。
+
+实现入口：
+
+- [capture_psf.c](../tests/capture_psf.c)：调用真实 producer 的测试专用 consumer，捕获或诊断，不生成 HDR。
+- [replay_psf.hip](../tests/replay_psf.hip)：CPU double reference、现有 atomic、两种 tile 原型。
+- [make_psf_fixture.c](../tests/make_psf_fixture.c)：单独标记的合成边界/热点/wing fixture。
+- [test_psf_capture.py](../tests/test_psf_capture.py)：边界限制、分类、串行/并行/索引摘要、拒绝覆盖验证。
+- [全部原始证据与索引](hip_psf_replay_2026-09-07/README.md)。
+
+## 2026-09-13 全天复测与下一步目标
+
+用户在重新构建 worker 私有预分桶版本后，再次完成同配置全天 adaptive 渲染；随后
+`git stash` 回到 `2d01c2c`，重新构建并复测原 atomic，之后用 `git stash pop` 恢复修改。
+该 HEAD 的 HIP 实现不读取 `HIP_PSF_ACCUMULATION`，所以 atomic 复测命令虽仍写着
+`adaptive`，实际是 atomic；不能把输出文件名或环境变量当作算法证据。
+
+| 全天实现 | splat wall | GPU event 阶段 | CPU bin | upload | process wall |
+| --- | ---: | ---: | ---: | ---: | ---: |
+| 历史 atomic | 480.500 s | 477.302449 s | 0 | 1.411367 s | 533.62 s |
+| 旧串行 adaptive | 586.763 s | 416.265471 s | 155.302 s，串行 | 7.506981 s | 640.35 s |
+| 新并行预分桶 adaptive | 282.944 s | 256.184375 s | 134.374 s，worker 累加 | 7.184765 s | 335.75 s |
+| 本次 atomic 复测 | 481.417 s | 478.336515 s | 0 | 1.432135 s | 534.37 s |
+
+四次总事件数均为 598,264,924、batches 均为 36,530；两次 adaptive 都选择 36,515 tile16
+和 15 atomic batches。新 adaptive 无 direct/wing/discard，references 为 27,216,530,468、
+tasks 为 107,238,420、merges 为 2,802,462，峰值 references/chunk 为 802,816。
+新 adaptive 和旧 adaptive 均已使用相同 payload 的黑体 LUT；catalog 加载分别为
+49.334/50.104 s。新版 bin 时间是各 worker 的经过时间之和，可以与 GPU 重叠，不能加到
+splat wall 上，也不能与旧版串行 bin 作等口径的关键路径比较。
+
+atomic 的 splat/GPU 复测仅比历史值高约 0.2%。相对本次 atomic，新 adaptive 的 splat
+快约 1.70×、GPU event 阶段快约 1.87×、完整进程快约 1.59×。这支持继续推进新版；
+尚不是相同 binary 内的 atomic/adaptive 配对，也不证明新版全天 HDR 数值正确性。
+新旧 adaptive 的 splat 差 303.819 s，其中 GPU event 阶段差 160.081 s；不能把全部收益
+归因于分桶并行化。旧版 GPU 阶段为何更慢仍未知，保留历史证据，**停止专项追溯**；仅当
+新版出现可重复退化或正确性问题且旧版信息有助定位时重新调查。
+
+新 adaptive 完整原文见
+[full_parallel_prebin_adaptive_user_2026-09-13.log](hip_psf_replay_2026-09-07/full_parallel_prebin_adaptive_user_2026-09-13.log)；
+atomic 复测仅收到结尾摘录，原样保存为
+[full_atomic_redo_user_2026-09-13_excerpt.log](hip_psf_replay_2026-09-07/full_atomic_redo_user_2026-09-13_excerpt.log)。
+两者均未提供运行时 binary hash，摘录不能代替完整命令和完整运行日志；本次只更新文档，
+没有重新运行 benchmark 或比较新生成的全天 HDR。
+
+### 新版优化目标与验证顺序（待实施）
+
+目标是在相同 RX 9070、4K lens map、全天 catalog、PSF/曝光/黑体参数和 HDR/PNG 输出下，
+将完整进程从 335.75 s 推进到 **240 s/张以内**。这是待验证目标，不是性能承诺；不能通过
+降低精度、删减事件、改变 tail/min-Y、缩小输入或省略输出来达标。atomic 保留为参考和
+显式可选路径，本次不修改默认算法。
+
+用户全程观察新版的 btop：GPU 常在约 94%，会反复降至约 80%，并非偶发；整机 CPU
+持续满载。用户另报告原 atomic 能吃满 GPU。旧串行 adaptive 当时没有观测，不能推断它
+不存在 GPU 不满载现象。上述是人工观测，未保存同步遥测，不能据此量化净算力利用率。
+新版 generation/submission 累计分别为 814.275/3712.364 s，后者包含分桶、锁等待和
+提交/完成等待；atomic 复测的 GPU 阶段占 splat wall 约 99.36%，进程仍为 1461% CPU。
+CPU 满载不等于有效 producer 工作，忙等是需测量的嫌疑，尚未定量确认。
+
+新版非 splat 阶段约 52.806 s；即使消除 splat wall 与 GPU event 阶段之间的全部
+26.760 s，总进程仍约 309 s。若其他阶段不变，240 s 目标要求 splat 不超过约 187.2 s，
+比当前 GPU event 阶段还低约 27%。该 event 区间包围 prepare/accumulate/merge，可能含
+提交间隙，不等同于三个 kernel 的净执行时间。因此同时调查管线空隙和 GPU 执行成本，
+不能把 btop 达到 100% 当作验收标准。
+
+1. 先比较已有新版 adaptive 与 atomic 全天 HDR：finite、逐像素误差、RGB/Y 总通量，
+   使用现有正确性阈值；记录输出 hash，不为这一步重跑全天。
+2. 增加可关闭的有界诊断，拆分 CPU 分桶、锁等待、锁持有、GPU 完成等待、staging 和
+   提交时间，记录线程 CPU time；GPU 分别测 prepare、accumulate、merge，并保留原总区间。
+   在新版代表性真实流式小样上同步记录 GPU busy、时钟、功耗、温度，先验证测量开销。
+   固定事件回放用于隔离成本，不能单独替代生产 producer/sink 的端到端证据。
+3. 若批间空隙显著，优先评估双缓冲 staging/上传，使下一批准备与当前批 GPU 执行重叠；
+   若共享锁争用显著，再对照专用提交线程加有界队列。这些是待验证候选，不是已选定实现。
+   明确缓冲 ownership、完成后复用和有界背压；单 sink 持有 GPU HDR，保留 direct fallback
+   的 finish/download/CPU/upload 顺序，不引入 per-event task 或无界排队。
+4. 管线改善后重测剩余成本；若主要时间仍在 kernel，则优化占比最大的实际 kernel；若
+   catalog 加载成为主要限制，再单独评估输入阶段。保留密集、分散和 mixed/direct 回归。
+   有界配对采用相同 binary/输入、预热后至少三次交错顺序复测，报告 wall、CPU time、
+   GPU 分阶段及波动，不累加重叠 worker 时间。每次预设 timeout，串行独占执行，保留完整
+   命令、Git/diff/binary/input hash、原始日志与退出码；GPU 不可用直接失败。
+5. 有界正确性与收益验证后再另行安排全天配对确认，同时报告完整进程和分阶段时间。
+   未达到 240 s 时记录剩余差距及实测瓶颈；不为解释旧版而额外运行全天。
+
+## 环境与测量纪律
+
+Git 基线 `5eccc31c99db96de2a0597babf2fd4c2149e91e7`，测量时在此基础上有未提交修改。
+没有覆盖用户已有的计划修改。生产 `src/hip_psf.hip` 未改；`src/frame.c` 的诊断钩子
+仅在 standalone 测试编译时启用。每次直接执行的 binary SHA256 在相应日志中；
+[源码、binary、lens map hash](hip_psf_replay_2026-09-07/source_binary_manifest.json)、
+[宿主环境](hip_psf_replay_2026-09-07/metadata.log)、
+[构建命令](hip_psf_replay_2026-09-07/build_commands.txt)与 `build*.log` 保存完整配置。
+
+Release / C `-O2 -march=native` / HIP `-O2 --offload-arch=gfx1201`，HIP 7.2，RX 9070。
+回放 CPU reference 为串行；diagnostic 最多 16 workers；混合 renderer fixture 为 4 workers。
+各进程重建相同 immutable cache：FWHM=2.7、beta=4.5、tail=1e-8，64 phase intervals、
+47px cache radius。没有清除文件系统 page cache；输入是重复读取的固定小文件。
+
+所有测试进程串行，回放超时 45 s、缩小 renderer 超时 60 s；未出现测试超时。
+早期 `v3_*` 期间部分编译活动重叠，全部 `v3_*` 仅用作探索/正确性证据。
+下表只用构建和回归结束后的 `final_*` 三次独立复测，不引用受构建干扰的时间。
+`run.py` 记录命令、原始 stdout/stderr、退出码和进程 wall，失败立即停止，限时进程被 kill
+后会 wait/reap；独占锁及启动前的进程检查防止本套工具重叠运行。
+
+## 固定输入、选择规则与实际覆盖
+
+使用已有 3840×2160 Schwarzschild lens map，不重新 tracing/refine。只读取两个指定
+catalog tile 的均匀 8,192 行子集，见 [输入 manifest](hip_psf_replay_2026-09-07/input_manifest.json)
+和 [重建脚本](hip_psf_replay_2026-09-07/prepare_inputs.py)。没有遍历完整全天 catalog。
+
+捕获器限制 CSV≤8 MiB、stars≤32,768、lens map≤64 MiB/单帧、triangle 范围≤131,072、
+缓存事件≤65,536、分类总数≤131,072。按 triangle ID、原 catalog 顺序捕获，保留所有
+7 个 event double，文本用 17 位有效数字 round-trip；header 保存实际数量与 PSF 参数。
+triangle 范围 `[0,130882)`；按未截断的局部 magnification 再筛选：
+
+| 区域 | 原始 tile | magnification | 最大捕获实际数 | 占用 32px 中心 tiles | 最大中心密度 |
+| --- | --- | --- | ---: | ---: | ---: |
+| 普通区域 | RA252/Dec048（Dec −42°） | [0,1.2) | 12,765 | 8 | 4,691 |
+| 银心视场密集区域 | RA262/Dec060（Dec −30°） | [0,2) | 65,536（到上限） | 30 | 7,778 |
+| 强放大区域 | 同上 | [2,1e6) | 16,454 | 367 | 176 |
+
+普通、强放大子集用完后没有复制事件凑足 65,536。事件文件名后缀表示请求上限，实际数量
+以 header 和 manifest 为准。实际 bbox、flux/support 范围、中心 tile 分布及事件 hash 见
+[events_manifest.json](hip_psf_replay_2026-09-07/events_manifest.json)。三种真实输入的
+support 均为 45.84777786185942px；变化 support/wing/边缘另由合成 fixture 覆盖。
+
+分散对照只平移完整处于画面内部的事件中心，保留 fractional phase（浮点平移舍入以内）、
+flux 和 support；本来裁切的事件不移动。每次都重新计算并断言实际 event–pixel 贡献数
+完全不变：真实和分散的 65,536 事件均为 **432,818,979** 个贡献。没有以裁切减少工作量。
+
+## 原型与 ownership
+
+每 chunk≤16,384 events。CPU 按 cache 遍历 support 的完整包围矩形建立所有相交 tile
+引用，PSF wings 可以进入多个 tile；GPU 用原来的圆形行范围再筛选，继续四点 phase
+cache 插值和 double RGB。每个像素由一个线程累计，不使用全局 double atomic。
+
+第一次朴素实现反复计算 phase、sqrt/行范围，4,096 普通事件的回放约 25–27 ms，慢于
+atomic。第二版为每个 chunk 在 GPU 预计算 phase、颜色×flux 和行范围，然后供像素线程复用。
+分散对照随后触发 128 MiB 部分和限制，进程已停止。最终版让≤256 引用的单列表 tile
+直接写回独占 HDR 像素；只有长列表分段才写部分和，第二阶段按固定 task 次序相加。
+这种修正保持内存上限，避免为整屏稀疏 tiles 分配一幅额外 double HDR。
+
+设备上固定复用：references 32 MiB、tasks 2 MiB、starts 128 KiB、partials 128 MiB，
+以及最多 16,384 事件的 Prepared/行范围约 12.875 MiB；合计额外预留 **175 MiB**。
+超出引用/任务/部分和容量立即报错，无隐式切换。全部缓冲由单个实验 sink 持有，单 stream
+顺序消费、同步后复用；每个 partial 元素都被覆盖写入，不需要 memset。最终样本实际
+scratch 使用峰值约 37.26 MiB，整个 CPU-reference+GPU 进程 RSS 最大 717,172 KiB。
+预留量和实际用量不同，RSS 包含 CPU HDR/reference/cache，不能当作生产额外 RAM。
+
+## 独立最终回放结果
+
+下表是 `replay_wall` 中位数（ms，三次）：包含 scratch 分配、分桶、上传、预计算、累积、
+合并、下载、清理，排除公共 sink/cache 初始化和 CPU reference。日志另报 `complete_replay`
+（加公共 GPU sink 创建）、`CPU_reference`、cache build、完整 `PROCESS_WALL`，避免混淆。
+
+| 输入 | 实际 events | atomic | tile16 | tile32 |
+| --- | ---: | ---: | ---: | ---: |
+| 普通 | 12,765 | 26.423 | 18.511 | 19.286 |
+| 银心视场 | 16,384 | 31.803 | 22.621 | 23.247 |
+| 强放大 | 16,384 | 26.536 | 23.814 | 25.388 |
+| 银心视场 | 65,536 | 104.107 | 69.823 | 73.093 |
+| 同等贡献分散对照 | 65,536 | 85.302 | 104.389 | 79.899 |
+
+含公共 GPU 创建的 65,536 密集回放为 137.111 / 102.323 / 105.949 ms。
+强放大 tile32 回放范围 22.801–29.410 ms，atomic 25.932–27.395 ms；三次样本不足以
+证明这里的稳定提升。完整数值、范围和全部重复见 [summary.log](hip_psf_replay_2026-09-07/summary.log)
+与 `final_*.log`，由 [final_cases.py](hip_psf_replay_2026-09-07/final_cases.py) 串行生成。
+
+分阶段日志同时记录实际贡献吞吐量。atomic 上传/kernel/download 使用 HIP event；
+候选分桶为 CPU wall，prepare/accumulation/merge 为包含 launch+stream sync 的 host wall。
+它们不能拿来做精确的纯 kernel 周期归因，完整回放 wall 才是算法比较依据。
+分散 tile16 的分桶本身约数十 ms，足以抵消其累积优势。
+
+[编译器资源记录](hip_psf_replay_2026-09-07/device_resources.log) 显示 atomic kernel
+62 VGPR，prepare 37，tile accumulation 21，merge 18，private segment 均为 0。
+生成的 atomic 代码仍有三个 `global_atomic_cmpswap_b64` 循环；候选不需要它们。
+这不是运行时 cache/occupancy/FP64 counter 测量，不能据此分摊 atomic contention 的比例。
+没有使用降低 HDR 精度、近似黑体颜色或改变 min-Y/tail 的方法。
+
+## CPU producer 独立测量
+
+诊断 consumer 在正常查询、inverse mapping、频移、黑体积分与 prepare/classification
+之后，仅计数与计算摘要。输出明确标记 `DIAGNOSTIC ONLY, no HDR`。
+parallel 模式每 worker 计数/摘要独占；汇总 checksum 与事件顺序无关，串行捕获仍保留顺序。
+indexed 模式从同一有界 CSV 预构建原生一度 tile 索引，worker 查询前已完全只读，不执行 I/O。
+
+为了比较完整相同工作而不受事件上限/调度停止次序影响，银心诊断 triangle 范围缩为
+`[0,40151)`，其他仍 `[0,130882)`。所有以下运行均未触顶，四种模式逐项核对
+cached/wing/direct/discarded/events 和 checksum 完全一致。各三次中位数：
+
+| 输入 | events | memory/1 worker | memory/16 | indexed/1 | indexed/16 |
+| --- | ---: | ---: | ---: | ---: | ---: |
+| 普通 | 12,765 | 2.8123 s | 0.3502 s | 0.0729 s | 0.0125 s |
+| 银心视场 | 16,895 | 1.1472 s | 0.1383 s | 0.0535 s | 0.00986 s |
+| 强放大 | 16,454 | 1.3845 s | 0.1493 s | 0.6836 s | 0.0751 s |
+
+CSV 全扫描明显夸大查询成本；生产判断应使用 indexed 列。强放大子集遍历大量分散 triangle，
+其独立 producer 时间在这一小输入上高于 GPU 回放，说明进一步加速 GPU 未必改善同等比例的
+端到端时间。这不是全天 CPU 下限，也不能与另一事件数量的回放直接相减。
+未修改黑体积分；没有把 `summed generation / workers` 当作独立计时。
+
+## 正确性与失败记录
+
+- 全部真实回放、分散对照和最终 45 次独立复测通过 finite/double HDR 检验。
+- [边界 fixture](hip_psf_replay_2026-09-07/fixture_generate.log)：32,771 events，33 wing-clipped，
+  exact/intermediate phases、屏幕内外、热点、三 chunk/缓冲复用。atomic、tile16、tile32
+  均覆盖中途 finish/download → CPU direct → upload → 继续累积。
+- 全部最终+边界最大 `max_abs=5.96856e-11`、`max_rel=5.98529e-13`；最坏 RGB 总通量
+  相对差≤2.83419e-14，Y≤1.15193e-14。沿用旧 replay 的 abs/rel<1e-10，另增加总 RGB/Y
+  相对误差≤1e-10 的检查，没有为结果放宽门槛；现有生产 primitive 的 rel≤1e-12 也通过。
+- [捕获/索引诊断回归](hip_psf_replay_2026-09-07/capture_indexed_regression.log)通过：真实 mixed
+  classification cached=2/direct=1，min-Y 场 discarded=3；串行/并行/索引摘要一致；验证
+  event cap、非法范围、拒绝覆盖已有文件。未用提高 min-Y 代替 producer 测量。
+- [HIP primitive](hip_psf_replay_2026-09-07/hip_primitive.log)、
+  [Minkowski mixed/min-Y integration](hip_psf_replay_2026-09-07/minkowski_integration.log)通过。
+- [Schwarzschild CPU](hip_psf_replay_2026-09-07/schwarzschild_cpu.log) /
+  [HIP](hip_psf_replay_2026-09-07/schwarzschild_hip.log)同一 8,192 星子集分类一致；
+  [24,883,200 个 FITS float32 样本完全一致](hip_psf_replay_2026-09-07/schwarzschild_hdr.log)。
+  此处测试的是保留的生产路径；tile 原型的 double 正确性由回放验证，不冒称已接入 renderer。
+- [`make -j1 test`](hip_psf_replay_2026-09-07/cpu_regression.log)通过（33.44 s）。
+
+保留三类早期非零退出：沙箱未暴露 GPU、v2 分散输入的 scratch 超限、读取器误拒绝合法
+wing-clipped support。后者的修复保留 event 的物理 support，仅在实际遍历时限制 cache 范围。
+未删失败日志，未在任何失败后不加分析自动扩大测试规模。
+
+## 最小复现
+
+从仓库根目录先按 [build_commands.txt](hip_psf_replay_2026-09-07/build_commands.txt) 构建。
+固定输入已随报告保留；原大 catalog/lens map hash 在 manifest。已有日志拒绝覆盖，重复
+运行请使用新标签和新的事件输出路径：
+
+```sh
+python3 benchmarks/hip_psf_replay_2026-09-07/run.py repeat_capture 60 \
+  build/Release/capture_psf \
+  output/lens/schwarzschild_galactic_center_R100_45deg_16_4_4k_.grlens \
+  benchmarks/hip_psf_replay_2026-09-07/center.csv \
+  0 130882 65536 /tmp/gr-psf-repeat.events 1e13 1e8 0 0 2
+python3 benchmarks/hip_psf_replay_2026-09-07/run.py repeat_atomic 45 \
+  build/Release/replay_psf /tmp/gr-psf-repeat.events 65536 atomic
+python3 benchmarks/hip_psf_replay_2026-09-07/run.py repeat_tile16 45 \
+  build/Release/replay_psf /tmp/gr-psf-repeat.events 65536 16
+python3 benchmarks/hip_psf_replay_2026-09-07/run.py repeat_tile32 45 \
+  build/Release/replay_psf /tmp/gr-psf-repeat.events 65536 32
+```
+
+以上是重跑示例，`repeat_*` 标签本次未执行；实际执行命令逐条保存在各原始日志。
@@ -0,0 +1 @@
+__pycache__/
@@ -0,0 +1,41 @@
+# 回放原始证据
+
+结果与限制见 [上级报告](../hip_psf_replay_2026-09-07.md)。
+
+- `build_commands.txt` / `build*.log`：构建命令与完整编译输出。
+- `input_manifest.json`：真实 catalog 的来源、均匀抽样规则、输入 hash；固定 CSV 随本目录保留。
+- `capture_*.log`：输入、triangle 范围、magnification 筛选、实际分类/事件数、停止位置与 producer 时间。
+- `*.events`：版本化文本文件，头含尺寸/实际事件数/PSF 参数，后续为 7 个 round-trip double。
+  文件名后缀表示请求上限，实际数量以头部为准，不能假定所有样本都有 65,536 项。
+- `events_manifest.json`：事件文件 hash、实际 bbox/flux/support 分布、32px 中心分桶统计。
+- `final_*.log`：构建完成后的独立性能对照；每种输入/算法三次。`v1/v2/v3` 属于探索记录。
+- `producer_*.log`：同一有限输入上的独立 producer 测量，memory 与 indexed-subset 必须分开解释。
+- `boundary_validated_*.log`：合成边界/热点/wing/multi-chunk/CPU direct 恢复的 double HDR 对照。
+- `*_regression.log` / `*_integration.log` / `schwarzschild_*.log`：集成和回归输出。
+- `device_resources.log`：编译器资源报告，不是运行时性能计数器。
+- `full_production_adaptive_user.log`：用户执行的旧串行分桶全天 adaptive 原始终端输出；命令和
+  HIP 计时在日志内，未嵌入执行时 binary/Git hash，不能当作 runner 的 provenance。
+- `full_parallel_prebin_adaptive_user_2026-09-13.log`：新版并行预分桶全天运行的用户完整附件原文。
+- `full_atomic_redo_user_2026-09-13_excerpt.log`：stash 回 HEAD 重编译后的 atomic 复测结尾摘录，
+  不是完整日志；该 HEAD 忽略命令中的 adaptive 环境变量。两份新记录均缺少运行时 binary hash。
+  当前方向为搁置旧 adaptive 慢因追溯、优化新版生产管线，240 s/张为待验证目标，详见上级报告。
+- `parallel_prebin_*.log`：producer 私有预分桶的有界回放、混合 direct 边界、HIP primitive、
+  小型真实 renderer 与可选 dummy support 诊断。`parallel_prebin_16workers_128.log` 是
+  OpenMP reduction 初值错误导致的零提交无效运行；有效数字以 `*_validated.log` 为准。
+- `full_dummy_support_user.log`：用户运行的真实全天 dummy support 分位数与第一遍计数原始输出；
+  没有 GPU/HDR，也没有在日志中记录执行时 binary hash。
+- `make_hotspot_fixture.py` / `center_hotspot*.events` / `hotspot_*.log`：从捕获的真实事件
+  保留颜色、flux、support 和亚像素余数，重排整数像素位置构成的明确反事实热点，验证
+  聚合 references/tile/list 指标的预测力，不作为物理星像。
+- `busy_center_*.log`：同一进程中额外 15 个 CPU 忙等线程的有界 HIP 回放对照。
+
+`run.py` 对测试进程使用独占锁，启动前检查已有 renderer/replay 进程，单独进程组限时；
+超时后 kill 并 wait/reap，任何失败停止后续执行。日志用独占创建，重跑应使用新的输出目录
+或新日志标签，不能覆盖本次证据。每个日志记录命令、超时、Git hash、直接执行的 binary hash、
+原始 stdout/stderr、进程 wall 和退出码。Python 集成脚本涉及的 binary hash 另在 metadata 中记录。
+用户粘贴的完整全天 adaptive 输出是上述例外，按原文另存并保留事后 binary hash 与
+输出图像的独立校验，不把事后 hash 误称为运行时记录。
+
+初次沙箱探测没有 ROCm 设备；宿主运行成功。`atomic_first.log` 不是 GPU 硬件故障证据。
+`v2_disperse_*_16_0.log` 的 scratch 超限后已停止，修正的是单列表 tile 的 ownership，未提高上限。
+`boundary_atomic.log` 是合法 wing-clipped 事件被读取器误拒绝，随后保留物理 support 后通过。
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/boundary.events 32771 adaptive mixed
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.691 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=32771 frame=128x96 mode=adaptive distribution=fixture-mixed-direct contributions=142133685 CPU_reference=0.271268845 create=0.036700010
+complete_replay=0.060321093 replay_wall=0.023621082 select=0.000166893 bin=0.002514124 upload=0.000438220 prepare=0.000985861 accumulation=0.016374943 merge=0.000088215 download=0.000132840 cleanup=0.000163078 events_s=1387362.339 contributions_s=6017238463.474 center_tiles=26 tile_chunks=2 atomic_chunks=1 refs=829409 tasks=3275 scratch_used_peak=25249440 scratch_device_reserved=184549376 RSS_KiB=319696 max_abs=5.9685589803848416e-11 max_rel=5.9595772318269279e-13 flux_R=2.8323267191886195e-14 flux_G=-5.5281251977629701e-15 flux_B=9.6507636840237455e-15 flux_Y=1.1503592402127278e-14
+PROCESS_WALL 1.117062220 EXIT 0
@@ -0,0 +1,7 @@
+COMMAND OMP_NUM_THREADS=16 make -B -j1 PSF_BACKEND=hip 'HIP_CXXFLAGS=--offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic' hip-psf-replay
+TIMEOUT 60s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+cc -DENABLE_PNG -DFRAME_PSF_EVENT_SINK=1 -DPSF_BACKEND_HIP -DSPACETIME_MINKOWSKI  -std=c11 -march=native -pipe -Wall -Wextra -Wpedantic -O2 -DNDEBUG -fopenmp -Isrc -MMD -MP -c src/optics.c -o build/Release/obj/minkowski/standard_sink1_hip/src/optics.o
+mkdir -p build/Release
+hipcc --offload-arch=gfx1201 -std=c++17 -O2 -Wall -Wextra -Wpedantic -fopenmp -Isrc -x hip tests/replay_psf.hip -x none build/Release/obj/minkowski/standard_sink1_hip/src/optics.o -lm -lpng  -o build/Release/replay_psf
+PROCESS_WALL 1.266911305 EXIT 0
@@ -0,0 +1,7 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+no ROCm-capable device is detected
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.667 s
+PROCESS_WALL 1.667466220 EXIT 1
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.679 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 frame=3840x2160 mode=adaptive distribution=captured contributions=432818979 CPU_reference=0.824280024 create=0.050632000
+complete_replay=0.121458054 replay_wall=0.070826054 select=0.000172138 bin=0.007817984 upload=0.001097918 prepare=0.001653194 accumulation=0.051779747 merge=0.000582457 download=0.004020136 cleanup=0.000195980 events_s=925309.214 contributions_s=6111013629.616 center_tiles=35 tile_chunks=4 atomic_chunks=0 refs=2973775 tasks=11935 scratch_used_peak=35382764 scratch_device_reserved=184549376 RSS_KiB=713084 max_abs=2.7105054312137611e-19 max_rel=1.9611487209714066e-14 flux_R=-2.8081518355845397e-17 flux_G=4.7080671715585728e-17 flux_B=5.9271432925574641e-17 flux_Y=2.0330567515243999e-17
+PROCESS_WALL 1.968497664 EXIT 0
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.662 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 frame=3840x2160 mode=adaptive distribution=captured contributions=432818979 CPU_reference=0.812095881 create=0.036637783
+complete_replay=0.104471922 replay_wall=0.067834139 select=0.000179052 bin=0.007610083 upload=0.001078129 prepare=0.001619816 accumulation=0.051049709 merge=0.000552416 download=0.004829631 cleanup=0.000203133 events_s=966121.205 contributions_s=6380547998.522 center_tiles=35 tile_chunks=4 atomic_chunks=0 refs=2973775 tasks=11935 scratch_used_peak=35382764 scratch_device_reserved=184549376 RSS_KiB=713056 max_abs=2.7105054312137611e-19 max_rel=1.9611487209714066e-14 flux_R=-2.8081518355845397e-17 flux_G=4.7080671715585728e-17 flux_B=5.9271432925574641e-17 flux_Y=2.0330567515243999e-17
+PROCESS_WALL 1.918472017 EXIT 0
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.664 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 frame=3840x2160 mode=adaptive distribution=captured contributions=432818979 CPU_reference=0.806693077 create=0.036690950
+complete_replay=0.103733778 replay_wall=0.067042828 select=0.000176907 bin=0.007581234 upload=0.001075745 prepare=0.001624107 accumulation=0.051224947 merge=0.000552177 download=0.004083938 cleanup=0.000195026 events_s=977524.403 contributions_s=6455858060.497 center_tiles=35 tile_chunks=4 atomic_chunks=0 refs=2973775 tasks=11935 scratch_used_peak=35382764 scratch_device_reserved=184549376 RSS_KiB=713112 max_abs=2.7105054312137611e-19 max_rel=1.9611487209714066e-14 flux_R=-2.8081518355845397e-17 flux_G=4.7080671715585728e-17 flux_B=5.9271432925574641e-17 flux_Y=2.0330567515243999e-17
+PROCESS_WALL 1.918304047 EXIT 0
@@ -0,0 +1,38 @@
+COMMAND OMP_NUM_THREADS=16 make -j1 test
+TIMEOUT 90s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+make SPACETIME=minkowski ENABLE_HDR=1 backend
+make[1]: Entering directory '/home/wyj/Code/C/GR_4d_raytracing'
+cc -O2 -DNDEBUG -fopenmp build/Release/obj/minkowski/hdr_sink1_cpu/src/catalog.o build/Release/obj/minkowski/hdr_sink1_cpu/src/frame.o build/Release/obj/minkowski/hdr_sink1_cpu/src/geodesic.o build/Release/obj/minkowski/hdr_sink1_cpu/src/lens_map.o build/Release/obj/minkowski/hdr_sink1_cpu/src/movie.o build/Release/obj/minkowski/hdr_sink1_cpu/src/observer.o build/Release/obj/minkowski/hdr_sink1_cpu/src/observer_track.o build/Release/obj/minkowski/hdr_sink1_cpu/src/optics.o build/Release/obj/minkowski/hdr_sink1_cpu/src/ray.o build/Release/obj/minkowski/hdr_sink1_cpu/src/spacetime_common.o build/Release/obj/minkowski/hdr_sink1_cpu/src/spacetime_minkowski.o build/Release/obj/minkowski/hdr_sink1_cpu/src/main.o -lm -lpng -lcfitsio -o build/Release/minkowski_sky
+make[1]: Leaving directory '/home/wyj/Code/C/GR_4d_raytracing'
+mkdir -p /tmp/gr_psf_event_sink_reference
+OMP_NUM_THREADS=16 build/Release/minkowski_sky --catalog assets/sky_grid_5deg.csv --output /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360.png --hdr-output --width 640 --height 360 --fov-deg 30 --look-ra-deg 1 --look-dec-deg 1 --exposure 0.1 --observer-radius 30 --observer-velocity 0 0 0 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --max-magnification 1e300 --max-cache-psf-flux 1 --psf-relative-tail 1e-8 --psf-min-y 0 --coarse-cell-pixels 16 --refine-max-level 0 --refine-angle-abs-deg 0.001 --refine-angle-rel 0.1 --refine-jacobian-min 1e-3 --refine-min-edge-pixels 0.5 --refine-min-area-pixels2 0.25 --catalog-load-workers 4
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.667 s
+Rendered 35 images from 5654 catalog stars to /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360.png (ok)
+PSF splats: cached 35, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+python3 scripts/fits_floatdiff.py tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits /tmp/gr_psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits
+floatdiff: shape=(640, 360, 3) samples=691200 mismatches=0 max_abs=0 max_rel=0 worst_sample=0
+make SPACETIME=schwarzschild ENABLE_HDR=1 backend
+make[1]: Entering directory '/home/wyj/Code/C/GR_4d_raytracing'
+cc -O2 -DNDEBUG -fopenmp build/Release/obj/schwarzschild/hdr_sink1_cpu/src/catalog.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/frame.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/geodesic.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/lens_map.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/movie.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/observer_track.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/optics.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/ray.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_common.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/spacetime_schwarzschild.o build/Release/obj/schwarzschild/hdr_sink1_cpu/src/main.o -lm -lpng -lcfitsio -o build/Release/schwarzschild_sky
+make[1]: Leaving directory '/home/wyj/Code/C/GR_4d_raytracing'
+OMP_NUM_THREADS=16 build/Release/schwarzschild_sky --catalog assets/sky_grid_5deg.csv --output /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360.png --hdr-output --width 640 --height 360 --fov-deg 60 --look-ra-deg 1 --look-dec-deg 1 --exposure 0.1 --observer-radius 30 --observer-velocity 0 0 0 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --max-magnification 1e300 --max-cache-psf-flux 1 --psf-relative-tail 1e-8 --psf-min-y 0 --coarse-cell-pixels 16 --refine-max-level 0 --refine-angle-abs-deg 0.001 --refine-angle-rel 0.1 --refine-jacobian-min 1e-3 --refine-min-edge-pixels 0.5 --refine-min-area-pixels2 0.25 --catalog-load-workers 4
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.665 s
+Rendered 5206 images from 5654 catalog stars to /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360.png (ok)
+PSF splats: cached 5206, cached wing-clipped 0, direct fallbacks 0, discarded below min-Y 0
+python3 scripts/fits_floatdiff.py tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits /tmp/gr_psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits
+floatdiff: shape=(640, 360, 3) samples=691200 mismatches=0 max_abs=0 max_rel=0 worst_sample=0
+./build/Release/test_observer_minkowski
+coordinate-camera regression passed
+./build/Release/test_observer_schwarzschild
+coordinate-camera regression passed
+./build/Release/test_geodesic
+./build/Release/test_frame
+./build/Release/test_schwarzschild
+./build/Release/test_observer_track
+./build/Release/test_catalog_prefetch
+python3 tests/test_camera_cli.py build/Release
+minkowski: CLI checks passed; single/movie PNG identical, map max error 0
+schwarzschild: movie lens map identical with 1, 4 and 16 threads
+schwarzschild: CLI checks passed; single/movie PNG identical, map max error 4.44e-16
+PROCESS_WALL 26.018675067 EXIT 0
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive disperse
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.682 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 frame=3840x2160 mode=adaptive distribution=synthetic-phase-preserving-dispersal contributions=432818979 CPU_reference=1.491110802 create=0.037611008
+complete_replay=0.117703199 replay_wall=0.080092192 select=0.000455141 bin=0.000000000 upload=0.000191523 prepare=0.000000000 accumulation=0.075263899 merge=0.000000000 download=0.004099738 cleanup=0.000207186 events_s=818257.044 contributions_s=5404009677.272 center_tiles=26986 tile_chunks=0 atomic_chunks=4 refs=0 tasks=0 scratch_used_peak=0 scratch_device_reserved=184549376 RSS_KiB=705516 max_abs=3.3881317890172014e-21 max_rel=8.4356460581299069e-16 flux_R=1.2382136141425945e-18 flux_G=1.811942792627668e-18 flux_B=1.5829277137138293e-18 flux_Y=1.5978644712371554e-18
+PROCESS_WALL 2.620178348 EXIT 0
@@ -0,0 +1,8 @@
+COMMAND OMP_NUM_THREADS=16 build/Release/replay_psf benchmarks/hip_psf_replay_2026-09-07/center_65536.events 65536 adaptive disperse
+TIMEOUT 45s
+GIT 11e703e33dffb1ff168ba11dd922e68b448116b9
+BINARY_SHA256 121b85ade12680929cf0f560e04485e2ad3d8a56ff9dcbba950a323f840c5151
+PSF cache ready: 64x64 phases, radius 47 px, relative tail 1e-08, tail abs 1e-06, boundary 1e-07, build 0.733 s
+device=AMD Radeon RX 9070 arch=gfx1201 events=65536 frame=3840x2160 mode=adaptive distribution=synthetic-phase-preserving-dispersal contributions=432818979 CPU_reference=1.488748074 create=0.038790941
+complete_replay=0.121706009 replay_wall=0.082915068 select=0.000465870 bin=0.000000000 upload=0.000181281 prepare=0.000000000 accumulation=0.077964972 merge=0.000000000 download=0.004236780 cleanup=0.000192881 events_s=790399.162 contributions_s=5220028049.767 center_tiles=26986 tile_chunks=0 atomic_chunks=4 refs=0 tasks=0 scratch_used_peak=0 scratch_device_reserved=184549376 RSS_KiB=705940 max_abs=3.3881317890172014e-21 max_rel=8.4356460581299069e-16 flux_R=1.377382799700594e-18 flux_G=1.939309838343059e-18 flux_B=2.0425953472603454e-18 flux_Y=1.7396938046841301e-18
+PROCESS_WALL 2.720085292 EXIT 0
				`@@ -0,0 +1 @@`
				`HIP PSF cache comparison: max_abs=2.8421709430404007e-14 max_rel=7.5319184269262976e-16`