Fix: reject invalid inverse lens-map weights

Check spherical area weight sums against a fixed 1e-8 tolerance and normalize accepted weights before interpolation. Skip invalid images in both catalog paths.

Add a thin-triangle regression for both parities, document the measured tolerance margin, and refresh HDR fixtures with strict comparisons restored.

tests/test_frame.c

@@ -330,6 +330,50 @@ int main(void) {
     goto done;
   }
   frame_lens_mesh_destroy(&fine_mesh);
+  /* Schwarzschild level-4/J=0.2 ring triangle: the old edge tolerance accepts
+   * (1,0,0) although it is outside, producing unsigned weights summing to
+   * 1.09608. Keep a genuine interior source after it to check that rejecting
+   * one source does not discard subsequent stars. Exercise both parities. */
+  const double thin_directions[3][3] = {
+      {0.99999998891116071, 0.00013431364716360775, 6.4323579270168807e-05},
+      {0.99999997228355786, -0.00021216644782556991, -0.00010206998544149922},
+      {0.9999927016945267, -0.0034455730513416835, -0.001650631403158936}};
+  LensVertex thin_vertices[3] = {
+      {.image_x = 40, .image_y = 40, .status = RAY_ENDPOINT_ESCAPED},
+      {.image_x = 48, .image_y = 40, .status = RAY_ENDPOINT_ESCAPED},
+      {.image_x = 40, .image_y = 48, .status = RAY_ENDPOINT_ESCAPED}};
+  LensTriangle thin_triangle = {.vertex = {0, 1, 2}};
+  FrameLensMesh thin_mesh = {.vertices = thin_vertices, .vertex_count = 3,
+                            .triangles = &thin_triangle, .triangle_count = 1};
+  Star thin_stars[2] = {
+      {.direction = {1, 0, 0}, .temperature_K = 7000, .amplitude = 1},
+      {.temperature_K = 7000, .amplitude = 1}};
+  for (int i = 0; i < 3; ++i) {
+    memcpy(thin_vertices[i].n_infinity, thin_directions[i],
+           sizeof thin_directions[i]);
+    memcpy(thin_vertices[i].camera_direction, thin_directions[i],
+           sizeof thin_directions[i]);
+    for (int axis = 0; axis < 3; ++axis)
+      thin_stars[1].direction[axis] += thin_directions[i][axis];
+  }
+  const double thin_norm = hypot(hypot(thin_stars[1].direction[0],
+                                      thin_stars[1].direction[1]),
+                                thin_stars[1].direction[2]);
+  for (int axis = 0; axis < 3; ++axis)
+    thin_stars[1].direction[axis] /= thin_norm;
+  StarCatalog thin_catalog = {.stars = thin_stars, .count = 2};
+  for (int parity = 0; parity < 2; ++parity) {
+    thin_triangle.vertex[1] = parity ? 2 : 1;
+    thin_triangle.vertex[2] = parity ? 1 : 2;
+    memset(hdr, 0, (size_t)width * height * 3 * sizeof *hdr);
+    if (frame_splat_catalog(&thin_mesh, &thin_catalog, hdr, width, height,
+                            test_exposure, &psf, NULL, 1.0, 1.0,
+                            psf_relative_tail, 0.0, 0, 1, NULL, NULL, NULL) != 1 ||
+        hdr[3 * (43 * width + 43)] <= 0.0) {
+      fputs("thin source-triangle inverse-map regression failed\n", stderr);
+      goto done;
+    }
+  }
   /* Refinement probes are temporary until their generation is complete.  A
    * shared diagonal probe must produce one stable midpoint and conforming
    * children only after its endpoint has been installed. */