Feat: Add analytic moving Alcubierre spacetime backend

Add a third analytic spacetime provider for the moving Alcubierre warp
bubble, x_s(t) = v_s*t with x_s(0) = 0.  The lab slices stay flat, so
alpha = 1, gamma_ij = delta_ij, beta^x = -v_s f(r_s), and K_ij follows
from the flat spatial metric; the time dependence enters through the
moving shape argument.  The exotic matter is treated as transparent, so
there is no capture: rays are only ACTIVE or ESCAPED, with a bubble-
centered escape radius R + 20/sigma.

Expose --alcubierre-vs, --alcubierre-radius, and --alcubierre-sigma
(|v_s| < 1).  Scale the per-ray step budget with the escape radius and
1/(1-|v_s|) so near-luminal grazing rays still escape, and reject
parameter combinations whose worst-case budget exceeds the cap.  Use a
cancellation-free shape formula for small sigma*R and reject derived
escape radii that overflow.

The regression test covers metric reconstruction, d_beta/K finite
differences, the translation isometry, small-sigma stability, the flat
limit, reflection symmetry, step convergence, and a near-luminal slow
ray.  build.md, usage.md, and README.md document the backend.

usage.md

@@ -92,6 +92,59 @@ The last example points outward from a camera moving inward inside the horizon.
 It needs no CSV trajectory or movie wrapper. These small images are camera
 checks; increase resolution and refinement for production renders.
 
+## Alcubierre warp-bubble spacetime
+
+`alcubierre_sky` renders the moving Alcubierre line element
+
+$$ds^2 = -dt^2 + \left[dx - v_s f(r_s)\,dt\right]^2 + dy^2 + dz^2,$$
+
+with the bubble center following the constant-velocity worldline
+`x_s(t) = v_s t` (a lab/non-comoving slicing fixed by `x_s(0) = 0`) and
+
+$$f(r) = \frac{\tanh(\sigma(r+R)) - \tanh(\sigma(r-R))}{2\tanh(\sigma R)},\qquad
+r_s = \sqrt{(x-x_s)^2 + y^2 + z^2}.$$
+
+The bubble therefore propagates through the coordinates, and the metric is
+time-dependent: the renderer evaluates `f(r_s)` and its spatial derivatives at
+each coordinate time, while the extrinsic curvature supplies the required
+`d_t gamma` information to the 3+1 null-ray equations. The exotic matter that
+would source the bubble is treated as optically transparent, so there is
+**no capture**: rays are only active or escaped. This is why the backend
+requires a sub-luminal `|v_s| < 1`; at or above `1` the metric develops an
+ergoregion/event horizon and static observers cease to exist, which is outside
+the current no-capture scope.
+
+| Option | Meaning / default |
+| --- | --- |
+| `--alcubierre-vs V` | Constant shift parameter, `|V| < 1` (default 0.5) |
+| `--alcubierre-radius R` | Bubble radius `R > 0` (default 5) |
+| `--alcubierre-sigma S` | Wall sharpness `S > 0` (default 1) |
+
+`f` decays to zero past `r_s = R` over a transition width `~1/sigma`, so the
+finite escape sphere is bubble-centered with radius `R + 20/sigma` and needs no
+CLI option; it follows the moving bubble, so rays terminate only once the local
+metric is flat to below double precision. The single-frame camera default is
+`(0,0,15)` at `t = 0`, when the bubble is still at the origin; it must lie
+inside the escape sphere, or the observer build fails with an explicit error.
+The per-ray step budget scales with the escape radius and `1/(1-|v_s|)`, so
+near-luminal `v_s` still lets grazing rays escape; combinations whose
+worst-case budget would exceed the internal cap are rejected at startup.
+
+Lensing and frequency shifts come from the bubble wall. The configuration is
+invariant under the isometry `(t, x) -> (t + T, x + v_s T)`, so observers
+related by it see identical escaping directions and frequency ratios. For
+example:
+
+```sh
+make -j PSF_BACKEND=cpu SPACETIME=alcubierre backend
+./build/Release/alcubierre_sky --catalog assets/sky_grid_5deg.csv \
+  --observer-radius 15 --look-ra-deg 90 --look-dec-deg -90 \
+  --alcubierre-vs 0.5 --alcubierre-radius 5 --alcubierre-sigma 1 \
+  --width 640 --height 360 --fov-deg 60 --exposure 1 \
+  --coarse-cell-pixels 16 --refine-max-level 2 --psf-direct \
+  --output output/imgs/alcubierre_wall.png
+```
+
 ## Movie image sequences
 
 Movie mode reads an observer-track CSV containing coordinate time, proper