test: solver-gradient certification + staircase FD methodology (phase 5 of #657)

[Jammy2211]

Summary

Phase-5 certification of the PointSolver implicit-diff gradients (#657; library PR linked below). Extends the point-source gradient certification script to the full variant matrix and re-verifies value invariance.

FD methodology for solver-chained fits (encoded in the script prose): the forward solve quantizes positions at pixel_scale_precision, so the computed likelihood is a staircase — central differences below the stair width read exactly zero while the implicit AD gradient (the exact-solve envelope derivative) is correct. Certification therefore uses a fine-precision solver (1e-5) + the per-parameter rel_steps FD sweep, with a justified 2% tolerance on the solver blocks (residual stair noise ~1–2%; a wrong rule misses by factors at every parameter and step).

Scripts Changed

• scripts/point_source/jax_grad/gradient.py — phase-5 marker note removed; four new blocks: FitPositionsImagePairAllSolved + PointSolved (solved β* through the solver, FD-certified), FitPositionsImagePairAll + Point (sampled centre, exercises the dβ term, FD-certified), FitPositionsImagePairRepeatSolved (finiteness + liveness only — min-selection subgradient, exclusion documented), fluxes+time-delays solved combo (nested autodiff through Hessian magnifications; H0 live). Solver-chained models carry no cosmology component (documented limitation: free cosmology cannot cross the custom_jvp boundary; harmless for 2-plane positions).

All blocks pass end-to-end; the four jax_likelihood scripts re-run against the library branch with every regression literal unchanged (value-invariance gate).

Upstream PR

PyAutoLabs/PyAutoLens#677

Test Plan

• scripts/point_source/jax_grad/gradient.py runs green end-to-end (all six blocks)
• scripts/point_source/jax_likelihood/{point,source_plane,image_plane,fluxes_time_delays}.py — literals unchanged
• Local smoke 20/21 — sole failure is the KNOWN WSL-laptop margin imaging/subhalo_recovery.py TIMEOUT(300s) (green on main CI; untouched by this diff; recorded in phase 3)

Generated by the PyAutoLabs agent workflow.