feat: Prodigy-vs-Nautilus point-source benchmark (#657 follow-up)

[Jammy2211]

Summary

Prodigy-vs-Nautilus benchmark on the point-source likelihoods (#657 follow-up, human-requested): two new free-centre cells mirroring the Nautilus anchors (pure sampler swap on the same 8-param PointFlux model/dataset), plus results for all six runs on the WSL dev laptop (CPU, viz disabled). Truth = simulator preset (er=1.6, centre (0,0)), truth-anchored logL computed per likelihood flavour.

cell	max logL	truth logL	wall s	best er / centre	verdict
nautilus / source_plane	−313.2	−33788	168	3.20 / (−0.37, −0.38)	likelihood bias: wrong model beats truth by ~4 orders of magnitude in χ²
prodigy / source_plane	−109.7	−33788	19.4	5.55 / (−0.63, −0.02)	out-optimizes Nautilus 8.7× faster on the same (biased) objective
nautilus / image_plane	+9.56	+7.20	739.7	1.623 / ~(0, 0)	reference anchor — truth recovered
prodigy / image_plane (64×300)	−79.9	+7.20	852.8	1.866 / (−0.02, 0.02)	missed the 5 mas basin (start-count limited; -inf underflow plateaus)
prodigy / image_plane (256×300)	−47.7	+7.20	3515.5	1.581 / (0.000, 0.001)	truth basin found; final polish plateaued (best logL flat from step ~250)
prodigy / image_plane_solved (64×300)	+2.37	+7.74	981.9	1.574 / (0.00, 0.01)	truth recovered THROUGH the solver — the recommended config works

Conclusions

1. The solver gradients demonstrably work in a real search: the solved-centre configuration (PointSolved + FitPositionsImagePairAllSolved, 5 params) converges to the truth basin with the default 64×300 budget, ~within 5 logL of the truth anchor, in ~16 min — gradients flowing through the lens-equation solve via the implicit-diff custom_jvp.
2. The free-centre image-plane cell needs 4× the starts to find the same basin (and still under-polishes at 300 steps) — consistent with the filed PairAll -inf-underflow plateau issue shrinking the gradient-reachable basin, and with the solved variant's dimensionality advantage.
3. The source-plane scalar-µ² likelihood is spectacularly biased on this dataset (truth logL −33788 vs −110 at wrong parameters): both samplers agree, so it's the objective, not the optimizer — direct evidence for the pairing guide's recommendation to search with the tensor-weighted solved fit and validate image-plane, and for the filed cluster PointSolved default swap.

Scripts Changed

• scripts/point_source/searches/multi_start_prodigy/image_plane.py — new free-centre cell (mirrors nautilus/point_source/image_plane.py)
• scripts/point_source/searches/multi_start_prodigy/source_plane.py — new free-centre cell (mirrors the nautilus anchor)
• scripts/misc/searches/sweep.py — both registered in CELLS beside the anchors
• results/searches/{nautilus,multi_start_prodigy}/point_source/** — the six result JSONs + PNGs above

Test Plan

• ruff check clean; AUTOLENS_PROFILING_SMOKE=1 import-check green for both cells
• All six cells executed end-to-end locally (this table)

Generated by the PyAutoLabs agent workflow.