Point-source phase A: PairAll log-sum-exp stabilization + free-centre tensor option

[Jammy2211]

Summary

Phase A of the point-source defaults campaign (#678): the two library prerequisites for the evidence campaign that decides the demonstrated defaults.

1. FitPositionsImagePairAll (all-to-all image-plane mixture) computed log(sum(exp(log_p))) literally, underflowing to -inf once the best model/observed pairing is ≳38σ — the prime suspect for the 256-start free-centre gradient-search plateau (2026-07-31 benchmark, autolens_profiling#99). The reduction is now a max-shifted log-sum-exp: mathematically identical wherever the literal form was finite, finite at arbitrarily large mismatch, restoring gradient flow. Zero-model-positions and inf-padded solver rows behave exactly as before (unit-tested).
2. FitPositionsSource (free-centre source-plane fit) gains a weighting class attribute: "magnification" (default) is byte-identical to existing behaviour (the Lenstool convention, comparisons untouched); "jacobian" opts into the per-image precision tensor Wᵢ = Aᵢ⁻ᵀΘᵢAᵢ⁻¹ + observed-plane normalization, reusing precision_tensor_components_from — the same tensor likelihood as FitPositionsSourceSolved but with the centre sampled as a free parameter rather than solved and marginalized.

API Changes

Additive only; no defaults change in this PR (the campaign's default swap is phase C, a separate PR with its own release notes).

• FitPositionsSource.weighting class attribute added ("magnification" default = unchanged behaviour; "jacobian" new tensor option), plus a residual_vectors property.
• FitPositionsImagePairAll values unchanged wherever previously finite; previously--inf extreme-mismatch likelihoods are now finite (loudly bad instead of gradient-dead).
  See full details below.

Test Plan

• Full test_autolens/ suite in the task worktree
• Existing pair_all literal tests pass unchanged (exact == asserts — value identity in the finite regime)
• New regression tests: extreme-mismatch finiteness, shifted-vs-literal equality, free-tensor == solved-tensor at the solved centre, observed-plane normalization, unknown-weighting raise
• wst scripts/point_source/jax_likelihood/{point,image_plane,source_plane,fluxes_time_delays}.py literal invariance (JAX jit/vmap parity)

Full API Changes (for automation & release notes)

Added

• FitPositionsSource.weighting — class attribute, "magnification" (default: the unchanged scalar µ²/σ² weighting + magnified-noise normalization) or "jacobian" (per-image precision tensor Wᵢ = Aᵢ⁻ᵀΘᵢAᵢ⁻¹ + observed-plane normalization matching FitPositionsSourceSolved).
• FitPositionsSource.residual_vectors — (n_positions, 2) vector residuals β̂ᵢ − c used by the tensor path.

Changed Behaviour

• FitPositionsImagePairAll.all_permutations_log_likelihoods / chi_squared (inherited by FitPositionsImagePairAllSolved): max-shifted log-sum-exp reduction. Identical values where the literal form was finite; extreme-mismatch (≳38σ) values are now finite instead of -inf/+inf. The no-model-image no_image_residual floor is unchanged.
• The unknown-weighting exception message (autolens/point/fit/solved.py) now names both class defaults instead of claiming the solved context.

Migration

• None required. Opt into the free-centre tensor with a one-line subclass: class MyFit(al.FitPositionsSource): weighting = "jacobian", passed via AnalysisPoint(fit_positions_cls=MyFit).

Part of #678 (phase A). Generated by the PyAutoLabs agent workflow.