feat: visibility-space iterative LM engine (interferometer phase 2a)

[Jammy2211]

Summary

Phase 2a of the interferometer potential-correction extension (#623; parent epic #618): the visibility-space iterative LM engine, al.pc.IterFitDpsiSrcInterferometer, plus IterDpsiSrcInvInterferometerAnalysis.

Scaling design per the sparse-operator requirement: the Levenberg–Marquardt loop runs entirely in the real-space normal-equation space. The penalized objective, gradient and Hessian are expressed through the joint curvature F = Aᵀ(TᴴC⁻¹T)A (rebuilt per accepted step via the sparse operator's FFT machinery from the re-traced mapper + correction-response triplets), the data vector D = Aᵀ·dirty_image and the once-precomputed scalar dᴴC⁻¹d:

P(x) = ½(dᴴC⁻¹d − 2xᵀD + xᵀFx) + ½xᵀRx

so no per-candidate NUFFT is required — cost scales with real-space mask pixels, independent of the visibility count. Each accepted step re-ray-traces the real-space grid through the corrected lens (macro model + InputPotential from the current δψ) and re-evaluates the source gradients from the current pixelized source reconstruction (PixSrcFactoryITP), exactly mirroring the imaging engine's feedback loop. Optional gauge constraints (⟨δψ,1⟩ = ⟨δψ,x⟩ = ⟨δψ,y⟩ = 0) via the shared KKT step; Laplace evidence with the complex-noise normalization.

Cites Cao et al. 2025 (https://github.com/caoxiaoyue/lensing_potential_correction; cite via https://github.com/caoxiaoyue/potential_correction_paper); methodology per the B1938+666 papers (Powell et al. 2025; Vegetti et al. 2026).

Phase 2b (next): the autolens_workspace_test layer (visibility subhalo-recovery regression + jax_likelihood_functions/interferometer/potential_correction.py).

API Changes

Added only: al.pc.IterFitDpsiSrcInterferometer and al.pc.IterDpsiSrcInvInterferometerAnalysis + docs entries.
See full details below.

Test Plan

• 5 new tests: χ² identity certification (the normal-equation χ² ≡ the directly-computed visibility χ² at the optimized state — the load-bearing check of the NUFFT-free loop), finite optimized state with cost beating the zero state, gauge constraints satisfied to 1e-6, finite Laplace evidence, loud missing-sparse-operator / missing-state errors.
• Full test_autolens/potential_correction suite: 51 passed.
• Full test_autolens suite run before commit (execution contract).

Full API Changes (for automation & release notes)

Added

• al.pc.IterFitDpsiSrcInterferometer(dataset, lens_start, dpsi_pixelization, src_pixelization, gauge_constraints=False, ..., n_iter=20, tol=1e-6) — solve_joint_optimization(), log_evidence(s, dpsi); requires dataset.apply_sparse_operator().
• al.pc.IterDpsiSrcInvInterferometerAnalysis(...) — af.Analysis over the engine (failed inversions → logged −1e30 penalty).
• docs/api/potential_correction.rst entries.

Migration

• None — additive only.

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