feat: visibility-space potential corrections — sparse-operator route (interferometer phase 1)

[Jammy2211]

Summary

Phase 1 of extending the potential-correction (gravitational imaging) subpackage to interferometer data (#623; parent epic #618): al.pc.FitDpsiSrcInterferometer jointly inverts visibilities for the pixelized source and pixelized potential corrections δψ, plus DpsiSrcInvInterferometerAnalysis for evidence-based hyper-parameter sampling. This reaches toward the technique's benchmark regime — the JVAS B1938+666 detections (Powell et al. 2025, Nat. Astron. 9, 1714; Vegetti et al. 2026) were made in visibility space.

The sparse-operator (w-tilde) route is the primary implementation, per the scaling requirement: the joint curvature [f | G]ᵀ·(TᴴC⁻¹T)·[f | G] (source mapping block f, correction response G = −D_s·D_ψ) is assembled through the dataset's InterferometerSparseOperator FFT machinery from extent-indexed COO triplets — one curvature_matrix_diag_from call over the concatenated blocks — and the data vector against the dirty image, so cost scales with real-space mask pixels, independent of the visibility count. χ² costs a single forward NUFFT of the reconstructed image. The dense transform_mapping_matrix route (real/imag row-stacked) is retained behind use_sparse_operator=False as the small-n_vis parity reference. Evidence uses the complex-noise normalization (noise_normalization_complex_from) with per-component χ².

The δψ mesh builds from the dataset's real-space mask via the existing PairRegularDpsiMesh; source gradients remain image-plane; dense_util's xp kernels are consumed unchanged (data-agnostic). Requires dataset.apply_sparse_operator() for the sparse route (loud InversionException otherwise — no silent fallback).

Phase 2 (follow-up on #623): the iterative LM engine's interferometer seam and the autolens_workspace_test scripts (visibility subhalo-recovery regression + jax_likelihood_functions/interferometer/potential_correction.py).

Cites Cao et al. 2025 (https://github.com/caoxiaoyue/lensing_potential_correction; cite via https://github.com/caoxiaoyue/potential_correction_paper).

API Changes

Added only — nothing removed or changed: al.pc.FitDpsiSrcInterferometer and al.pc.DpsiSrcInvInterferometerAnalysis, plus docs entries.
See full details below.

Test Plan

• 4 new tests: sparse route ≡ dense route on the interferometer_7 fixture (curvature, data vector, evidence — the load-bearing parity), end-to-end finite evidence with correct block shapes, hand-computed dense evidence terms (solution/χ²/noise normalization), and the loud missing-sparse-operator error.
• Full test_autolens/potential_correction suite: 46 passed.
• Full test_autolens suite run before commit (execution contract).

Full API Changes (for automation & release notes)

Added

• al.pc.FitDpsiSrcInterferometer(dataset, lens_start, source_start, dpsi_pixelization, src_pixelization, src_image_mesh=None, settings_inversion=None, use_sparse_operator=True, preloads=None) — visibility-space joint source+δψ inversion; log_evidence, solve_src_dpsi, best_fit_source/best_fit_dpsi, model_visibilities, sparse (curvature_matrix_diag_from w-tilde) and dense (operated_mapping_matrix) routes.
• al.pc.DpsiSrcInvInterferometerAnalysis(...) — af.Analysis with the visibility evidence as likelihood (failed inversions → logged −1e8 penalty).
• docs/api/potential_correction.rst entries for both.

Migration

• None — additive only.

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