W1 · Phase 4 Stage 1: PositionsLH plumbing in the searches framework + hazard transects

[Jammy2211]

Blocks: Gate B pt 2, Phase 5 (every positions-on arm), W2.

Scope

1. Positions plumbing in scripts/misc/searches/_setup.py: every target builder accepts positions={off, on} and threads positions_likelihood_list (threshold set: 0.3 fixed and SLaM-style factor-3 auto; penalty factor 1e5 / 1e8) into the analysis; positions come from the simulator's positions.json (truth positions — record the idealization). Remove the pixelized raise_inversion_positions_likelihood_exception=False short-circuit behind the same switch. --config-name must carry the positions arm so identifiers/results stay disjoint (same discipline as the seed/tier tags — read _samplers.multi_start_unique_tag first).
2. Stage-1 characterisation (laptop / RAL CPU, eager value_and_grad): transects through the threshold and across the θ_E=0 basin; record hinge/plateau/cliff in the hazards ledger; sensitivity to penalty factor and threshold. H4.2 (new failure modes: lane fling, fence oscillation) measured, not assumed.
3. phase_04_positions/RESULTS.md Stage 1 write-up.

Pre-req shipped: CP-1 PositionsLH fix (PyAutoLens#699/#700).

[Jammy2211]

Shipped: PR #168 merged — SEARCHES_POSITIONS/_THRESHOLD/_FACTOR plumbing (single-plane imaging/interferometer; other cells raise), arm tag composed into unique_tag + config_name for every sampler, results-JSON collision fix, committed dataset/imaging/hst/positions.json, Stage-1 transects + phase_04_positions/RESULTS.md (auto threshold collapses to 0.2; hinge jump 2.0e5/2.0e8; exact-zero interior plateau; argmax-switch below every threshold; penalty/likelihood grad ratio ≈1 outside), positions_penalty hazards check. Next: W2 (#160).