feat: cluster + group scaling relations in Lenstool convention (reference-anchored, fixed exponent)

[Jammy2211]

Summary

Moves every scaling-relation composition in the workspace to the reference-anchored convention used by Lenstool and standard in published group/cluster analyses (Limousin et al. 2005; Elíasdóttir et al. 2007; Bergamini et al. 2019), replacing the free two-parameter scaling_factor * L ** scaling_exponent form that referee feedback (assessed in #237) correctly flagged as non-standard:

• Normalization anchors to a reference galaxy (the brightest scaling member): b0_i = b0_ref * (L_i / L_ref) ** 0.5 — the free parameter is the reference member's lens strength, physically interpretable with an easy-to-motivate prior range (the old scaling_factor had units arcsec/L^β that changed with β).
• Exponent fixed at the Faber-Jackson value 0.5 (b0 ∝ σ², σ ∝ L^¼), not sampled; the Bergamini et al. 2019 kinematic calibration (σ ∝ L^0.27–0.28, i.e. b0 exponent ≈ 0.55; r_cut exponent from the fundamental plane) is documented as the refinement, and freeing the exponent is shown as a one-line systematics test.
• Truncation radius scales too: rs_i = rs_ref * (L_i / L_ref) ** 0.5, mirroring Lenstool's r_cut ∝ L^½ (cluster dPIE tier; the group tier uses Isothermal, no truncation radius — prose points at the cluster example).
• Cluster tier dimensionality drops 2 → 1 free parameter (model N = 13 → 12); prose everywhere explains that only luminosity ratios enter, with the magnitude-catalogue conversion given.

Scripts Changed

• scripts/cluster/simulator.py — truth relation → reference-anchored (b0_ref = 0.12, exponent 0.5, rs scaled); regenerates dataset/cluster/simple/.
• scripts/cluster/modeling.py — single free b0_ref (U(0,1)), fixed exponents, rewritten __Scaling Relation__ prose (referee/Lenstool rationale, Bergamini refinement).
• scripts/cluster/start_here.py — mirrors modeling.py.
• scripts/cluster/likelihood_function.py — truth-tier rebuild matches the new relation (b0 + rs scaled).
• scripts/cluster/csv_api.py — prose reference updated.
• scripts/group/features/scaling_relation/{simulator,modeling,fit,likelihood_function,modeling_for_luminosities}.py — same convention for the group three-tier API (einstein_radius_ref anchored to the brightest member). The group dataset needs no regeneration: both scaling members share L = 0.45, so luminosity ratios are 1 and the truth radii are unchanged.

Not in scope (follow-up noted on the issue): scripts/imaging/features/scaling_relation/, scripts/group/slam.py, guides/advanced/multi_plane.py still show the old form.

Validation

• Cluster simulator ran end-to-end with the new truth relation: both sources still produce 3 multiple images at sensible positions (point_datasets.csv in the diff); scaling_galaxies.csv regenerated.
• Model-composition structural check: rebuilt the modeling.py model and asserted prior_count == 12 with b0_ref the tier's only free parameter; instance check confirms the brightest member anchors exactly (b0 = b0_ref, rs = 10.0") and the faintest scales to b0_ref·√(0.05/0.40) (0.354×).
• Group family: dataset unchanged by construction (equal luminosities → ratios 1); scripts not re-run (fit/likelihood scripts take minutes; convention change is arithmetic-identical at ratio 1).
• Dataset note: two illustrative PNGs (tracer.png, galaxies_images.png) are deleted in this commit — the old ones depicted the previous truth model; their regeneration via subplot_tracer on the 14-galaxy multi-plane tracer is pathologically slow with current galaxy-scale plot defaults (the exact problem feat: cluster-scale visualization — per-plane critical curves/caustics aplt helpers PyAutoLens#578 addresses) and will be push-appended to this branch if the background render completes, else they regenerate on any user simulator run.
• Full modeling runs are gated by the known cluster TEST_MODE slowness (no_run.yaml-parked scripts, pre-existing — see feat: LensTool-native dPIE parameterization (from_lenstool) + parity validation PyAutoGalaxy#485 discussion).

Validation checklist (--auto run — in-session directives)

• Effective level: supervised (header: supervised, cap: feature → supervised); one-shot ship authorized in-session by the user, Heart YELLOW acked in-session
• Human: convention matches the referee's recommendation as intended?
• Human: merge, amend, or reject — then log the outcome

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