feat: cluster/group examples on Lenstool-native dPIE default + reference-anchored SLaM scaling

[Jammy2211]

Summary

Workspace phase of PyAutoLabs/PyAutoGalaxy#506 (library PR: PyAutoLabs/PyAutoGalaxy#509, pending-release): migrates every cluster/group example onto the Lenstool-native default dPIE and expresses all scaling-relation tiers in the reference-anchored convention of published analyses (Limousin+05, Elíasdóttir+07, Bergamini+19), so a reader of those papers knows exactly what the model is doing. Also absorbs the deferred lenstool-scaling-slam (PR3 of #265): the group SLaM pipelines drop the non-standard scaling_factor * L^scaling_relation (both free) parameterization for the reference-anchored form.

Scripts Changed

Cluster suite — modeled in σ_LT-space (Lenstool .par parameters, priors in km/s / arcsec):

• cluster/simulator.py — truths now sigma (330/210 km/s mains; sigma_ref = 85 km/s tier), r_core/r_cut, redshift_object/redshift_source (final-plane anchored, same convention as NFWMCRLudlowSph); scaling relation sigma ∝ L^0.25, radii ∝ L^0.5 (Lenstool potfile vdslope/slope = 4).
• cluster/modeling.py — main lenses free (sigma, r_core, r_cut); tier's single free parameter is sigma_ref (interpretable prior in km/s — the referee's point); N=12 unchanged (validated end-to-end in TEST_MODE).
• cluster/start_here.py (Abell 2744) + dataset/cluster/a2744/{mass.csv,prep.py} — BCG rows converted to σ-space (290 km/s ≙ b0≈3.0" at z=0.308→5.662); 188-member tier on sigma_ref.
• cluster/csv_api.py — mass.csv rows for the default dPIE now carry the .par keywords verbatim; internal rows remain possible via dPIEMassB0*.
• cluster/likelihood_function.py — truth reconstruction in σ-space.
• cluster/lenstool/{data,modeling}.py + README — dPIEMassLenstool → dPIEMass (the default class is the Lenstool parameterization now).
• dataset/cluster/simple/* — regenerated with the σ-space truths (b0 values preserved to ~0.5%).
• weak/features/strong_lensing/a2744.py — same σ-space model as cluster/start_here.py.
• guides/profiles/mass.py — default-class construction demos + dPIEMassB0 mention.

SLaM pipelines (absorbs lenstool-scaling-slam, PR3 of #265):

• group/slam.py, group/features/linear_light_profiles/slam.py (both scaling sites each) — einstein_radius = einstein_radius_ref * (L/L_ref)^0.5, exponent fixed at Faber–Jackson, single free einstein_radius_ref, reference luminosity anchored to the brightest main lens (BGG) from the preceding light fit. Only the BGG's luminosity anchors the relation — its (free) mass is deliberately not coupled to the tier.
• group/features/scaling_relation/modeling.py — cluster-analogue prose updated to the σ-space form.

Notebooks regenerated for every changed script (pre-existing potential-correction catalogue drift excluded per #265's precedent).

Test Plan

• scripts/check_sizes.sh — all scripts within tolerance.
• cluster/csv_api.py, guides/profiles/mass.py run clean.
• cluster/modeling.py + cluster/likelihood_function.py end-to-end in TEST_MODE (N=12; composition validated).
• Dataset regeneration verified: solved multiple images ray-trace back to the source coordinate in the final plane (RMS ~3e-4", matching the pre-swap dataset's behaviour).
• Companion autolens_workspace_test PR re-validates the 6-leg Lenstool parity + FD sweeps.

Merge gate

Library-first: merge after PyAutoLabs/PyAutoGalaxy#509 (pending-release).

🤖 Generated with Claude Code

https://claude.ai/code/session_01K5MpYSYekRWVtoUmExAgKB