Transferable Hierarchical Coupling Law for Per-Galaxy a0 Variation in SPARC Galaxies (v8 — Phases 126-134)

v8 — Phases 126-134: Transferable hierarchical coupling law for per-galaxy a0 variation, with external validation. Final Claim Per-galaxy a0 is governed by a transferable, regime-dependent, hierarchical baryon-halo coupling law: A 3-axis structural core (MHI, Mhost, MeanRun) sets the baseline A dominant kinematic coupling channel (VfResid = residual kinematic excess beyond baryonic prediction) mediates halo physics into a0 A secondary outer-halo channel (lh_outerImprove) contributes independently The coupling activates sharply at Vflat ~ 181 km/s; strongest in high-Vflat galaxies ~36% of the coupling signal is irreducibly encoded in multi-scale dynamical integration External Validation (Phase 134) Trained on N=45 published-quality galaxies, tested on N=10 crude-quality holdout galaxies: Core alone: fails (transfer gap = -11.5%) Core + raw Vflat: modest (gap = 10.0%) Core + VfResid: strong (gap = 56.9%, r = 0.801) 5-axis (Core + VfResid + lhOuter): strongest (gap = 66.0%) All coefficient signs preserved. Regime-restricted training outperforms full training. The transferable signal is the residual dynamical excess channel, not raw structural variables. Key Numbers Internal LOO gap (N=45): Core = 44.1%, Core+VfResid = 61.1%, 5-axis = 65.4% External transfer gap (N=10 holdout): Core+VfResid = 56.9%, 5-axis = 66.0% VfResid drivers: haloK explains 29%, best-5 explains 52%, 36% irreducible Regime: VfResid delta = +27.8pp in Vflat≥120 regime; unstable in low-Vflat Caveats: holdout sample N=10 (directional, not conclusive); all crude quality; all Vflat≥120 (regime split not independently tested externally). All analysis scripts and machine-readable results included for full reproducibility. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157).