Structured Regime-Dependent Coupling Law for Per-Galaxy a0 Variation in SPARC Galaxies — with Physical Interpretation (v11 — Phases 126-134, 200-204, 300-303)

v11 — Complete scientific narrative: empirical discovery (Phases 126-134), external validation (Phases 200-204), and physical interpretation (Phases 300-303). Central Result Per-galaxy a0 variation in SPARC is governed by a structured, regime-dependent baryon-halo coupling law. The dominant transferable channel (VfResid) encodes a regime-dependent dynamical integration effect — accumulated baryon-halo processing that genuinely amplifies in deeper potential wells. This is supported by external validation on N=94 independent galaxies and physical interpretation via hypothesis testing. What is new in v11 (Phases 300-303) Phase 300: Sample salvage recovers 35 additional external galaxies (N=59→N=94), preserving all correlations Phase 301: VfResid driver analysis — haloK is shared #1 predictor (r=0.598 int, 0.511 ext); pure structural models fail (LOO R²=−0.144); irreducible fraction 35.8%/68.5% still predicts a0 Phase 302: Regime law — hidden residual (after removing haloK) predicts a0 at r=0.299 low-V vs r=0.749 high-V internally; both slope and correlation strengthen (slope ratio 2.6:1), ruling out pure observability Phase 303: Physical interpretation — H4 (dynamical integration) wins (score 10) over H1 (halo response, 7), H3 (feedback, 7), H2 (assembly, 4); logMeanRun is the only regime-strengthening proxy; gas fraction fades at high-V Established Results (Phases 126-204) Hierarchical coupling law: Core (44.1%) + VfResid (+17pp) + lhOuter (+4pp) = 65.4% LOO gap External validation: complete hierarchy replicates in N=59 independent galaxies, 8/8 checks pass, VfResid dominates by 30-76pp even after improving environmental proxy Leading Physical Interpretation H4: Dynamical integration — an accumulated product of baryon-halo interaction that deepens with potential well depth. haloK captures the halo-amplitude component; logMeanRun provides a partial handle on integration depth. Gas fraction and morphology are relevant at low Vflat but fade in the high-Vflat regime where the coupling law is strongest, consistent with a transition from feedback-dominated to integration-dominated physics. Caveats All data from SPARC survey; cross-survey replication needed Hypothesis scoring is heuristic, not formal Bayesian model comparison Hypotheses are not mutually exclusive High-Vflat subsamples remain small (N=8-21) Not peer-reviewed Claim: structured, regime-dependent coupling law with external support and a leading physical interpretation based on dynamical integration. All analysis scripts, external validation program, physical interpretation program, and machine-readable results included for full reproducibility. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157).