Comprehensively Validated Regime-Dependent Coupling Law for Per-Galaxy a0 Variation in SPARC Galaxies (v10 — Phases 126-134, 200-204)

v10 — Phases 126-134 (internal analysis) + Phases 200-204 (comprehensive external validation on N=59 independent SPARC galaxies). Central Result VfResid (kinematic residual) dominance over structural/environmental channels is independent of environmental proxy quality. The complete hierarchical coupling law replicates externally with all 8 hierarchy checks passing. External Validation Program (Phases 200-204) Phase 200-201: Data assembly (N=59) and blind prediction with frozen N=45 coefficients Phase 202: Complete hierarchy replication — 8/8 checks pass, VfResid dominates in all regimes, P>99.6% Phase 203: Environmental decomposition — improved logMhost (r: 0.232→0.542) proves Core is real but VfResid still dominates by 30-76pp Phase 204: Final synthesis — lhOuter genuine but reduced after Mhost correction (+18.1pp→+8.3pp very-high-V) Key External Numbers RegimeNVfResid-only gapVfResid margin over improved CoreFull sample59+47.5%+40.3 ppVflat ≥ 12016+48.5%+30.0 ppVflat ≥ 1808+75.4%+76.3 ppQ=1 + Vflat ≥ 12011+63.8%+43.0 pp Key Numbers (Internal, N=45) LOO gap: Core = 44.1%, Core+VfResid = 61.1%, 5-axis = 65.4% Initial holdout (N=10): Core+VfResid = 56.9%, 5-axis = 66.0%, r = 0.801 VfResid drivers: haloK explains 29%, best-5 explains 52%, 36% irreducible Caveats All data from SPARC survey; cross-survey replication needed High-Vflat external subsamples still small (N=8-16) Best logMhost estimator (Model C) explains only ~29% of real variance lhOuter contribution partially inflated by Mhost error absorption in initial estimates Not peer-reviewed All analysis scripts, external validation program, and machine-readable results included for full reproducibility. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157).