Externally Validated Regime-Dependent Coupling Law for Per-Galaxy a0 Variation in SPARC Galaxies (v9 — Phases 126-134, 200-201)

v9 — Phases 126-134 (internal analysis) + Phases 200-201 (external validation on N=59 SPARC galaxies outside training sample). Central Result The coupling-law picture now has external support beyond the original N=45 sample. The strongest transfer appears in higher-Vflat galaxies and collapses in lower-Vflat systems, consistent with a regime-dependent law rather than a universal one. Hierarchical Structure (reproduced externally) Structural core alone fails in all regimes (gap = -53% full sample) VfResid is the dominant transferable channel (carries all positive gap) Signal strengthens monotonically with Vflat Low-Vflat regime fails, exactly as predicted by internal regime law External Validation Summary (Phase 201) RegimeNCore+VfResid gapr(VfResid, a&sub0;)Full sample59+8.2%0.713Vflat ≥ 12016+34.3%0.841Vflat ≥ 1808+48.7%0.858Q=1 + Vflat ≥ 12011+59.0%0.830Vflat < 12043-3.9%— Key Numbers (Internal) Internal LOO gap (N=45): 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 External sample uses cruder logA0 (fewer RAR points) and estimated logMhost High-Vflat external subsample still small (N=8-16) All data from SPARC survey; cross-survey replication needed Not peer-reviewed All analysis scripts, external validation program, and machine-readable results included for full reproducibility.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).