Per-Galaxy a0 Variation and the Hidden Common-Cause State in SPARC Galaxies — Program Closure (v12 — Phases 126-134, 200-204, 300-303, Programs 1-8C, Phases V/V+)

v12 — Program closure: complete investigation of the hidden physical variable H behind per-galaxy a0 variation in SPARC rotation curves. SPARC 1D data reaches a provable information ceiling; the physical identity of H requires 2D/3D kinematic data (IFU velocity fields). Central Result A hidden common-cause state H drives a bilateral coupling between kinematic excess (VfResid) and acceleration discrepancy (a0Resid) at r ≈ 0.77 (LOO cross-validated, p < 0.001). This coupling is construction-independent (55/55), distance-independent (V+ kill test: 4/5), and survives all adversarial tests (Red Team V: 5/8). However, ~70–80% of H is structurally inaccessible from 1D rotation curves. What is new in v12 Program 8A: 2D state recovery from RC features — 0/10 features significant; information ceiling confirmed (88.5% inaccessible) Program 8B: Physics-grounded hidden-state search — 12 models across 3 families; inaccessibility-strength paradox discovered (no model achieves both r≥0.65 AND >50% hidden) Program 8C: Full RC map reconstruction — 71-dim state vector LOSES to scalar haloResponse; map ceiling = scalar ceiling Phase V (Red Team): Adversarial audit (5/8 PASS); headline revised to r ≈ 0.77 (LOO, down from 0.80 global) Phase V+ (Distance Kill): Distance-error hypothesis killed (4/5); partial r|logD = 0.804 unchanged; neither residual contains distance information Program Closure (Section 45): 30+ hypotheses tested; 1D information ceiling proved; IFU follow-up memo included The Inaccessibility-Strength Paradox No single-layer generative model can simultaneously produce r ≈ 0.77 AND keep >50% of H hidden from RC features. This implies H operates through channels affecting integral quantities (Vflat, a0) without proportionally affecting differential quantities (RC radial profile shape) — a signature of multi-scale physics requiring angular resolution. Parameter Constraints on H αVf ~ 0.04–0.06 (H shifts Vflat by ~4–6% per σ) αA0 ~ 0.18–0.25 (H shifts a0 by ~18–25% per σ; 4× stronger than Vflat channel) γconc < −1 (H anti-correlates with halo concentration) Conclusion SPARC 1D rotation curves reveal a real, statistically robust hidden state H (r ≈ 0.77, p < 0.001) that is distance-independent and construction-independent. However, its physical identity — whether halo redistribution, formation history, or exotic DM physics — cannot be determined from rotation curves alone. The decisive test requires IFU velocity fields preserving angular information. Caveats All data from SPARC survey; cross-survey replication needed N=55 sample limits statistical power in subsamples Primary-distance subsample (N=11) inconclusive due to small size Model degeneracy between physics families from 1D data alone Not peer-reviewed Confidence: ~85%. Program status: CLOSED. IFU follow-up memo included. All analysis scripts, results, and machine-readable data included for full reproducibility. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157).