Four-Axis State Law for Per-Galaxy a0 Variation: VfResid Identified as Baryon-Halo Coupling Proxy (v7)

v7 — Phases 126-132: Four-axis state law and physical decoding of the fourth axis. Primary Model C: logA0 = 4.120 - 0.339*logMHI - 0.175*logMhost + 0.449*logMR + 0.631*logVflat (LOO gap = 52.1%, nested CV 45/45, N=45 published SPARC subset). Core result: The three-axis core (logMHI, logMhost, logMeanRun) is firmly established. The fourth axis is operationally represented by logVflat, but its predictive content does not come from baryonic structure alone. Key finding (Phases 129-132): Baryonic structure explains 92.2% of Vflat variance but adds only +0.4pp above the core. The remaining 7.8% kinematic residual (VfResid) adds +17.1pp. VfResid correlates with dark halo strength (haloK, r=+0.60), anti-correlates with MOND improvement (r=-0.54), and is clean on all systematics. Reducibility test (Phase 132): No observable bundle can replace VfResid. Best replacement haloK reaches 49.1% vs VfResid 61.1%. Fold-internal VfResid adds +9.4pp above core (genuine signal). Interpretation: The fourth axis encodes baryon-halo coupling efficiency — the excess dynamical support beyond baryonic structure. All scripts and results included. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157).