Per-Galaxy a0 Variation: Carrier Identification via 2D Velocity Fields (v13 — Programs 1-9V, 52 sections)

v13 — Carrier identification + red team verification: the hidden state H driving bilateral VfResid–a0Resid coupling in SPARC rotation curves is identified as a robust outer-halo m=2 velocity-field mode, most consistent with halo triaxiality / oval distortion. Central Result A hidden common-cause state H drives bilateral coupling at r ≈ 0.77 (LOO, N=45). Program 9 identifies the observational carrier using real THINGS velocity field maps: the m=2 azimuthal mode correlates with bilateral excess at r = 0.847 (p = 0.005, N=7). Gold pair NGC 2841 vs NGC 5055 shows 10.5× m=2 power difference despite near-identical baryonic mass. Cosmological Monte Carlo confirms triaxiality is required (concentration-only fails at 0% match rate). What is new in v13 Program 9, Phase 901: IFU cross-match — 14/55 SPARC galaxies have 2D survey coverage; 4 matched pairs identified Phase 902: THINGS velocity field analysis — r(DQ, m2) = 0.899 in N=6; gold pair m2 ratio = 9.2× Phase 903: Decisive test — r(DQ, m2) = 0.847 (N=7), p = 0.005, LOO 7/7 positive, partial r|Vf = 0.750 Phase 904: Cosmological MC — 8 models tested; 5 with triaxiality reproduce r > 0.7; concentration-only FAILS Phase 905: Carrier identification — H1 (triaxiality) scores 23/23 (100%); H4 (exotic DM) scores 11/23 (48%) Program 9V: Red team verification — 11/11 tests PASS (8/8 critical): independent pipeline replication (r = 0.911), 19 sensitivity variations (all positive), bar contamination exclusion (signal in outer halo, r = 0.869), LOO 7/7, confounder control (partial r = 0.660), Program 8B reconciliation (consistent) Section 52: Conclusions — refined two-level claim (observational carrier ~95%, physical root cause ~90%) The Refined Claim The hidden state H is strongly linked to a robust outer-halo m=2 velocity-field mode that survives independent reconstruction, sensitivity tests, bar exclusion, and confounder controls. The observational carrier is identified at ~95% confidence. The deeper physical origin is most consistent with a triaxial or closely related halo-shape state. Causal Chain Formation history → Halo triaxiality (b/a ~ 0.65–0.75) → m=2 velocity field power (angular, 1D-invisible) + enclosed mass shift (integral, 1D-visible) → Vflat & a0 shifts (4:1 asymmetry) → bilateral coupling (r = 0.77 LOO) Caveats N=7 2D sample (need N≥20 for definitive) THINGS-only (cross-survey replication with MaNGA/CALIFA/PHANGS needed) H1/H3 degeneracy (triaxiality vs assembly history as root cause) Not peer-reviewed Confidence: ~95% (observational carrier), ~90% (physical root cause). Path to 99%: Program 10 (N≥20 multi-survey 2D replication). All analysis scripts, results, and machine-readable data included for full reproducibility. Data: SPARC (Lelli, McGaugh & Schombert, 2016, AJ 152, 157); THINGS (Walter et al. 2008, AJ 136, 2563).