Per-Galaxy a0 Variation: Angular Velocity-Field Complexity as Carrier of Hidden State — Final Unified Reference (v19, Programs 1-12, DM-5D, Phase Frozen)

v19 — Final unified reference version. DM-1 through DM-5D complete. Phase FROZEN. Archive (1.4 MB): analysis scripts, result JSONs, source code, full documentation including Final Synthesis. What Is Established: H is real. Hidden variable H drives bilateral Vf_Resid–a0_Resid coupling at r = 0.77 (LOO, p < 0.001, N = 55), replicated on N = 59. Red team: 11/11 pass. shapeAmplitude is the minimal robust carrier of H. r = 0.80, p = 0.028, LOO 7/7 positive, bootstrap 97.8%, bar-exclusion stable. Defined as total non-axisymmetric velocity-field power at m ≥ 2. 1D rotation curves hide H by construction. Azimuthal averaging erases all m ≥ 2 by mathematical identity. No exotic physics needed to explain hiding (DM-5B). CDM + complex halo shape is the only surviving model. 3 killed (CDM smooth, MOND, Fuzzy DM), 2 no signal (SIDM, WDM). 12/12 constraints pass (DM-1). Compatible with earlier THINGS literature. Trachternach+08 found simple elongation (m=2) small on average — we agree. Our metric is broader: m=2 is <1% of total non-axi power; odd modes dominate. Partial r(shape,DQ|elongation) = 0.635 vs partial r(elongation,DQ|shape) = 0.092 (DM-5D, 4/4 pass). What Is Not Yet Settled: outerSupport as 2nd predictor (partial r = 0.50, but N = 7 insufficient to confirm) Out-of-sample magnitude (LOO R² low at N = 7 for all models) R² = 0.90 multi-parameter model was overfitting (LOO R² = −1.055 for M3) Phase Status: FROZEN. No new analysis until new 2D kinematic data (WALLABY, MeerKAT MHONGOOSE, SKA). Core prediction: r(DQ, shapeAmplitude) > 0.5 with N > 20. Data: SPARC (Lelli, McGaugh & Schombert 2016); THINGS (Walter et al. 2008).