Per-Galaxy a0 Variation: Angular Velocity-Field Complexity as Carrier of Hidden State (v16 — Programs 1-12, Dark Matter Discrimination)

v17 — Hiddenness paradox resolved. DM-5A + DM-5B complete. Single archive (3.2 MB): analysis scripts, result JSONs, source code, data files, documentation. Core Result (unchanged): Hidden state H drives bilateral Vf_Resid-a0_Resid coupling at r = 0.77 (LOO, p < 0.001, N = 55). shapeAmplitude (total non-axisymmetric power, m ≥ 2) captures H at r = 0.80, confirmed DM-4V. DM-5A: CDM Triaxial Consistency (5 tests): Amplitude range (3.3×), correlation direction (r = 0.79 positive), and radial behavior (6/7 outer m=2) are all CDM-consistent. Mode spectrum is NOT simple triaxial: m=3 carries 55% of non-axi power, odd modes dominate. Overall: PARTIALLY CONSISTENT (3 PASS, 1 PARTIAL, 1 FAIL). The halo shape driving H is more complex than a simple oval. DM-5B: Hiddenness Paradox (4 tests): B1: Non-axi modes carry 15.8% of velocity-field power, ALL destroyed by azimuthal averaging. CONFIRMED. B2: 2D coupling (r=0.79) vs 1D visibility (r=0.12) — 3× tradeoff. CONFIRMED. B3: Mode combination boost 1.09× (individual modes already strong). WEAK. B4: shapeAmplitude R²=0.63 alone, 0.90 with extras. NECESSARY NOT SUFFICIENT. Overall: HIDDENNESS PARADOX RESOLVED. Azimuthal averaging erases all m ≥ 2 by construction — this IS the hiding mechanism. CDM + complex halo shape is sufficient. No extra dark-sector physics required at this level. Model status: DEAD: CDM smooth, MOND, Fuzzy DM. No signal: SIDM, WDM. LEADING + SUFFICIENT: CDM + complex halo shape. Data: SPARC (Lelli, McGaugh & Schombert 2016); THINGS (Walter et al. 2008).