判伪Campaign A, Milestone S10: A Four-Bin Wide-Binary Velocity-Dispersion Test of Low-Acceleration Dynamics — Null Result under Pre-Registered Criteria

We present the decisive measurement of Campaign A: binned projected relative velocities of 800 wide-binary pairs drawn from the El-Badry et al. 2021 Gaia EDR3 wide-binary catalog (VizieR J/MNRAS/506/2269), extracted in four projected-separation bins (2–5, 5–10, 10–20, 20–30 kAU; 200 pairs each) and evaluated against Newtonian expectations with success criteria, noise declarations, and a three-zone verdict rule fixed before computation (protocol vΩ.32.23). For each pair we form the distance d = 2000/(ϖ₁+ϖ₂) pc, the projected relative velocity v_rel = 4.74·Δμ·d/1000 km/s, the Newtonian circular-speed scale v_N = 36.5/√(sepAU) km/s, and the internal-to-critical acceleration ratio a/a₀ = 7.42×10⁷/sepAU² (nominal total mass 1.5 M⊙; a₀ = 1.2×10⁻¹⁰ m/s²). Results: median v_rel = 0.745, 0.543, 0.435, 0.296 km/s in bins 1–4 against v_N = 0.677, 0.442, 0.321, 0.237 km/s. Apparent observed-to-Newtonian ratios (1.10–1.36) exceed unity in all bins, but astrometric noise deconvolution — σ(v) estimated from position-error proxies, with a pre-registered readability rule (a bin is readable only if median v_rel ≥ 2×median noise) — yields intrinsic signals of 0.652, 0.414, 0.330, 0.222 km/s, i.e. 0.96, 0.94, 1.03, 0.94 of v_N, with no rising trend across a/a₀ = 8.8 → 0.13. Only bin 1 crosses the readability threshold (0.745 vs 0.721 km/s; 3% margin). Per the pre-registered verdict rule, bins 1–2 consistent with Newtonian within 2σ plus no trend in any bin places the result in Zone A: the tested low-acceleration kinematic-modification node is falsified at the campaign's power level and entered into the correction ledger. Honest boundaries, registered with the criteria and not invoked as exemptions: the bin-1 margin is marginal; the noise estimate uses position-error proxies (true proper-motion-error substitution queued); the falsification binds only above the noise floor (weaker modifications remain power-limited); the pre-registration protocol carried a conversation-ledger timestamp predating the analysis but lacks an external archival timestamp — a governance lesson recorded in the deposit. Under the campaign's tidal-environment stellar-effect (TESE) reading, the null constrains the stellar kinematic response coefficient to <5% (bin 1, 68% confidence) across the scanned range. All data, queries, and the locked protocol accompany this document (Zenodo v3.0).