Same Stars, Two Gravities: The Wide-Binary Test and the Estimators That Divide It

At separations beyond a few thousand AU, a binary's internal acceleration falls below the galactic scale a₀ ≈ 1.2×10⁻¹⁰ m/s². Lagrangian modified-dynamics theories (AQUAL/QUMOND), with the Galactic external-field effect charged, predict an effective gravitational boost γ ≡ G_eff/G ≈ 1.35–1.40 there — relative velocities ~18% above Newtonian. Newtonian gravity (with or without dark matter, which is dynamically irrelevant at these densities) predicts γ = 1. On the same Gaia DR3 parent catalogue (El-Badry et al. 2021), Chae (2023–2026) and Hernandez et al. (2023–2024) measure γ ≈ 1.4–1.5 at low acceleration, claiming the anomaly at up to ~5σ and, in a 36-system three-dimensionally vetted sample, γ = 1.60 (+0.17/−0.14); Banik et al. (2024) and Pittordis, Sutherland and collaborators (2023–2025) measure consistency with Newton, claiming its verdict at up to 19σ. Both cannot be measurements. An estimator-forensics analysis (Boufourou 2026, an unrefereed 2026 preprint, not yet independently replicated) localizes the disagreement experimentally: in synthetic catalogues of known Newtonian truth with 20–30% residual hierarchical triples, a standard median-based estimator (even with a perfect eccentricity correction) recovers γ = 1.08–1.13, manufacturing an excess of 0.08–0.13 — up to a third of the claimed 0.4–0.5 excess — from pure Newton; tail-truncated and mixture-likelihood estimators recover γ ≤ 1.04 on the same synthetic data; and on the real 81,088-pair sample the calibrated estimators read γ = 1.045 [1.025, 1.068] and γ = 1.05 [1.04, 1.07] (mixture fit, triple fraction 0.15), rejecting 1.4 within that analysis at Δln L = 129. A second reanalysis shows the small-sample anomaly is equally structural: freeing the semimajor axis moves the 36-system result from γ ≈ 1.56–1.60 to γ = 1.12 (+0.27/−0.22) (Saad & Ting 2026, preprint). The counterweight is also printed: rigorously vetted individual systems (3 of 12 ESPRESSO-observed pairs admitting no bound Newtonian orbit, Pasquini et al. 2026) are not dissolved by ensemble forensics. Verdict: undecided — and now decidable. The defect in the wide-binary test is not in the stars; it is in the estimators, localized to three named levers (residual triple fraction, eccentricity prior, separation deprojection), and the deciding instruments are named: Gaia DR4, for which a frozen protocol already exists, and per-system radial-velocity orbits. Neither gravity is confirmed. Anyone quoting either camp's sigma as a fact about nature is quoting an estimator's opinion of itself.