宽双星引力测试的估计器取证：偏心率-三星耦合产生伪信号，以及为盖亚DR4制定的预注册协议
Estimator forensics for the wide-binary gravity test: the eccentricity-triple coupling manufactures a pseudo-signal, and a pre-registered protocol for Gaia DR4
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中文总结 AI 辅助
本研究针对盖亚DR3宽双星引力测试的分歧，揭示偏心率-三星耦合产生伪信号，校准三类估计器后在盖亚DR4预注册协议中以高显著性排除γ=1.4的类MOND异常，证实争议可判定。
中文摘要 AI 辅助
对盖亚（Gaia）DR3宽双星的分析对一项宣称的低加速度异常得出了截然相反的结论：来自同一星表的研究分别给出γ=Geff/G≈1.4（Chae 2024、2025、2026；Hernandez等人2024）和高显著性下的牛顿引力结果（Banik等人2024；Pittordis等人2025）。我们在实验层面定位了分歧所在。一个生成模型——开普勒双星系统加上含光心和时间平均效应的层级三星系统——在未调整的情况下通过了Pittordis等人（2025）的验证。我们将已知真值的合成星表与三类估计器进行对比：完全中位数估计器即便进行了完美的偏心率校正，仍会从仅含20%-30%残余三星系统的纯牛顿宇宙中恢复出γ=1.08-1.13，这一结果接近宣称的异常值；而尾部截断估计器和混合似然估计器则分别恢复出≤1.04和1.00。所有三类估计器均能以≥1.26的置信度恢复注入的类MOND增强信号（2千天文单位以上γ=1.4）：在稳健估计下，两种假设从未重叠，因此该争议可判定。我们将校准后的估计器应用于Chae（2024）的81088对样本，测得γ=1.045[1.025,1.068]（2-30千天文单位），联合混合拟合给出γ=1.05[1.04,1.07]，三星占比f_trip=0.15，与独立测量的0.17一致；γ=1.4的假设被以约16σ的显著性拒绝。我们在Zenodo上为盖亚DR4制定了一份带时间戳的预注册协议，届时γ的统计显著性σ_stat将小于0.005，使估计器系统误差成为主导因素。
英文摘要
Analyses of Gaia DR3 wide binaries reach opposite verdicts on a claimed low-acceleration anomaly: gamma = Geff/G ~ 1.4 (Chae 2023-2026; Hernandez et al. 2024) versus Newtonian at high significance (Banik et al. 2024; Pittordis et al. 2025), from the same catalogue. We localize the disagreement experimentally. A generative model -- Keplerian binaries plus hierarchical triples with photocentre and time-averaging effects -- is validated without tuning against Pittordis et al. (2025). Synthetic catalogues of known truth are confronted with three estimator families: a full-median estimator, even with a perfect eccentricity correction, recovers gamma = 1.08-1.13 from purely Newtonian universes containing 20-30% residual triples -- half-way to the claimed anomaly -- while a tail-truncated estimator and a mixture likelihood recover <= 1.04 and 1.00. An injected MOND-like boost (gamma = 1.4 above 2 kau) is recovered at >= 1.26 by all three: the hypotheses never overlap under robust estimation, so the controversy is decidable. Applying the calibrated estimators to the 81,088-pair Chae (2024) sample we measure gamma = 1.045 [1.025, 1.068] (2-30 kau), and a joint mixture fit gives gamma = 1.05 [1.04, 1.07] with f_trip = 0.15, consistent with the independent 0.17; gamma = 1.4 is rejected at ~16 sigma. We freeze a pre-registered protocol, time-stamped on Zenodo, for Gaia DR4, where sigma_stat(gamma) < 0.005 will make estimator systematics fully dominant.
