A quality framework for testing gravity with wide binaries: no evidence for MOND

Wide binaries (WBs) offer a unique opportunity to test gravity in the low-acceleration regime, where modifications such as Milgromian dynamics (MOND) predict measurable deviations from Newtonian gravity. We construct a rigorous framework for conducting the wide binary test (WBT), emphasizing high quality sample selection, filtering of poor astrometric solutions, contamination mitigation, and uncertainty propagation. We show that undetected close binaries, chance alignments, and improper treatment of projection effects can mimic MOND-like signals. We introduce a checklist of best practices to identify and avoid these pitfalls. Applying this framework to Gaia DR3 data, we compile a high-purity sample of WBs within 130 pc with projected separations of 1–30 kAU, spanning the transition between the Newtonian and MOND regimes. We find that the scaled relative velocity distribution of wide binaries does not exhibit the 20 per cent enhancement expected from MOND and is consistent with Newtonian gravity across all separations. A meta-analysis of previous WBTs shows that apparent MOND signals diminish as methodological rigour improves. We conclude that when stringent quality controls are applied, there is no observational evidence for MOND-induced velocity boosts in wide binaries. Our results place strong empirical constraints on modified gravity theories operating between a₀/10 and 200 a₀, where a₀ is the MOND acceleration scale. Across this range of internal accelerations, Newtonian gravity is up to 1500× more likely than MOND for our cleanest sample.