Sharp-threshold modified gravity: falsifiable wide-binary predictions with Gaia
Abstract
We derive, from a tension interface and with no adjustable parameter, the transition function relating the observed acceleration to the Newtonian acceleration in the low-acceleration regime. It differs qualitatively from the usual interpolating functions: it predicts a sharp threshold at the front, rt = √A = 0.322 rMOND, where the Newtonian acceleration reaches the universal front acceleration 12πGσ/c²; a steep transition, Newtonian to better than 10⁻³ well inside the threshold where a continuous interpolation already departs from Newton; a narrow interference peak at γ = 1.656 followed by a dip to 1.323; and an asymptotic plateau of γ ≈ 1.80–1.90 whose height is fixed by the local baryonic slope. The same normalisation gives a₀ = 1.203×10⁻¹⁰ m·s⁻² and a plateau velocity of 200 km/s for 10¹¹ M☉ — one equation and one unit, from stars to galaxies. We provide the discriminating curves and the code; we do not adjudicate the ongoing observational controversy.
A pre-registered shape test
A companion protocol specifies, in advance, how the prediction is to be confronted with Gaia — and freezes every choice before the velocities are examined. Status: frozen 12 September 2026 and published before any execution on 14 September under 10.5281/zenodo.22715013, which fixes its priority. It is a test of location, not amplitude: it measures where the transition occurs, and whether it occurs at the same place for stars of different masses, rather than estimating any global enhancement factor.
The pairs are placed on a single axis, ξ = s / √Mtot (separation in AU, mass in solar masses), on which every pair lands regardless of mass. The location of the knee is predicted, not sought, and the two values are written before the computation:
- ξ⋆ = 2266 AU·M☉−½ — if the transition is a sharp threshold (the profiles of the mass bins superpose in ξ).
- ξ⋆ = 7030 AU·M☉−½ — if it is a continuous MOND-type interpolation.
The two are a factor 3.1 apart; the acceptance window is ±20 %. If the profiles superpose no better in ξ than in s, neither is supported.
The protocol runs both published cut sets (Chae; Cookson et al.) in parallel, names its own biases before reading the results, and states three stopping rules in advance under which it declares itself inconclusive. It reports its own corrections in the open — including a count revised against the files on 12 September. It does not arbitrate the observational controversy; it states where the prediction can be falsified.
Executed 15–16 September 2026 on Gaia DR3. With the cuts of Chae (54 257 pairs), the test does not recover the predicted location: the empirical knee falls at ξ = 3 691, between the two windows, and the mandatory mass-mixing control shows that the observed rise is not structured by mass. The test does not decide, for a stated reason — the unresolved-companion model was not specified — and it awaits DR4. It does establish that in the control window, inside the threshold for every mass, the two published selections depart from the Keplerian reference in opposite directions. The six reports, two robustness checks and their scripts are in the deposit. The Cookson-type selection (358 pairs) was declared insufficient by the rule written in advance.
Reproduction
The numerical claims are meant to be checked, not believed. Two self-testing Python scripts accompany the work:
reproduce_letter.py — reproduces every number in the Letter from scratch, with no input other than measured constants; nothing is fitted.
nonkeplerian_dynamics.py — a drop-in dynamical step parameterised by the constants of the motion (E, L), valid for non-closing orbits; its self_test() reproduces the Newtonian identity to 5×10⁻¹⁵, checks the exact velocity decomposition against the generator, and measures the Keplerian-approximation error for each law (threshold law: 1.70 / 7.16 / 11.51 %, median / 90th / 99th).
How to cite
Côté, L. (2026). Sharp-threshold modified gravity: falsifiable wide-binary predictions with Gaia. Zenodo. https://doi.org/10.5281/zenodo.22801278
Part of a larger framework
This prediction is derived within the Theory of the Intersection of Fields, a geometric framework in which the acceleration scale that governs the low-acceleration regime follows from a single measured density rather than being posited.