The acceleration discrepancy is not a universal law of local acceleration: a null-controlled wide-binary test and a three-scale synthesis
We ask whether the mass discrepancy in galaxies, clusters and wide binaries can be described by a single modified law of gravity that depends only on the local acceleration -- the defining property of MOND -- under a strict reproduce-with-control, exact-or-refuse discipline (Yeshwanth's Theorem, with Nidra-codegod, an AI self-consistency derivation engine built by the author). At the common scale a0 = 1.2e-10 m/s^2, three independent measurements are mutually incompatible with any such law. (i) In 175 SPARC galaxies the radial-acceleration relation is reproduced (g_dagger = 1.13e-10 m/s^2, 0.144 dex, null second parameter) -- MOND's home, where it fits. (ii) In the full 12-cluster X-COP sample the relation breaks: clusters lie about 3.7x (3.1-4.6x) above the galaxy law at 80-150 kpc -- MOND under-predicts. (iii) In 102,672 nearby Gaia wide binaries (El-Badry, Rix and Heintz 2021) the naive low-/high-acceleration velocity ratio (1.128) is shown by a Newtonian Monte-Carlo null to be a measurement-noise artifact (null = 1.129); demanding velocity precision (sigma_vtilde < 0.1) the null returns to 1.010 and the data to 1.017 [0.999-1.034], about 6-7 sigma below the external-field MOND prediction (1.129) and consistent with Newton -- corroborated by injected-MOND positive controls (recovered at 1.13 and 1.50) and three independent hidden-companion filters (RUWE, image multi-peak, radial velocity). The three results deviate from the galaxy law in opposite directions, so the discrepancy is not a function of local acceleration alone: it depends on whether a mass halo is present -- the structural signature of dark matter. We state this discriminator as Yeshwanth's Criterion. We do not reproduce the CMB or Bullet-Cluster evidence (cited), and we state plainly the problem this leaves open: why galaxies obey so tight a MOND-like law if the dark sector is particulate.
Authors
- Yeshwanth Gopal
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-13
- DOI
- https://doi.org/10.5281/zenodo.23328093
- Primary Topic
- Cosmology and Gravitation Theories
- Type
- preprint