A regime-dependent constitutive exponent in SPARC rotation curves: phenomenological evidence beyond a universal MOND interpolation

Abstract

The universal interpolation function is a foundational assumption of modified Newtonian dynamics (MOND) phenomenology: that a single function relates observed and Newtonian accelerations across all rotation-supported galaxies. We test this assumption directly on the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. Within the one-parameter constitutive family β(g) = (a 0 /g)^p, which contains the canonical deep-MOND scaling as the p = 1 limit, we fit p galaxy-by-galaxy and confront the universal-p hypothesis with the resulting population statistics. To our knowledge, this is the first direct galaxy-by-galaxy test of the universality assumption within a parametric family of MOND-class interpolations, examined across six complementary statistical diagnostics. The baryonic Tully–Fisher slope on 135 flat-curve galaxies is 3.47 ± 0.10 (orthogonal distance regression), consistent with the p = 3/4 prediction of 7/2 within ≈1σ and incompatible with the MOND slope of 4 at ≥4σ (statistical) across all error models tested. Galaxy by galaxy, p = 3/4 is preferred over p = 1 in 106 of 175 galaxies (binomial p = 0.006). The population distribution of best-fit p has a median of 0.82 with an intrinsic dispersion three times broader than any single-p synthetic catalog can reproduce (Kolmogorov–Smirnov p < 10 −11 ), already rejecting universal p. The exponent correlates with the outer acceleration at Spearman ρ = +0.49 (p < 10 −10 ), progressing monotonically from 0.63 through 0.83 to 1.11 across three regime terciles, representing a structure that survives partial-correlation control for outer curve kinematics and is absent from alternative binnings. A regime rule calibrated on half the sample outperforms canonical MOND on the held-out half in 97–99 of 100 random 50–50 train–test splits (≥91/100 across split ratios). A Bayesian information criterion (BIC) comparison yields ΔBIC = −12,112 in favor of the regime rule over MOND on n = 3,215 data points; the critical control against the universal-p free model (ΔBIC = −3,620, two extra parameters) rules out parameter inflation. The structured failure of universality is itself the testable prediction; any successor framework must reproduce the regime structure documented here.