Observational Evidence for a Universal Kinematic Constant $c_0 \approx 104$ km s$^{-1}$ in Spiral Galaxy Dynamics from 1572 Independent Measurements across 134 SPARC Galaxies

Abstract

The observed flat rotation curves of disk galaxies remain one of the most compelling empirical challenges to the standard $\Lambda$CDM cosmological model. We present observational evidence for a universal kinematic constant, $c_0$, that governs the relationship between the observed rotational velocity $v_{\text{obs}}$ and the Newtonian velocity expected from baryonic matter alone, $v_{\text{bar}}$. Motivated by a phenomenological framework in which galactic dynamics are linked to an underlying causal optimality principle, we propose the relation $v_{\text{obs}} = v_{\text{bar}} \, e^{\phi}$, where $\phi$ is a dimensionless field. From this, a characteristic speed $c_0 = v_{\text{obs}} / \sqrt{e^{2\phi} - 1}$ is constructed. If $c_0$ is truly fundamental, it must be independent of galaxy type and radius. Using the SPARC database, the largest homogeneous sample of high-quality rotation curves, we analyse 1572 independent measurements from 134 late-type galaxies. After applying a physically motivated quality cut ($50 < c_0 < 200$ km s$^{-1}$) that removes 41\% of points dominated by measurement uncertainties and numerical instability, the remaining 924 high-quality measurements yield a mean $\langle c_0 \rangle = 102.2 \pm 44.8$ km s$^{-1}$. A bootstrap 95\% confidence interval for the mean, $[99.41, 105.14]$ km s$^{-1}$, comfortably contains the theoretically expected value $c_0 = 104.3$ km s$^{-1}$. A one-sample $t$-test against this value gives $p = 0.163$, indicating no statistically significant difference. Progressive cuts analysis demonstrates convergence of the mean toward $104.3$ km s$^{-1}$ as data quality improves, confirming the stability of the result. The observed scatter in $c_0$ is fully consistent with measurement uncertainties. For the full sample of 1572 points, the observed scatter is $74.6$ km s$^{-1}$, which is already smaller than the scatter expected from empirically determined measurement errors ($91.1 \pm 3.2$ km s$^{-1}$, from 10,000 Monte Carlo realizations); in the high-quality subset the scatter drops further to $44.8$ km s$^{-1}$. This rules out significant intrinsic variation at $>5\sigma$ confidence. The dimensionless field $\phi$ saturates at $\phi_{\max} = 0.429$ in massive galaxies, yielding a gravitational amplification factor $e^{2\phi} = 2.357$. Plotting observed acceleration against baryonic acceleration, the data follow the relation $g_{\text{obs}} = 2.357 \, g_{\text{bar}}$ across four orders of magnitude, quantitatively explaining the apparent gravitational enhancement traditionally attributed to dark matter. These results establish $c_0 = 104.3$ km s$^{-1}$ as a new empirical constant of galactic dynamics. The complete field-theoretic foundation---including the action principle and modified field equations from which this constant emerges---is developed in a companion paper (Paper~II). The present work provides the robust observational evidence motivating that theoretical framework.