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

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.