The Fundamental Speed Theory: A Mathematically Consistent Vector-Tensor Theory for Galactic Dynamics Without Dark Matter Results from 171 SPARC Galaxies

We present the Fundamental Speed Theory (FST), a dimensionally consistent vector–tensor framework in which galactic dynamics arise from a dimensionless kinetic field \(\nu^{\mu}\) with explicit \(\hbar\) and \(c\), and fixed characteristic scales \(L_0=10\) kpc and \(M_0=\hbar/(cL_0)\). Using the SPARC rotation-curve database, we perform a hierarchical stress test of predictivity: Level 3 (no galaxy-specific fitting) reproduces \(65.7\%\) of galaxies with mean \(\chi_{\nu}^{2}=0.809\); Level 2 (parameters estimated directly from the data, still no fitting) reaches \(93.6\%\) with mean \(\chi_{\nu}^{2}=0.347\) on the 160 galaxies with \(\chi_{\nu}^{2}<3\); and Level 1 (fitted \(M,r_d\)) fits all 171 galaxies with mean \(\chi_{\nu}^{2}=0.170\) (\(91.2\%\) with \(\chi_{\nu}^{2}<0.5\)). A key result is theoretical economy: the observable predictions collapse to a single acceleration scale, \(A_0=(c_1+c_3)\nu_0^2c^2/L_0=2.42\times10^{-10}\,\mathrm{m/s^2}\), yielding a coefficient-free and unified formulation that reproduces the full theory identically across the entire sample (i.e., FST is effectively a one-parameter theory at the galactic level). We further confirm robustness via (i) a 3D numerical boundary-forcing experiment showing negligible deviation from the 1D quasi-spherical profile in tested cases, and (ii) a sign-convention swap producing identical fits when implemented consistently. Solar System bounds are satisfied because the relevant effect is set by the galactic field gradient, giving an acceleration at Earth \(\sim 8\times10^{-15}\) of Newtonian gravity. Code and full fit tables are publicly archived on Zenodo.