Bradley Oscillation Field Theory: First-Principles Derivation of the Radial Acceleration Relation and Galactic Rotation Curves

We present a zero-parameter continuum mechanics derivation of flat galactic rotation curves, the Baryonic Tully-Fisher Relation (BTFR), and the Radial Acceleration Relation (RAR) operating strictly on flat, uncurved Minkowski spacetime ($\\eta_{\\mu\\nu}=\\text{diag}(-1,1,1,1)$). By treating the scalar vacuum as a physical wave-transmission substrate with exponential impedance ($Z(\\Phi)=e^\\Phi$), gravitational propagation splits into a three-dimensional spherical expanding wave and a trapped two-dimensional cylindrical wave floor. Reinterpreting the Hubble constant ($H_0$) as the intrinsic harmonic attenuation coefficient of the scalar medium, we derive the kinematic acceleration floor from first principles as $a_B = \\frac{c_0 H_0}{2\\pi} = 1.0422 \\times 10^{-10} \\text{ m/s}^2$. This establishes the Rene Limit $r_R = \\sqrt{GM_b/a_B}$, where a critical scalar impedance mismatch induces Total Internal Reflection, trapping outer disk stars within a stable, two-dimensional cylindrical potential well. Step-by-step evaluations demonstrate that local planetary orbits ($r \\ll r_R$) remain $>98.3\\%$ Keplerian ($4.78 \\text{ km/s}$), while macro galactic systems (NGC 3198, $r \\gg r_R$) yield flat rotation speeds ($150.11 \\text{ km/s}$) matching SPARC observations without non-baryonic dark matter halos or empirical interpolation functions.