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

Bradley Oscillation Field Theory: Analytic Derivation of Galactic Rotation Curves and the Radial Acceleration Relation This repository contains the complete manuscript, code, and empirical validation suite for Bradley Oscillation Field Theory applied to galactic rotation kinematics. ABSTRACT & THEORETICAL FRAMEWORK We present an analytic derivation of galactic rotation profiles and the Radial Acceleration Relation (RAR) within Bradley Oscillation Field Theory, an effective field framework evaluated on flat spacetime coordinates without non-baryonic dark matter. By formulating the field equations for continuous baryonic distributions through an effective scalar wave action, boundary conditions across thin disk geometries induce an impedance-matched transition from isotropic 3D dilution to a 2D cylindrical waveguide mode. This boundary coupling asymptotically anchors far-field circular velocities to v_flat = (G * M_b * a_B)^(1/4), where the characteristic acceleration scale a_B = c_0 * H_0 / (2*pi) = 1.042211e-10 m/s^2 is identified with cosmological phase relaxation (H_0 = 67.40 km/s/Mpc) under a parameter-free forward prediction (N_fit = 0). EMPIRICAL BENCHMARK: SPARC DATABASE (175 GALAXIES) Evaluated across the complete Spitzer Photometry and Accurate Rotation Curves (SPARC) database (N = 175 disk galaxies, N = 3,391 observational velocity points) using canonical mass-to-light ratios (Upsilon_disk = 0.50, Upsilon_bulge = 0.70): Zero Fitted Parameters (N_fit = 0): Universally fixed acceleration scale and canonical stellar population priors. Velocity Precision: Pointwise median raw velocity residual of 12.07 km/s across all 3,391 data points (7.12 km/s for gas-rich dwarfs). Goodness-of-Fit: Per-galaxy median reduced chi_nu^2 = 10.10 (chi_nu^2 = 3.42 for dwarfs), with elevated intermediate values systematically attributable to observational inclination and distance uncertainties. Scaling Laws: Direct analytic recovery of the Radial Acceleration Relation (RAR) and exact slope-4.0 Baryonic Tully-Fisher Relation (BTFR). ARCHIVED FILES BradleyGalacticRotation.pdf: Full theoretical and empirical manuscript. Bradley_SPARCC_evaluation.py: Reproducible Python evaluation pipeline (auto-downloads SPARC catalog). sparc_175_galaxies_atlas.pdf: Complete 175-galaxy rotation curve visual atlas. sparc_summary_results.csv: Full numerical metrics, residuals, and chi_nu^2 values per galaxy. PNG files: High-resolution figures for global scaling relations and residual distributions.