Invariant Origin of the Radial Acceleration Relation

This repository accompanies the manuscript “Invariant Origin of the Radial Acceleration Relation,” introducing the Covariant Relativistic Extended Scalar Theory (CREST) as a structural explanation for galaxy scaling laws. The work proposes that the empirical radial acceleration relation (RAR) emerges from invariant quantities governing galactic structure: χ (structural support field), η (coherence fraction), I (informational gradient), and F (irreversibility index). Within this framework, the observed acceleration is not an independent law but follows from an invariant functional of baryonic structure, written as g_obs = g_bar * F(Phi_inv). A semi-analytic reconstruction of the support field χ(R) is developed directly from baryonic mass models, establishing the mapping Sigma_bar(R) → χ(R) → g_chi(R). In the weak-field galactic regime, this yields the leading-order relation g_chi ≈ sqrt(a0 * g_bar), which reproduces the empirical backbone relation g_pred = g_bar + sqrt(g_bar * a0). The repository includes the full manuscript, galaxy rotation curve data and baryonic mass models, reconstructed acceleration profiles, residual diagnostics, a worst-fit galaxy subset for stress testing, and Python scripts implementing the full analysis pipeline. Key results include reproduction of the RAR without invoking particle dark matter, identification of structured residuals correlated with support-state observables, and the first semi-analytic construction of a galaxy-scale support field sourced by baryonic acceleration. The framework suggests that galaxy dynamics are governed by a support-field response rather than an independent dark matter component, with the RAR functioning as a constraint equation and deviations encoding structural information. The galaxy-scale phenomenology and covariant formulation are established, while full cosmological validation remains an open direction. All results are reproducible using the included data and scripts.