Shear-Dependent Amplitude Coupling in a Two-Field RMB (Space–Matter–Motion) Model of Galaxy Rotation Curves

This work presents a systematic empirical and theoretical analysis of galaxy rotation curves within the RMB (Space–Matter–Motion) framework. A log-potential model of the form vₘodel² = vbar² + ARMB * r / (r + rc) is fitted to 107 galaxies from the SPARC database. The results show that the RMB amplitude scales tightly with the rotational kinetic energy: ARMB ≈ alpha * vflat² with a global median alpha0 = 0. 990 and a scatter sigma (log alpha) = 0. 326 dex. A partial-correlation analysis identifies the normalised velocity shear Sₘean = average of (r/v * dv/dr) as the dominant secondary predictor of the residual amplitude scatter (rₚartial = 0. 420, p = 0. 00001, FDR-corrected). This leads to a shear-dependent coupling of the form: alpha = alpha0 * exp (delta * Sₘean) with delta = 0. 828. The scale radius rc is found to be independent of all tested baryonic proxies (disc scale length, acceleration scale, HI mass, effective radius). It is therefore treated as a free RMB field-state parameter, likely encoding the cosmological embedding of each galaxy at formation epoch. The field-theoretic metric coupling epsilonₘet = g (Y0 / sₜilde²) / g (Y0) is derived directly from the Lagrangian without additional free functions. All stability conditions are satisfied, and the lensing-slip constraint |eta - 1| < 0. 025 holds for chi <= 0. 1. A three-channel structure (matter, time, lensing) is identified. The RMB contribution to the local clock rate is of order 10^-8 to 10^-7 on galactic scales. Galaxy lensing time delays are identified as the most accessible near-term observational test of the model. This repository contains the full analysis pipeline, processed data products, and figures required to reproduce the results. Data Source: The analysis uses data from the SPARC database (Lelli et al. 2016). All credit for the original observations remains with the SPARC team.