On the Origin of the RMB Scale Parameter as a Boundary-Condition Observable: Reparametrisation, Emergent Inner Scale, and Formation-Driven Dynamics

This record contains the preprint and reproduction package for RMB Paper II: a covariant field-theoretic analysis of the scale parameter r_c in the Raum–Materie–Bewegung (RMB) framework for galaxy rotation curves. Paper I (doi:10.5281/zenodo.20004320) established that the RMB amplitude scales universally as A_RMB ∝ v_flat^2, while the scale radius r_c remained unexplained and uncorrelated with all tested baryonic observables. This work addresses the physical origin of r_c through three contributions: 1. Covariant field extension A mass term introduces a Yukawa screening length r_c = sqrt(2) / (a_0 * m_phi), implying that r_c is the inverse effective field mass (m_phi c^2 ≈ 10^-28 to 10^-26 eV). 2. Orthogonal reparametrisation (P, G_in) Replacing (A, r_c) with P = A and G_in = A / r_c reduces the correlation from r = 0.78 to r = 0.22. The inner gradient is stable: G_in ≈ 0.60 a_0 across n = 108 SPARC galaxies. Partial-correlation analysis confirms that G_in is not an independent baryonic observable (r_partial = 0.08, p = 0.42, controlling for v_flat). 3. r_c as a mathematical consequence The stationary RMB field equation is elliptic and contains no intrinsic length scale. Any length scale must arise from boundary conditions, not local physics. r_c therefore encodes the cosmological formation history of the RMB field. A pre-registered observational test (H2: environmental dependence of r_c at fixed v_flat) is defined with decision criterion |Δ log r_c| > 0.2 dex and Mann–Whitney p < 0.01. Contents • Reproduction package (Paper2Reprod.zip):- make_paper2_reparam_figure.py — reproduces Figure 1 - rmb_alpha_catalogue.csv — RMB fitted parameters (n = 108) - paper2_figures.png, paper2_stats.csv - README.md - sparc/ (Lelli et al. 2016) Reproduce:python make_paper2_reparam_figure.py --sparc-dir sparc