A normalization-independent estimate of the evolution index of the radial-acceleration scale

Abstract

Scripts reproducing every number, table and figure in the article "A normalization-independent estimate of the evolution index of the radial-acceleration scale" (I. Salganik). The analysis estimates the shape parameter n of the one-parameter family a₀(z) = A E(z)ⁿ without fixing the multiplicative local normalization A. A candidate curve is projected onto the free-intercept linear basis in which the measurement is reported, by weighted least squares over 0.33 ≤ z ≤ 1.44 on 2×10⁵ uniformly spaced points. Because the projection is linear in the curve, A cancels from the ratio R(n) of projected slope to projected intercept, and the index follows by inverting R against the observed ratio. The inversion uses Brent root finding on the monotonic branch below the zero of B₀(n), which is weighting-dependent — it lies at n = 1.968 under uniform weighting and moves lower as the measure is tilted toward high redshift — so the bracket is set per weighting by a preliminary scan. No new data are included or required. The analysis consumes only two published fitted coefficients, b₀ = 1.00 ± 0.04 and b₁ = 1.59 ± 0.105 with the alternative-halo variant b₀ = 1.05, b₁ = 1.63, from Ciocan et al., Astron. Astrophys. 709, L16 (2026), together with Ωm = 0.315 from the Planck 2018 TT,TE,EE+lowE+lensing baseline, Planck Collaboration, Astron. Astrophys. 641, A6 (2020). Both are hard-coded and cited in the source. reproduce_tables.py regenerates Table 1, Table 3, the Ωm sensitivity, the alternative-halo check, the projected intercept of Sec. VIII, the mass offsets of Sec. IX and the pole location, printing each computed value beside the value printed in the article. make_figures.py regenerates Figures 1 and 2; output is greyscale by construction, with models separated by line style, marker shape and hatch rather than hue. Requires only Python 3, NumPy, SciPy and Matplotlib. No network access, no input files, runs in seconds. The regression package ROXY is cited in the article as the method used by the observational analysis; it is not used here and is not a dependency.