The radial acceleration relation as a Bose-occupation form: an algebraic identity, a no-fit SPARC evaluation, and a redshift test

This record accompanies the manuscript of the same title and contains itscomplete corrected reproduction archive. Four results are reported in decreasing order of security. (1) Exact: writingthe McGaugh, Lelli and Schombert radial acceleration relation as Newton plus ahalo term gives the zero-chemical-potential Bose occupation identityg_halo/g_bar = 1/(exp(x)-1), with x = sqrt(g_bar/a0); its low- andhigh-acceleration limits have the Rayleigh-Jeans and Wien forms. (2) Empirical:with a0 fixed externally at cH0/(2 pi), the no-fit SPARC evaluation isstatistically indistinguishable from the fitted-a0 benchmark under a pairedper-galaxy comparison (-1.2 sigma), with scatter 0.1338-0.1443 dex dependingon sample cuts and flat residuals. (3) Constructive: a geometric single-modeequilibrium realizes the crossover conditionally on the stated deep-regimescaling, response mapping, and self-averaging assumptions. On the 75high-acceleration points, the additive form has a marginal residual offset of-0.0578 +/- 0.0298 dex (1.9 sigma, galaxy-clustered), while the occupationform gives +0.0143 +/- 0.0307 dex; the present sample does not distinguish theoccupation form from the suppressing Simple interpolation function. (4)Observational: a0 = cH(z)/(2 pi) requires redshift evolution with the observedsign, while the measured magnitude is 15-50 per cent faster than H(z),depending on the modelling framework; this tension remains open. The archive contains the manuscript PDF and LaTeX source, both SPARC inputtables, generated residual and sample-accounting tables, both figure PDFs, themain reproduction scripts, targeted verification scripts, pinned Pythonrequirements, and a README giving exact commands, conventions, and runtimes.The physical interpretation is explicitly conditional; the Bose-formrewriting itself is an exact algebraic identity for the stated empiricalparametrization.