The Galaxy Acceleration Scale as a Causal-Horizon Threshold: A Parameter-Free Account of the Radial Acceleration Relation and a Falsifiable Prediction for Its Redshift Evolution

Galaxy kinematics obey a tight radial acceleration relation (RAR) with a characteristic scale \(g_\dagger \approx 1.2\times10^{-10}\,\mathrm{m\,s^{-2}}\), numerically close to \(cH_0/2\pi\). I propose a physical origin for this scale. If the gravitational response of a system is limited by a causal completion time \(\tau_{\mathrm{grav}} \sim c/g\), then accelerations below \(a_0 = \xi\,cH(z)\), with \(\xi\) an order-\(10^{-1}\) geometric coefficient, cannot complete a response cycle within the causal horizon time \(1/H\), and the effective dynamics transitions to \(g_{\mathrm{eff}}=\sqrt{g_N a_0}\). A hierarchical fit to the SPARC sample (149 galaxies, 3152 points) with the interpolating function \(g_{\mathrm{obs}}=g_{\mathrm{bar}}/[1-e^{-\sqrt{g_{\mathrm{bar}}/a_0}}]\) and per-galaxy mass-to-light, distance, and inclination nuisance parameters yields \(a_0=(1.11\pm0.03)\times10^{-10}\,\mathrm{m\,s^{-2}}\), i.e. \(\xi = 0.157\pm0.004\) for the local \(H_0=73\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\), consistent with \(1/2\pi = 0.159\) within \(1\sigma\); equivalently, if \(\xi=1/2\pi\) is taken as exact, the fit returns \(H_0 = 2\pi a_0/c = 71.8\pm1.6\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\). With \(a_0\) fixed to \(cH_0/2\pi\) the framework reproduces individual rotation curves with zero free parameters per galaxy. The transition shape is likewise derived rather than adopted: memoryless completion with horizon-limited retries gives the parameter-free implicit law \(g_{\mathrm{bar}}=g_{\mathrm{eff}}(1-e^{-g_{\mathrm{eff}}/a_0})\), whose deep-regime approximation is the McGaugh fitting function itself. On SPARC the derived law is the most universal shape tested, and combined with environmental fields computed from 2MRS it returns \(\xi = 0.158\pm0.004\), matching \(1/2\pi\) at the half-percent level. A pre-registered extension in which failed completion attempts load the local stellar node column, with zero new fitted parameters, matches the empirical function's fit quality and independently returns \(\xi = 0.1589\). Environmental fields rebuilt from the Tully 2015 group catalog with halo-scale masses reproduce published external-field estimates, close the long-standing bulge-sample anomaly for the first time, and give the best universal-model evidence of the program; they also reveal that \(\xi\) carries a \(\sim\)15% systematic set by the environment configuration (\(\xi = 0.16\)–\(0.20\), consistent with \(1/2\pi\) at the low end), which supersedes the statistical precisions above. Unlike MOND, where \(a_0\) is a constant of nature, this mechanism requires \(a_0(z)=\xi\,cH(z)\). A pre-registered assembly of current kinematic constraints (MUSE-DARK III, Tully–Fisher zero points, SPARC anchor) finds the \(H(z)\) scaling to be the best model by information criteria and evidence, with a free-rate fit landing on the predicted rate, but the evolution detection is only 1.1–1.5\(\sigma\) once honest cross-survey systematics are imposed; \(z\approx2\) declining rotation curves remain in qualitative tension, and a single internally homogeneous survey to \(z\sim1.5\) would decide the test at \(\sim4\sigma\). The mechanism further implies an external-field effect, and Bayesian model comparison on SPARC favors including it (\(\Delta\ln Z = +37\)); environmental fields computed independently from the 2MRS catalog with the same law reproduce published large-scale-structure estimates, and with those fields the fit returns \(\xi = 0.157\pm0.004\). An apparent galaxy-to-galaxy variation of the effective scale at the 0.14 dex level remains, however, favored over strict universality (\(\Delta\ln Z = +102\)); it survives heavy-tailed error models, velocity floors, radial mass-to-light gradients, and the node-load extension, and localizes in galaxies whose baryonic mass depends most on stellar modeling. For solar-neighborhood wide binaries the predicted enhancement is \(G_{\mathrm{eff}}/G = 1.35\)–\(1.44\) at separations beyond \(\sim10^4\) AU, with a parameter-free transition at 2–8 kAU. Solar-system ephemerides discriminate between formulations of the mechanism: the algebraic completion law is Cassini-safe identically, while a nonlinear-Poisson field embedding of any RAR-compatible transition law, including the one derived here, is excluded at \(8\sigma\) by the Cassini quadrupole bound, so the eventual covariant theory must be of modified-inertia type. The mechanism supplies exactly that: its retry ledger, read as a response statement, is a modified-inertia law \(\mu(a) = 1-e^{-a/a_0}\) whose solar-system quadrupole falls four orders of magnitude below the Cassini bound, whose time-nonlocality is forced by the retry queue rather than added, and whose attempt count yields the identity \(M_{\mathrm{eff}}/M_b = \nu\): lensing equals dynamics with no adjustable structure, as weak-lensing measurements of the radial acceleration relation find. If deposits persist on the horizon timescale and stream ballistically (a new postulate, labeled as such), the Bullet Cluster's lensing geometry follows with no further freedom, the \(\chi^2\) over the published apertures dropping from 46 to 13; the relaxed-cluster hydrostatic shortfall is quantified from three well-measured clusters at a factor 3.4–4.6 at 300 kpc, declining to \(\simeq2\) at 1 Mpc, and remains unexplained; the cosmological background is taken to be standard throughout. Several claims made in earlier preprints of this program are corrected here.