The Dark Sector over Finite Substrate Galactic Dynamics, the Radial Acceleration Relation, and the Cosmological Acceleration Scale
Abstract
Galaxy dynamics and the accelerating expansion are the two standing tensions of large-scale gravitation. We develop both from one finite relational substrate on which gravitation is the synchronisation of elementary clocks. Synchronisation reproduces Newton's law at high acceleration and carries an intrinsic resolution floor, fixed by the expansion rate, at \(a_{0}=cH_{0}/2\pi\) - within ten percent of the observed scale, with no free parameter. Below the floor the field is read in a Fourier-conjugate chart where the registered force is an amplitude rather than a gradient, giving the geometric-mean law \(g_{\mathrm{eff}}=\sqrt{g_{\mathrm{bar}}a_{0}}\), hence flat rotation curves and the baryonic Tully-Fisher relation \(v^{4}=GMa_{0}\). The crossover is fixed by a finite first-passage registration and reproduces the empirical radial acceleration relation \(g_{\mathrm{obs}}=g_{\mathrm{bar}}/(1-\exp(-\sqrt{g_{\mathrm{bar}}/a_{0}}))\) with no fitted function; the intrinsic scatter follows as the disk's dynamical temperature and the external-field effect as the total-field dependence of the registration. In merging clusters the coherence-weighted enhancement follows the collisionless galaxies, predicting the lensing offset, and the cluster-core excess is predicted to be the coherent amplitude addition of the core's synchronised components. The cosmological constant is the curvature of the finite chart, \(\Lambda\sim1/\Omega\). The single quantity left to the totality is the…
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