Variational Backbone and Regime Closures XIX (RAR): Cosmic Horizon Readout and Galactic Dynamics Entropy, boundary gap, and the RAR as one Schur footprint

This paper gives the VBRC horizon-readout account of the galactic radial acceleration relation and its cosmological capstone role in the series. The claim is not that the cosmological horizon is a material shell exerting a force on galaxies. The claim is that a finite cosmological protocol has a boundary, read as the cosmic horizon, and that the unread sector associated with that boundary enters retained laws only through a licensed boundary summary. In this language, “beyond the horizon” is protocol-relative readout language, not a directly accessible spatial region. The construction uses the earlier VBRC layers. Part V reads elimination residues as mass or gap data. Part VI supplies the dual closed-summary response. Part XIV treats horizons as boundary events whose mass, entropy, and temperature conversion are common-source outputs of one effective-operator path. Part XVIII shows that dark-matter-like and dark-energy-like readouts must lift to one dual-Schur residual source. Applied to the cosmic horizon, these ingredients produce a single boundary summary whose lowest coupled gap is read as a horizon acceleration scale. Under the named global horizon-clock gates, this gives a structural value near 1.19e-10 m s^-2, to be compared with the empirical RAR scale rather than advertised as a per-galaxy fitted constant. A rotating galaxy does not feel a propagated horizon force. It reads the dominant boundary residual through overlap with its own baryonic field. This gives a rotation-readout law in which the observed acceleration contains the baryonic term together with a boundary-summary contribution controlled by the global acceleration scale and a transition envelope. In the deep isolated regime the same structure yields the baryonic Tully-Fisher scaling. Dark-matter phenomenology in galaxies and dark-energy phenomenology in the metric channel are then treated as correlated readouts of one horizon residual: the local dynamical channel and the isotropic metric channel. They are not independent fluids and not primitive forces. The remaining assumptions are localized in named gates, including the Hubble-patch realization, the clock-instance window, the stationary readout normalization, and the transition-profile gates. The paper therefore presents a gated horizon-readout mechanism for the RAR and its dark-sector correlation, not a completed cosmological data-fitting program.