Temporal Interpretation – Quantum Compatibility, Emergent Geometry, and Effective Galactic Dynamics

Version update This version introduces a structural clarification of the manuscript. The previous explicit mesoscopic-to-galactic exponent-projection step has been removed in order to avoid presenting the macroscopic galactic operator as a direct consequence of mesoscopic exponent compression. The mesoscopic analysis is now retained as a structural result: it shows that local temporal holonomy and global frustration survive finite-domain aggregation as a compressed collective profile. The galactic section has been reformulated as a separate macroscopic forward projection based on observable baryonic quantities, especially the local dynamical time Tdyn (r) T ₃ₘ₍ (r) Tdyn (r), together with the global scales Δτgal ₆₀₋Δτgal and a∗a^*a∗. The abstract, introduction, conclusion, and appendices were updated accordingly, removing obsolete quantities and scripts associated with the former exponent-projection step. The revised manuscript therefore makes clearer the distinction between: (i) the microscopic and mesoscopic temporal-compatibility framework; (ii) the open problem of deriving the full continuum macroscopic operator; and (iii) the empirical forward SPARC test of the time-activation operator. Abstract This work develops a temporal framework across scales, from quantum compatibility to emergent geometry and galactic dynamics. Within the Temporal Interpretation (TI) of quantum mechanics, proper time is taken as physically primary and branch coexistence is reformulated in terms of temporal compatibility. A minimal unitary model with dense internal spectra is used to define an operational compatibility threshold, Δτcompat, marking the onset of effectively inaccessible coherent recombination. The analysis is then extended to the classical domain, where classical reality is reformulated as a regime of successful temporal synchronisation, horizons as losses of recoverable compatibility, and geometry as an emergent structure arising from temporal relations, holonomy, and non-integrability. At the collective level, temporal compatibility is no longer controlled only by pairwise relations, but by a crossing scale Δτcross, bounded global frustration, and multi-regime exponent compression from local structure to mesoscopic aggregation. This provides the structural basis for a macroscopic time-activation operator, in which collective temporal desynchronisation is expressed as an effective geometric response. The galactic regime is tested using baryonic data from the SPARC sample under a strictly forward methodology: no dark halo is fitted, no inverse reconstruction of the observed rotation curve is performed, and no per-galaxy tuning is allowed. The best-performing projection is a time-activation operator controlled by the local baryonic dynamical time Tdyn (r). A refined global sweep identifies a macroscopic temporal activation scale Δτgal ≈ 2 × 1015 s and an effective acceleration normalisation a* ≈ 9 × 10-11 m s-2 across 171 valid galaxies. The model substantially improves over the purely baryonic prediction and reproduces a large part of the dynamical discrepancy usually attributed to dark matter. These results suggest that the weakly bound outer regime of disk galaxies may encode a macroscopic manifestation of collective temporal desynchronisation. The emergent contribution behaves as a gravitational elasticity: it remains suppressed in strongly bound inner regions and increases as baryonic dynamical times become longer and baryonic acceleration decreases. Although the full derivation of the macroscopic operator from the microscopic compatibility framework remains open, the agreement between temporal-frustration structure and the SPARC time-activation response indicates that temporal compatibility may be physically operative across scales. This record contains the manuscript and a supplementary ZIP archive (TI scripts. zip) with the Python scripts used in the numerical and computational workflow discussed in the article, including local compatibility tests, multi-branch frustration analysis, mesoscopic aggregation, macroscopic projection, and the forward galactic sweep.