A Minimal Structural Coherence Model for Galactic Dynamics and Cosmology

We present a minimal structural coherence framework in which gravitational dynamics emerge from a scale dependent effective dimension. The model is governed by a single coherence function that follows a volumetric scaling of accessible structural states, leading to an effective dimension that smoothly interpolates between inner and outer regimes. This formulation yields a modified acceleration law with a single characteristic acceleration scale that is not fitted but derived from fundamental constants. Using a parameter free coherence scale, the model reproduces galaxy rotation curves across 165 galaxies from the SPARC dataset, achieving a correlation of about 0.96, low scatter of about 0.11 dex, and naturally recovering the baryonic Tully Fisher relation with slope close to 4.1. We extend the same framework to cosmology and test it against Pantheon plus supernovae with full covariance, Hubble parameter measurements, and baryon acoustic oscillation data. The model achieves a total chi squared difference of about 0.5 relative to Lambda CDM, indicating near statistical equivalence. The framework does not require dark matter or dark energy components, instead attributing observed phenomena to a gradual loss of structural coherence across scales. These results suggest that gravitational dynamics at both galactic and cosmological levels may emerge from a deeper coherence based structure underlying spacetime.