Galactic Dynamics and the Dark Matter Problem: A Metric Torsion Solution via the PR-TAU 5.2.3 Protocol

This paper demonstrates that galactic rotation anomalies, traditionally attributed to hypothetical "Dark Matter," are emergent effects of a non-Euclidean vacuum rigidity. By introducing the operational circular constant KGeo ≈ 3.143405 in place of the Euclidean π, we show that the vacuum's intrinsic torsion creates a geometric confinement pressure. We derive a modified centripetal acceleration that accounts for flat rotation curves in spiral galaxies using only baryonic mass. This model unifies microscopic proton mass derivation with macroscopic galactic dynamics through a single metric parameter.