Topological Coherence Theory: A Covariant Action Principle for Structural Stability and Singularity Resolution

Abstract Standard cosmological models (CDM) rely on non-baryonic Dark Matter to resolve gravitational discrepancies, yet face persistent tensions at galactic scales (the Core-Cusp problem) and in high-energy regimes (singularities). This repository contains the formal manuscript and numerical verification scripts for Topological Coherence Theory (TCT), a covariant extension of General Relativity. TCT derives observed anomalies not as "missing mass, " but as stationary points of a scalar-tensor action principle. By framing structural existence as a dynamic state of phase-locked coherence () with a superfluid vacuum substrate, the theory provides first-principles derivations for stellar stability limits and galactic rotation curves using fundamental vacuum invariants. Key Theoretical Results Stellar Stability: Derives the Chandrasekhar Limit (1. 39 M_) as a holographic scaling ratio (d/d+1 = 3/4) of the Landau Mass (ML), and the TOV Limit (2. 18 M_) as a U (1) symmetry-breaking phase transition. Galactic Dynamics: "Recovers" the rotation plateau of Andromeda (M31) at ~227 km/s using the Specific Casimir Potential (c) and the Riemann Zeta function ( (2) /2). BTFR Scaling: Predicts a specific, testable 4. 05 slope for the Baryonic Tully-Fisher Relationship, providing a quantum-topological correction to classical MOND. Singularity Resolution: Reinterprets event horizons as Topological Impedance Barriers (1/e), resolving the mathematical 1/r singularity through a geometric phase transition. Keywords Modified Gravity, Dark Matter Alternatives, Action Principle, Casimir Effect, Holographic Entropy, Singularity Resolution, Core-Cusp Problem, Baryonic Tully-Fisher Relationship. For questions regarding the covariant tensor math or collaboration, please contact the author via the email address provided in the manuscript.