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

Abstract Standard cosmological models ($\Lambda$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 manuscript presents the Topological Coherence Hypothesis (TCH), a covariant extension of General Relativity derived from a scalar-tensor action principle. TCH models structural existence as a dynamic state of phase-locked coherence ($\Xi$) with a superfluid vacuum substrate. By introducing a scalar coherence field coupled to the metric $g_{\mu\nu}$, we demonstrate that observed galactic rotation curves and stellar stability limits arise as stationary points of the vacuum action. Key Theoretical Results This framework transitions from heuristic modeling to a formal field theory, deriving its coefficients from fundamental vacuum invariants: Galactic Dynamics: Derives the master velocity equation from the Specific Casimir Potential ($\Phi_c$) and the Riemann Zeta function ($\zeta(2)/2$). This recovers the M31 rotation plateau and predicts a specific 4.05 slope for the Baryonic Tully-Fisher Relationship (BTFR), offering a quantum-topological correction to classical MOND. Stellar Stability: Proves that the Chandrasekhar Limit ($1.39 M_\odot$) is governed by the holographic scaling ratio $d/(d+1) = 3/4$ applied to the fundamental Landau Mass ($M_L$). Singularity Resolution: Reinterprets event horizons as Topological Impedance Barriers ($1/e$ threshold), where phase-locked coherence dissolves into a high-entropy edge state, resolving the mathematical $1/r$ singularity. Falsifiability TCH offers a unique, falsifiable resolution to the Core-Cusp problem by predicting a flat topological core ($\nabla \Xi = 0$) at galactic centers. This prediction stands in contrast to the divergent cusps of CDM and can be validated by high-resolution astrometry from GAIA and early-universe observations by JWST. Keywords Modified Gravity, Action Principle, Hawking Radiation, Holographic Entropy, Singularity Resolution, Landau Mass.