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

Standard cosmological models (ΛCDM) rely on ad-hoc parameters—non-baryonic Dark Matter and mathematical singularities—to resolve gravitational discrepancies. We present the Topological Coherence Hypothesis (TCH), a covariant scalar-tensor framework that models spacetime not as empty geometry, but as a physical, superfluid vacuum substrate. By synthesizing constraints from Fluid Dynamics (vacuum stiffness), Quantum Field Theory (Casimir invariants), and Information Theory (entropic limits), TCH offers a unified, parameter-free derivation of structural stability across scales. We demonstrate that gravitational anomalies are actually stationary points of this vacuum action: Galactic Dynamics (The Superfluid Response): We derive the master velocity equation from the Specific Casimir Potential (Φc) and the Bosonic Spectral Sum (k=ζ(2)/2). This recovers the M31 rotation plateau and predicts the Baryonic Tully-Fisher Relationship (BTFR) with a precise slope of 4.05, replacing Dark Matter with a mass-dependent vacuum amplification. Stellar Stability (The Holographic Limit): We prove that the Chandrasekhar Limit (1.39M_) is an emergent holographic scaling ratio ($3/4$) applied to the fundamental Landau Mass (ML), linking stellar structure directly to vacuum topology. Singularity Resolution (The Information Bound): Event horizons are reinterpreted as Topological Impedance Barriers where phase-locked coherence drops below the Shannon limit ($1/e$). This resolves the $1/r$ singularity into a finite, high-entropy edge state. TCH resolves the Core-Cusp problem by predicting flat topological cores (∇ Ξ = 0) at galactic centers, a falsifiable prediction testable via GAIA and JWST observations.