Topological Coherence Theory: A Scale-Invariant Framework for Structural Integrity and Galactic Dynamics

Abstract Standard cosmological models (CDM) rely on non-baryonic Dark Matter to account for gravitational discrepancies across galactic scales. This paper introduces Topological Coherence Theory (TCT), a relational framework that redefines structural existence as a dynamic state of phase-locked coherence () with the vacuum substrate. By establishing a universal scaling law between stochastic tolerance (w²) and algebraic connectivity (₂) through the Basel Resonance (k = ²/12), we derive a master velocity equation anchored to the Fine Structure Constant (₅ₒ) and the Spherical Flux Dilution of the vacuum manifold ( (4) ²). Key Findings Galactic Dynamics: TCT recovers the Baryonic Tully-Fisher Relationship (M v⁴) with an emergent slope of 4. 05, resolving galactic rotation curves without Dark Matter. Scale Invariance: The theory demonstrates that vacuum impedance is scale-invariant, accurately predicting the Chandrasekhar Limit (1. 36 M_), the TOV Limit for neutron stars (2. 19 M_), and the Proton-to-Electron mass ratio (1833. 5) from first principles. Inertial Exemption: We propose a modification of inertial mass governed by topological connectivity, preserving Galilean Invariance for isolated bodies while recovering network effects in galactic disks. Keywords: Modified Gravity, Dark Matter Alternatives, Galactic Rotation Curves, Baryonic Tully-Fisher Relation, Information Theory in Physics