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

Standard cosmological models (ΛCDM) 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 (Ξ) with the vacuum substrate. By establishing a universal scaling law between stochastic tolerance (w²) and algebraic connectivity (λ₂) through the Basel Resonance (k = π²/12), we derive a master velocity equation anchored to the Fine Structure Constant (αfs) and the Spherical Flux Dilution of the vacuum manifold ((4π)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.