THE COHERENCE METRIC - A Purely Topological Derivation of Scale Invariant Spacetime Constant via Dural-Fractal Coherence Modulation

This paper introduces the Coherence Metric, a novel dural-fractal spacetime framework that provides a purely topological derivation of fundamental physical constants and cosmic boundaries, fulfilling Hermann Weyl’s 1918 vision of scale invariance. By nesting an orthogonal square grid (potential energy) with intersecting circular trajectories (kinetic energy), we identify a scale-invariant 11.07% path discrepancy that acts as a perpetual geometric motor via accumulated Berry phases. The resulting scale-dependent metric smoothly modulates spacetime dimensions from a 1–2D grid structure to 3–4D compact matter. Bounded strictly between Iteration 0 (Planck scale) and Iteration 200 (Cosmic Exoskeleton) via a modified Heaviside coherence modulator, the model analytically derives the constituent quark mass (~331 MeV), nuclear binding energies, and the observed dark energy density (10−47 GeV) as static surface tensions of a stable, non-expanding universe.