Emergent Time from Harmonic Curvature: Time as a Gradient of Coherence in a Torsional Vacuum

This paper presents the Harmonic Curvature Model (HCM), a foundational reformulation of temporal dynamics that treats time not as a fundamental dimension, but as an emergent property arising from relational phase coherence decay across a discrete vacuum substrate. By introducing torsional hysteresis into the vacuum lattice structure, the author derives the arrow of time as "geometric memory" accumulation, effectively resolving the "frozen formalism" problem in quantum gravity. The study provides explicit field equations and recovers gravitational time dilation as a coherence-density effect, while predicting distinct deviations from General Relativity in extreme coherence regimes. Proposed experimental validations include measuring time dilation suppression in Bose-Einstein condensates and frequency shifts in superconducting Josephson junctions.Keywords Emergent Time, Harmonic Curvature Model (HCM), Torsional Hysteresis, Quantum Coherence, Vacuum Lattice. Arrow of Time, General Relativity, Bose-Einstein Condensate (BEC), Superconducting Circuits, Gravitational Time Dilation, Geometric Memory, Wheeler-DeWitt Equation.