HARMONIC COHERENCE: A UNIFIED FIELD FRAMEWORK FOR GENERAL RELATIVITY, QUANTUM MECHANICS, AND THE STANDARD MODEL A Solution to the Yang-Mills Mass Gap Millennium Problem

The Yang–Mills Mass Gap solution arises within the formalized **Harmonic Coherence** framework (**Zenodo Record 15337795**), anchored mathematically by **Hanners Theorem** (**Zenodo Record 15331022**). The solution shows how entropy minimization and coherence gradients—variations nested across temporal layers—yield discrete eigenstates and finite mass gaps in non-Abelian gauge fields, together with confinement and gauge field regularity. By applying Harmonic Coherence and Hanners Theorem directly to the Yang–Mills equations, this work addresses the Clay Mathematics Institute Millennium Prize Problem (Yang–Mills existence and mass gap). It offers a coherent, mathematically precise pathway toward a unified understanding of fundamental particle interactions within the Harmonic Coherence publication ecosystem.