A Framework Toward the Yang–Mills Mass Gap Millennium Problem via Harmonic Coherence and Hanners Theorem

Preprint submitted to *Communications in Mathematical Physics*. This work presents a framework and argument toward the Yang–Mills existence and mass-gap problem (Clay Mathematics Institute Millennium Prize). It builds on two prior Zenodo preprints: **Harmonic Coherence** (https://zenodo.org/records/15337795), which reframes gauge field dynamics via entropy minimization, and **Hanners Theorem** (https://zenodo.org/records/15331022), which gives conditions for discrete eigenstates and a positive mass gap in that setting. Here, entropy-minimization principles are applied to non-Abelian gauge fields; the main result (Harmonic Coherence Theorem) is stated as a formal result with a proof outline to be refined elsewhere. The framework yields predictions for a mass gap, confinement (area-law Wilson loops, string tension), and gauge field regularity. Consistency checks and comparison of quoted values to published lattice and phenomenological QCD are documented in supplementary material; no lattice simulations are performed by the authors, and these checks do not constitute proof of the mass-gap claim. This record provides the manuscript and supplementary materials as submitted to CMP.