This document is not a proof of the Yang-Mills mass gap. It does not satisfy the Wightman axioms, does not construct a quantum Yang-Mills theory in four dimensions, and does not produce the mathematical proof required by the Clay Mathematics Institute’s Millennium Prize Problem. What this document offers is narrower and more modest: a set of conceptual notes identifying structural parallels between Coherence Cosmology (SR103EN/SR104EN) and the conceptual core of the Yang-Mills mass gap problem. The connections proposed here are ontological, not mathematical. They are intended as a conceptual bridge toward future mathematical formalization. The Clay Mathematics Institute states that progress will require “the introduction of fundamental new ideas both in physics and in mathematics. ” This document proposes that the structural ontology of Coherence Cosmology — specifically, the coherence condition (antichain) and the no-isolation principle (Definition 20) — may be one source of such new ideas. The three potential points of contact are: 1. Color neutrality as antichain condition: color-neutral composites satisfy a condition analogous to the antichain condition — no single color charge dominates or stands in an unbalanced ordering relation to the others. A single gluon cannot form a color-neutral structure alone and therefore cannot exist as an isolated coherent local structure within Uₜotal. 2. Confinement as a consequence of Definition 20: every local structure exists only as a function of its interference relations with all other structures. A gluon’s coherent section is defined only through its color-charge relationships. Remove those relations and the coherent section becomes undefined. Confinement is not merely energetic — it is ontological. 3. Mass gap as minimum coherence threshold: the lightest physical state above the vacuum is the glueball — a color-neutral bound state of gluons with mass on the order of 1-2 GeV. In the language of Coherence Cosmology, the glueball is the simplest color-neutral structure that can satisfy the antichain condition. Its mass represents the minimum structural complexity required for coherent color-neutral existence within Uₜotal. This document addresses Stage 1 (conceptual correspondence) only. Stages 2-4 — formal mapping between antichain structure and SU (3) color space, connection to the Yang-Mills energy spectrum, and proof — are open problems requiring collaboration with mathematicians specializing in quantum field theory and gauge theory. Prerequisite: SR103EN Formalization DOI: 10. 5281/zenodo. 20405659 Prerequisite: SR104EN Formalization DOI: 10. 5281/zenodo. 20405676 Related: Structural Hints for Quantum Gravity DOI: 10. 5281/zenodo. 20407643
Masashi Saito (Wed,) studied this question.