What question did this study set out to answer?

This document aims to identify conceptual parallels between Coherence Cosmology and the Yang-Mills mass gap problem to inspire future mathematical formalization.

May 29, 2026Open Access

Structural Hints for the Yang-Mills Mass Gap from Coherence Cosmology

Key Points

This document aims to identify conceptual parallels between Coherence Cosmology and the Yang-Mills mass gap problem to inspire future mathematical formalization.
Identified structural parallels using ontological connections between concepts in Coherence Cosmology and the Yang-Mills problem.
Discussed three points of contact: color neutrality, confinement, and mass gap based on coherence requirements.
Outlined the implications of the coherence condition and no-isolation principle for mass gap understanding.
Proposed that gluons cannot exist in isolation, requiring color neutrality for local coherent structures.
Established that confinement includes ontological aspects beyond energy considerations in relation to local structures.
Identified the glueball as the minimum mass state supporting coherent color-neutral existence, with mass around 1-2 GeV.

Abstract

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

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