What does this research mean for the field?

The Euclidean Yang-Mills measure exists on ℝ⁴ for any compact simple Lie group and bare coupling g>0, uniquely satisfying the Osterwalder-Schrader axioms and unconditionally possessing a positive mass gap. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To unconditionally construct the Euclidean Yang-Mills measure on ℝ⁴ for any compact simple Lie group and establish the existence of a positive mass gap for all bare coupling constants.

August 30, 2026Open Access

PROOF OF EXISTENCE AND MASS GAP FOR YANG-MILLS IN FOUR DIMENSIONAL SPACE-TIME : Via Quantum Coherence Metric, Tube Diagonalization, Stochastic Forcing and Finite Wilsonian Iteration — Unconditional for All g>0

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To unconditionally construct the Euclidean Yang-Mills measure on ℝ⁴ for any compact simple Lie group and establish the existence of a positive mass gap for all bare coupling constants.
Formulated a quantum coherence metric coupling L² geometry with an inverse covariant Laplacian operator.
Established a curvature-dimension bound CD(K_eff, ∞) via Uhlenbeck tube diagonalization around Wilson loops.
Combined stochastic forcing bounds with finite Wilsonian renormalization group iterations to map arbitrary bare couplings to weak effective regimes.
Unconditionally constructed the Euclidean Yang-Mills measure on ℝ⁴ verifying Osterwalder-Schrader axioms OS0 through OS4.
Demonstrated the existence and uniqueness of the infinite volume limit for any compact simple Lie group G and coupling g > 0.
Proved a strictly positive mass gap bound Δ(g) ≥ c₀ m_dyn(g) > 0 governed by the dynamic QCD mass scale.

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Implication

Mathematical analysis proves existence and a positive mass gap for four-dimensional Yang-Mills theory across all bare couplings, establishing a rigorous foundation for quantum gauge fields.

Cite This Study

Jean Florent Romaric GNAYORO (2026) studied this question.

synapsesocial.com/papers/6a93f0a36c1a8fb52e79ce7b https://doi.org/10.5281/zenodo.22145363

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Implication

Mathematical analysis proves existence and a positive mass gap for four-dimensional Yang-Mills theory across all bare couplings, establishing a rigorous foundation for quantum gauge fields.

PROOF OF EXISTENCE AND MASS GAP FOR YANG-MILLS IN FOUR DIMENSIONAL SPACE-TIME : Via Quantum Coherence Metric, Tube Diagonalization, Stochastic Forcing and Finite Wilsonian Iteration — Unconditional for All g>0

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Discussion

Implication

Cite This Study

PROOF OF EXISTENCE AND MASS GAP FOR YANG-MILLS IN FOUR DIMENSIONAL SPACE-TIME : Via Quantum Coherence Metric, Tube Diagonalization, Stochastic Forcing and Finite Wilsonian Iteration — Unconditional for All g>0

Key Points

Discussion

Implication

Cite This Study

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