Sci - The Yang-Mills Mass Gap as a Persistence Criterion: A Pre-Geometric Characterization

Sci - The Yang-Mills Mass Gap as a Persistence Criterion: A Pre-Geometric Characterization Armstrong Knight — intent-tensor-theory.com — 2026 The Yang-Mills existence and mass gap problem — one of the Clay Mathematics Institute's seven Millennium Prize Problems — asks for a rigorous proof that Yang-Mills quantum field theories possess a strictly positive mass gap. This paper proposes a pre-geometric characterization of the mass gap as a direct consequence of the persistence criterion of Dimensionless Mathematics. In the ITT framework, a Yang-Mills excitation stably exists as a particle if and only if its selection number S_YM ≥ 1. Zero-mass non-Abelian gauge excitations are excluded because non-Abelian self-interaction generates non-vanishing boundary phase residue (𝔦_YM ≠ 0), preventing them from satisfying the triple closure condition. The mass gap is the persistence criterion expressed in post-geometric language. The ITT closure operator L^ITT_YM is defined, the admissibility condition is stated, and the candidate mass gap theorem is proposed: 𝒜_ITT[W] = 1 implies inf Spec(L^ITT_YM) > 0. The paper explains why Abelian gauge theories (U(1), QED) have massless excitations (photons achieve closure) while non-Abelian theories (SU(N), QCD) do not. Connection to asymptotic freedom, lattice QCD, and the standard explanation of confinement is established. Open derivations are listed. No claim of proof of the Millennium Problem is made; the paper presents a pre-geometric research hypothesis and a specific proof program.