A Structural Framework for the Mass Gap in Yang-Mills: Geometric Conjecture

This preprint introduces a structural framework for the Yang–Mills mass gap problem. The central result is a rigorous local coercivity theorem near irreducible anti–self–dual (ASD) backgrounds on S4, establishing a strictly positive lower bound for the quadratic fluctuation operator. Building on this result, the work formulates Conjecture 5.1, a geometric energy bound in local charts of the configuration space A/G. The framework postulates a structural misalignment parameter, thetaYM, defined as the geodesic distance between gauge configurations, and shows that SYM ≥ C (thetaYM)^2 locally. Conditional consequences include: A categorical formulation (DYM) encoding duality and holonomy composition. The emergence of a minimal intermediate state (“z-state”) with mass in the 20–90 MeV band, interpreted as the spectral gap. Compatibility with Osterwalder–Schrader axioms (OS–1 to OS–3 rigorously, OS–4/5 conditionally). A gauge-invariant regularization scheme combining dimensional regularization and Wilson lattice action. Falsifiable predictions for lattice QCD under ’t Hooft twisted boundary conditions: quadratic mass dependence on twist, residue growth, and universality across SU(2)/SU(3). This is not claimed as a solution to the Clay Millennium Problem, but as a phenomenological framework with rigorous local results and testable predictions that may guide future lattice investigations and mathematical analysis.