Structural Framework for the Yang–Mills Mass Gap Problem in Four Dimensions

This record provides the formal mathematical derivation corresponding to the conceptual and structural framework introduced in the author's earlier preprint: "Structural Framework for the Yang–Mills Mass Gap Problem in Four Dimensions" (Zenodo, Version v4). While the initial manuscript presented the analytical strategy and contraction-based mechanism in a structural form, the present version develops the associated functional-analytic framework in detail, including lattice geometry, block-minorization bounds, and L-uniform renormalization stability gates. Together, the two records form a consistent and complementary pair:– the former establishes the conceptual transfer-operator and contraction mechanism,– the present manuscript supplies the explicit mathematical formalization required for spectral gap persistence under controlled renormalization flow. This version corresponds to the manuscript submitted to the Journal of Mathematical Physics (tracking number: JMP26-AR-00505) and is intended as a preprint reference during the peer-review process.