Yang–Mills Mass Gap via Residual Topological Density: Main and Auxiliary Papers (v7.6)
Yang–Mills Mass Gap via Residual Topological Density: Main and Auxiliary Papers (v7.6)
This release (v7.6) is a coordinated set of the Main paper and seven Auxiliary notes for a modular program toward the SU(N) Yang–Mills mass gap. The organizing scalar is the residual topological density \(\delta_{\phi}\). The proof chain follows\[\delta_{\phi} > 0 \;\;\Rightarrow\;\; \lambda_{\min}(-\Delta_{M}) > 0 \;\;\Rightarrow\;\; m_{0} > 0,\]linking IR rigidity, a moduli–space spectral gap, and the Hamiltonian gap. The suite documents OS-window sealing (OS1–OS5) via an MMLS/SAPZ variational–entropic framework, refined finite–range decomposition and Mosco convergence (including singular strata), entropy–trace control for low modes, and a decision/estimation pipeline integrating numerical CI with analytic dashboards. **New in v7.6:** tightened cross-references, a QOP (operator proximity) rate note, a gauge-fixing/Gribov robustness section in the Main paper, and synchronized dashboards across Aux C–Z. (Program overview and the core chain are summarized in the Main abstract; OS sealing and its variational inequality are summarized in Aux G/H; unconditional FRD/Mosco foundations are summarized in Aux D; entropy–trace sealing is summarized in Aux I; and the decision matrix is summarized in Aux F.) Interested researchers are kindly asked to contact the author at leeclinic@protonmail.com for collaboration.
Yang–Mills mass gap Clay Millennium Problem Osterwalder–Schrader axioms BRST formalism Log–Sobolev inequality Cluster expansion Finite-range decomposition Mosco convergence Gauge fixing Topological invariants Supersymmetric Yang–Mills Residual topological density Spectral gap, Yang–Mills mass gap Clay Millennium Problem Osterwalder–Schrader axioms BRST formalism Log–Sobolev inequality Cluster expansion Finite-range decomposition Mosco convergence Gauge fixing Topological invariants Supersymmetric Yang–Mills Residual topological density Spectral gap
Yang–Mills mass gap Clay Millennium Problem Osterwalder–Schrader axioms BRST formalism Log–Sobolev inequality Cluster expansion Finite-range decomposition Mosco convergence Gauge fixing Topological invariants Supersymmetric Yang–Mills Residual topological density Spectral gap, Yang–Mills mass gap Clay Millennium Problem Osterwalder–Schrader axioms BRST formalism Log–Sobolev inequality Cluster expansion Finite-range decomposition Mosco convergence Gauge fixing Topological invariants Supersymmetric Yang–Mills Residual topological density Spectral gap
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