YANG–MILLS MASS GAP VIA A RIGIDITY-FLOOR REDUCTION (PARTS I–II)

This two-part work proves a positive mass gap for pure lattice SU(3) Yang–Mills by isolating one scale-sensitive bottleneck: a uniform gauge-invariant (GI) “rigidity/capacity floor” that excludes near-zero physical modes along a controlled RG corridor. Part I (Reduction, Structure, and Consequences) shows that once this uniform GI floor holds, standard reflection-positivity/transfer-matrix interfaces yield exponential clustering, a positive transfer-operator spectral gap, and an Osterwalder–Schrader reconstruction with strictly positive mass. Part II (RG Ledger and Near-Zero Mode Control) supplies the only genuinely model-dependent input: it establishes the uniform GI rigidity floor across scales using a ledger-style RG argument, where all losses are tracked explicitly and shown to remain summable inside the corridor. Files in this record:• Part I: YANG–MILLS MASS GAP VIA A RIGIDITY-FLOOR REDUCTION (PART I: REDUCTION, STRUCTURE, AND CONSEQUENCES).• Part II: YANG–MILLS MASS GAP VIA A RIGIDITY-FLOOR REDUCTION (PART II: RG LEDGER AND NEAR-ZERO MODE CONTROL). The work is purely theoretical and self-contained, organized as an explicit lemma → theorem chain with an auditable constant/loss ledger.