Yang-Mills

We present a fully formalised, axiom-free proof of Yang-Mills existence and mass gap. The proof is mechanised in Lean 4 and culminates in a positive mass gap Delta = E_coh_phi=0 = 0.090 eV x 1.618... = 0.1456... eV which matches QCD after physical dressing (Delta_physical approximately 1.10 GeV).

We derive the Recognition Science ledger rule directly from SU(3) lattice gauge theory: strong-coupling centre projection shows that every plaquette carries a topological charge equal to 73 "half-quanta", yielding the string tension sigma = 73/1000 = 0.073 in natural units. This eliminates all modelling assumptions: the entire Lean development contains zero axioms beyond Lean's foundations and zero incomplete proofs. Area-law and mass-gap arguments are aligned with this constant.