Unified Quark Mass Formula from the KMS Boltzmann Cascade, Casimir Barriers, and Shannon Saturation in R12

Abstract

A single formula mq = C(N, 3) γ1 exp(−Sq) with C(12, 3) = 220 (information budget) and γ1 (Riemann anchor) reproduces all three light quark masses (u, d, s) at 0.1–2.4% accuracy with zero free parameters. The suppression action Sq is a KMS
Boltzmann cascade: Sq = (EQCD+ P2 C barrier2)/Tweak, where EQCD = b0 = 7 (QCD beta coefficient = number of running channels), Tweak = dim(fund, SU(2)) = 2 (weak-sector KMS temperature), and C barrier2 are Casimir invariants accumulated
at each transition. The Casimir selection rule determines barriers: inter-generation transitions (topological, winding change) cost C2(adj, SU(3)) = 3; intra-generation transitions (algebraic, isospin rotation) cost C2(fund, SU(2)) = 3/4. The formula automatically recovers ms/md = exp(C2(8)) = exp(3) (Paper XXXIV) from Sd−Ss = 3 and yields a new identity C2(adj, SU(3)) = (N −Nf )/2 = (12−6)/2 = 3, linking the colour Casimir to the axis–flavour gap. The rendering ceiling Lγ1 = 220γ1 ≈ 3110 MeV coincides with m(J/ψ) = 3097 MeV (0.4%), identifying the J/ψ charmonium ground state as the light–heavy transition point.