Heavy Quark Masses from Axis Saturation, Casimir Distribution, and Crossing Space in R12

Abstract

The three heavy quark masses (mt , mb, mc) are derived from the rendering algebra R12 ∼= M12(C) through three distinct but structurally connected protocols. The top quark mass mt = N γ1 + 2d/2 cos2 θW arises from axis saturation (Paper V, §9) and Dirac channel counting (Paper XXXIII), with the independent consistency check yt =√2 mt/v ≈ 1. The bottom quark mass mb =
N2γ1(Cadj2 +Z/Cadj2 +Z2/C(8)2)(1+K) arises from a Casimir distribution expansion where vacuum friction Zn distributes equally among dim(fund) gauge states—a direct application of KMS equipartition and the prime–composite theorem (Paper XXXIII). The charm quark mass mc = (dim Sym20(C N+1)−Z)γ1 arises from the crossing space of the W=2 topological winding, identified as the traceless symmetric rank-2 tensor on C13 (the 13th meta-axis of Paper II). The three representation dimensions—N = 12, N(N+3)/2 = 90, N2 = 144—form the natural hierarchy dim(CN ) < dim(Sym20(CN+1)) < dim(MN (C)). All three predictions lie within 0.04σ of PDG values with zero free parameters. Two unifying laws are identified: the Gauge Boson Casimir Mass Law and the Generation–Tensor Correspondence.