D62: Gauge Boson Masses from Combinatorial Axioms — Derivation of v, M_Z, M_W and Prediction of M_H in the Projective Dynamic Logo Framework

Building on the derivation of the Standard Model gauge group SU(3)×SU(2)×U(1) as an unconditional theorem of the four combinatorial axioms C1–C4 of the Projective Dynamic Logo (PDL) programme (D57–D61), this document addresses the question of gauge boson masses. A formal definition of gauge boson mass is provided as the minimal coherence excitation cost of a transport mode in Coh(K₄)≅ℤ₂³. The electroweak vacuum expectation value is derived as v = N_tot²/(R_e·k₁)·m_p from the structure of the SU(2) sequencing network (676 ppm). The ratio M_Z/M_W = 1/cos(θ_W) is an unconditional theorem, with the deviation of 5182 ppm from experiment understood as a tree-level vs. physical angle effect. An analytical chain for M_Z via the running electromagnetic coupling yields M_Z/m_p = 97.179 at 84.6 ppm (3.67σ); the residual tension is traced precisely to the absence of sub-proton hadronic closures pending OP-D59-1. The Higgs mass is predicted at M_H/m_p = 133.611, consistent with experiment at 1.49σ. The decay cascade is mapped onto the ℤ₂³ topology: four primary decompositions, neutrino exit at level 2 carrying 12.2% of M_H, and a structural cross-section estimate within 17871 ppm. Five open problems are precisely formulated.