D62: Gauge Boson Masses from Combinatorial Axioms — Derivation of v, MZ, MW and Prediction of MH 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 = Nₜot²/ (Rₑ·k₁) ·mₚ from the structure of the SU (2) sequencing network (676 ppm). The ratio MZ/MW = 1/cos (θW) 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 MZ via the running electromagnetic coupling yields MZ/mₚ = 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 MH/mₚ = 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 MH, and a structural cross-section estimate within 17871 ppm. Five open problems are precisely formulated.