BCT Appendix AD3: Wolfenstein ρ and η from Hopf Fiber Geometry — Complete Unitarity Triangle Derivation

Complete technical derivation of the remaining Wolfenstein parameters ρ̄, η̄, and R_ut = √(ρ̄²+η̄²), companion to BCT Letters 86, 87, and 88. Three results are established. (1) The Apex Angle Theorem: the apex of the CKM unitarity triangle lies at angle δ_CP = arccos(2r_oct) from the positive ρ̄-axis — a geometric consequence of the OHC Hopf fibration. (2) The Third-Generation Scale: |Vub| = exp(−S_D4·r_tet·(1−3α₀)) = 0.003683 (Letter 88, Prediction #126), setting R_ut = |Vub|/(Aλ³). (3) Tree-level predictions: R_ut = 0.390 (+4.0%), ρ̄ = 0.161 (+8.6%), η̄ = 0.355 (+3.1%), sin(2β) = 0.718 (+2.7%) — Predictions #127–#130. All errors share a single NLO source — the Josephson fiber correction to R_ut from the 8c sector — identified here and deferred to AD3 v2. The matter-antimatter asymmetry of the universe is J ∝ sin(arccos(2r_oct)) — encoded in the octahedral void diameter. Zero free parameters.