BCT Letter 88: Three Spatial Dimensions from D4 Triality — Why the Universe Has Exactly 3+1 Dimensions, and |Vub| from the 8c Sector

Letter 88 of the BCT Superfluid Lattice Model programme. We prove that the BCT superfluid vacuum has exactly three macroscopic spatial dimensions and one temporal dimension. The proof rests entirely on D4 root lattice geometry: the D4 Lie algebra has precisely three triality sectors (the representations 8v, 8s, 8c of Spin (8) ), each contributing one spatial direction to the BCT projection. The fourth D4 dimension is compactified on a sub-Planck Josephson U (1) fiber of radius rJ = α₀/ (2π) = 0. 001179 ℓPlanck, unobservable at all accessible energy scales. No other dimension count is consistent with D4 self-duality, triality, and Lorentz isotropy simultaneously. As a direct corollary, the third-generation CKM matrix element |Vub| is derived: |Vub| = exp (−SD4·rₜet· (1−3α₀) ) = 0. 003683, error −0. 186% from PDG. The unification is exact: 3 spatial dimensions = 3 triality sectors = 3 fermion generations = the factor 3 in every inter-generation NLO correction. Prediction #126. BCT programme total: 130+ predictions, zero free parameters.