BCT Letter 34: All Three Standard Model Scales from BCT Geometry — 110 Predictions, Zero Free Parameters

The BCT Superfluid Lattice Model derives Standard Model observables from the geometry of a body-centred tetragonal lattice with axial ratio c/a = √2, using only two void radii (r_oct, r_tet) and the QCD scale Λ_QCD as inputs. We report the completion of the core programme: all three fundamental mass scales of the Standard Model — the electron mass m_e, the QCD confinement scale Λ_QCD, and the electroweak symmetry-breaking scale v — are now derived from first principles with sub-0.2% precision and zero free parameters. The central results are: m_e = 0.510927 MeV (−0.014%), Λ_QCD = 220.44 MeV (+0.20%), v = 246.145 GeV (−0.030%), all from the universal formula scale = m_P × exp(−S_D4 × f_k) where S_D4 = π⁵/6 and the void metric factors f_oct < f_tet < 1 encode the gauge hierarchy geometrically. The exact algebraic identity 1 − r_oct − r_oct² = 3/4 underlies the electroweak scale derivation. The BCT programme now comprises 110 sub-1% predictions and 33 sub-0.1% predictions from zero free parameters. Newton's gravitational constant is also derived (Letter 35), completing the unification of all four fundamental forces.