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 (rₒct, rₜet) and the QCD scale ΛQCD as inputs. We report the completion of the core programme: all three fundamental mass scales of the Standard Model — the electron mass mₑ, the QCD confinement scale ΛQCD, 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: mₑ = 0. 510927 MeV (−0. 014%), ΛQCD = 220. 44 MeV (+0. 20%), v = 246. 145 GeV (−0. 030%), all from the universal formula scale = mP × exp (−SD4 × fₖ) where SD4 = π⁵/6 and the void metric factors fₒct < fₜet < 1 encode the gauge hierarchy geometrically. The exact algebraic identity 1 − rₒct − rₒct² = 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.