The Higgs Scale as Emergent Mesh Geometry

This appendix proposes a first-principles origin for the electroweak scale within MFET, deriving the Higgs vacuum expectation value as a crystallization threshold of the Micro-Wormhole Mesh from the framework's structural inputs (Planck energy, the regulator ε, the anyonic fixed point θ*, the Hausdorff and spectral dimensions, and the Landauer constant). The construction yields v ≈ 243.5 GeV (1.1% below the measured value) and, combined with a predicted quartic self-coupling, a Higgs boson mass of 124.1 GeV (0.8%), framed as an emergent-geometry response to the hierarchy and fine-tuning problems. Yukawa couplings are interpreted geometrically as the normalized overlap of a fermion configuration with the Higgs threshold mode, bounded between 0 and 1, with maximum mass v/√2 attained at perfect overlap and the top quark sitting at near-maximum overlap (y_t ≈ 0.99). A Ginzburg–Landau crystallization free-energy functional underlies the picture.