The Electroweak Scale from Recursion Phase Separation

The Standard Model Lagrangian paper identified the Higgs field as the phase separation
order parameter Φ ∝ ∆R(Dst) of the Cohesion UFT recursion medium. This paper
derives the quantitative structure of the electroweak sector from that identification. The
electroweak vacuum expectation value v ≈ 246 GeV is established as an empirical anchor
for the recursion resistance at the electroweak density threshold REW, with v = ℏc/REW.
From this single anchor, the W and Z boson masses, the Higgs self-coupling λ, and
the Weinberg angle θW are derived as geometric ratios — without additional free
parameters. The key predictions are: mW /mZ = cos θW from the phase alignment ratio
of the n = 2 and n = 6 recursion modes; mW = gv/2 and mZ =
p
g
2 + g
′2 v/2 from
the SU(2) × U(1) phase connection masses; and λ = m2
H/2v
2 ≈ 0.129 as the curvature
ratio of R(Dst) at the electroweak density threshold. The ratio mW /mZ = cos θW is
confirmed to within 0.5% against the observed values. The Standard Model has one free
parameter at the electroweak scale — v itself — and all other electroweak observables
follow from the recursion phase geometry. The first-principles derivation of v from the
R(Dst) calibration is the primary open problem.