vev_GeV
The Higgs vacuum expectation value is fixed at 246.22 GeV. Electroweak physicists cite this constant when deriving W and Z masses from symmetry breaking. It enters as a direct numerical definition that anchors all subsequent electroweak calculations in the Recognition Science framework.
claimThe vacuum expectation value of the Higgs field is $v = 246.22$ GeV.
background
The module derives electroweak boson masses from the Higgs mechanism, where the vacuum expectation value breaks SU(2)_L × U(1)_Y to U(1)_EM. In Recognition Science this scale corresponds to the J-cost minimum on the phi-ladder. The upstream shell definition supplies the energy scale as E_coh times block capacity at each level n, which informs placement of the electroweak rung.
proof idea
This is a direct numerical definition that assigns the constant 246.22 to vev_GeV in GeV units. No lemmas or tactics are applied.
why it matters in Recognition Science
This constant feeds vev_determines_scale, weak_coupling_g (which yields g ≈ 0.653), vev_electron_ratio, and gf_matches (which verifies the Fermi constant within 10%). It realizes the phi-ladder placement for the electroweak scale in the RS mechanism and is consistent with the forcing chain steps T5–T8.
scope and limits
- Does not derive the numerical value from the Recognition functional equation.
- Does not include experimental uncertainty or error bounds.
- Does not identify the precise phi-ladder rung or gap(Z).
- Does not address the Berry creation threshold or Z_cf.
Lean usage
theorem scale_check : wBosonMass_GeV < vev_GeV := by simp only [wBosonMass_GeV, vev_GeV]; norm_numformal statement (Lean)
56def vev_GeV : ℝ := 246.22
proof body
Definition body.
57
58/-- Weak mixing angle sin²θW (on-shell scheme). -/