wZRatio
plain-language theorem explainer
The definition identifies the W to Z boson mass ratio with the cosine of the Weinberg angle. Researchers deriving electroweak parameters from J-cost minimization in Recognition Science cite this relation when connecting the Higgs vacuum expectation value to measured masses. It is realized as a direct one-line abbreviation to the real cosine function.
Claim. The ratio of W to Z boson masses satisfies $m_W / m_Z = cos θ_W$, where θ_W is the Weinberg angle.
background
The Electroweak Symmetry Breaking module identifies the Higgs potential with the J-cost functional and locates the vacuum expectation value at the J-cost minimum. Upstream constants supply the observed masses m_W = 80.377 GeV and m_Z = 91.1876 GeV. The local setting derives spontaneous symmetry breaking SU(2)_L × U(1)_Y → U(1)_EM from ledger selection within the J-cost landscape.
proof idea
The declaration is a one-line definition that directly applies the cosine function to the input Weinberg angle.
why it matters
This definition supplies the mass-ratio relation required by the electroweak breaking mechanism in SM-009. It links the observed ratio to the Weinberg angle inside the J-cost framework and supports the forcing-chain steps that fix D = 3 and the eight-tick octave. No downstream uses are recorded, leaving open its integration with the full phi-ladder mass formulas.
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