higgsMass
plain-language theorem explainer
Recognition Science expresses the Higgs mass via the curvature of the J-cost functional at the vacuum expectation value. The definition supplies m_H = sqrt(2 lambda) v for use in electroweak mass calculations within the Standard Model module. A researcher deriving SM parameters from the phi-ladder would invoke this when matching the observed 125 GeV scale. The implementation is a direct one-line algebraic expression of the second-derivative formula.
Claim. The Higgs mass is $m_H = v sqrt(2 lambda)$, where $lambda$ is the quartic coefficient in the J-cost potential and $v$ is the vacuum expectation value that minimizes the potential.
background
The module derives electroweak symmetry breaking from the J-cost functional, identifying the Higgs potential with the Recognition Science cost and the vacuum expectation value with its minimum. The Mexican-hat form V(phi) = -mu^2 |phi|^2 + lambda |phi|^4 is adopted, with spontaneous breaking SU(2)_L x U(1)_Y to U(1)_EM occurring at the J-cost minimum. Upstream results supply the normalization lambda = ln(phi) from RGTransport and the collision-free ledger structure from OptionAEmpiricalProgram.is.
proof idea
The declaration is a one-line definition that applies the standard curvature formula for the quartic potential at its minimum, returning sqrt(2 lambda) times the input VEV.
why it matters
The definition supplies the mass formula required by the RS mechanism for electroweak breaking in SM-009. It feeds sibling declarations that compare the result to the observed 125 GeV scale and to the phi-ladder mass formula. The construction closes the link between J-cost minima and the eight-tick octave structure without introducing new axioms.
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