lambda_RS
plain-language theorem explainer
The Recognition Science quartic coupling is fixed at one half by the second derivative of the J-cost function at unity. Electroweak model builders cite this value when deriving the Higgs mass from the vacuum expectation value in the phi-ladder picture. The definition is a direct assignment that encodes the curvature relation without further steps.
Claim. The Recognition Science quartic coupling satisfies $λ_{RS} = 1/2$, which equals $J''(1)/2$ for the function $J(x) = (x + x^{-1})/2 - 1$.
background
The Q3 Representations module formalizes the quaternion group Q3 as the symmetry group of the eight-tick cycle. Under electroweak symmetry breaking the Higgs doublet splits into three Goldstone modes eaten by the W and Z bosons and one physical spin-zero Higgs. The quartic coupling enters the Mexican hat potential that sets the Higgs mass scale relative to the vacuum expectation value.
proof idea
This is a direct definition that assigns the real number one half to lambda_RS. It implements the relation lambda_RS equals J''(1)/2 by explicit constant assignment.
why it matters
This definition supplies the quartic coupling that appears in higgsMassSq_over_vev, which states m_H squared equals v squared when lambda_RS equals one half. It closes the derivation of the Higgs mass in the phi-ladder picture of electroweak breaking and traces to the J-uniqueness property in the forcing chain. The downstream theorem higgsMassSq_simplifies then confirms the simplification.
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