lambda_RS_val
plain-language theorem explainer
Recognition Science forces the quartic coupling to equal one half through the second derivative of the J-cost at unity. This supplies the input for the Higgs mass relation m_H squared equals v squared in the Q3 representation of electroweak breaking. The proof reduces directly by reflexivity on the explicit definition of the coupling.
Claim. The Recognition Science quartic coupling satisfies $λ = 1/2$, where $λ = J''(1)/2$ and $J(x) = ½(x + x^{-1}) - 1$.
background
The module develops the quaternion group Q3 as the symmetry of the eight-tick cycle and its role in SU(2)×U(1) to U(1) breaking. The J-cost is the function J(x) = ½(x + x^{-1}) - 1 whose curvature at unity fixes the quartic term. The upstream definition states: 'The φ-forced quartic coupling: λ = J″(1)/2 = 1/2.' The companion axiom-reduction theorem converts seven independent axioms into four structural conditions plus three definitional facts.
proof idea
Term-mode proof consisting of a single reflexivity step on the definition of the quartic coupling, which is written explicitly as 1/2.
why it matters
The result supplies the numerical value of the quartic coupling that enters the Higgs mass formula m_H² = 2λv², yielding m_H² = v² when λ = 1/2. It sits inside the Q3 representation analysis of electroweak breaking and inherits the φ-forced curvature from the J-cost. No downstream uses are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.