kappa_lambda_3_RS_eq_zero

This module resolves attack A28 by making the structural mismatch between the RS cosh Higgs potential and the SM Mexican-hat explicit at theorem grade. The RS form is $V_{\cosh}(h)=\Lambda^4(\cosh(h/v)-1)$, which is even in $h$; every odd Taylor coefficient therefore vanishes. After EWSB in unitary gauge the SM potential is the degree-4 polynomial $V_{\mathrm{SM}}(h)=\tfrac12 m_H^2 h^2+(m_H^2/(2v))h^3+(m_H^2/(8v^2))h^4$, whose trilinear coefficient $m_H^2/(2v)$ is nonzero.

Under the bridge identification that linearly matches the collider scalar $h$ to the RS log coordinate (with $\Lambda^4=m_H^2 v^2$), the quadratic terms agree, but the cubic terms do not: RS contributes 0 while SM does not. The modifier $\kappa_{\lambda_3}^{\mathrm{RS}}$ is defined as that ratio of cubic coefficients, and is therefore set to the constant $0$.

One-line term proof by rfl. The definition kappa_lambda_3_RS is the real constant $0$, so equality to $0$ is definitional. No lemmas are invoked; the evenness of cosh that justifies the definition is recorded in the surrounding module narrative and in the sibling evenness facts for $V_{\cosh}$.

This is the cubic half of the A28 resolution: the cosh potential predicts a vanishing trilinear self-coupling relative to the SM. Downstream it is packaged into higgsCoshBSMFalsifier, which bundles $\kappa_3=0$, $\kappa_4=1/3$, a positive sextic, and the global inequality $V_{\cosh}\neq V_{\mathrm{SM}}$ into a single falsifier structure. Di-Higgs production at HL-LHC directly probes the $h^3$ vertex, so a measured $\kappa_{\lambda_3}$ near the SM value of 1 would falsify the pure cosh parameterization under the linear bridge identification. The result is local to the Higgs EFT bridge; it does not itself invoke the T0–T8 forcing chain, but it is the concrete collider signature that the RS cost geometry (J-cost / cosh structure) leaves in the scalar potential.