RSPreservesLongitudinalUnitarity
plain-language theorem explainer
Recognition Science researchers cite this definition as the precise condition under which the RS Higgs EFT bridge preserves longitudinal unitarity in vector-boson scattering. It requires the scalar-exchange residue to equal the negative of the gauge-exchange residue. The declaration is introduced by a direct equality with no lemmas or tactics applied.
Claim. The RS Higgs EFT bridge preserves longitudinal unitarity precisely when the scalar-exchange residue satisfies $a_{scalar,RS}=-a_{gauge}$, where $a_{gauge}$ is the residue from gauge-exchange diagrams in the high-energy longitudinal $W_L W_L$ amplitude.
background
The module parametrizes the high-energy longitudinal vector-boson scattering amplitude by a gauge-exchange residue $a_{gauge}$ and a scalar-exchange residue $a_{scalar}$. The cancellation condition is the requirement that their sum vanishes, which cancels the leading $s^2/v^4$ growth and leaves a bounded amplitude. This formalizes the Lee-Quigg-Thacker structural identity. The RS framework supplies the scalar residue via the J-cost Taylor expansion once the canonical normalization map of the Higgs EFT bridge is fixed.
proof idea
The declaration is a direct definition whose body is the equality $a_{scalar,RS}=-a_{gauge}$. No upstream lemmas are invoked and no tactics are used.
why it matters
This definition supplies the hypothesis for the cancellation theorem in the same module and is referenced inside the master certificate for the Higgs EFT low-energy limit. It realizes the conditional statement that RS cost geometry produces the exact opposite-sign residue needed for unitarity preservation. The module notes that a full kinematic four-point amplitude with Mandelstam variables remains open.
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