higgsEFTLowEnergyLimitCert_inhabited
plain-language theorem explainer
The declaration certifies that the master certificate structure assembling the Recognition Science cost geometry to Standard Model effective field theory chain is non-empty. A physicist deriving collider observables from phi-ladder mass formulas would cite it to confirm the full bridge is constructible. The proof is a one-line term that directly applies the structure constructor to the component certificates from the imported bridge modules.
Claim. The type of the master certificate for the Higgs EFT low-energy limit is inhabited: there exists a structure $C$ whose components bundle the RS cost geometry to canonical Higgs EFT, the electroweak mass relations and Weinberg angle, the SM-normalised Yukawa couplings on the phi-ladder, the tree-level observable skeleton, and longitudinal vector scattering unitarity.
background
The module bundles five Lean modules that formalise the chain from RS cost geometry through effective scalar coordinate and canonical Higgs EFT to Standard-Model gauge masses, Yukawa couplings, collider observables, and longitudinal-VV unitarity preservation. The master certificate exposes one named, auditable component per module, each carrying its own proof tag (THEOREM, CONDITIONAL_THEOREM, OPEN_NORMALIZATION, etc.). HiggsEFTLowEnergyLimitCert is defined as the structural composition of these certificates; no new theorems are proved here, only an exposed surface for the chain.
proof idea
The proof is a one-line term-mode wrapper that applies the constructor of the HiggsEFTLowEnergyLimitCert structure, supplying the pre-existing certificates from the imported bridge modules (HiggsEFTBridgeCert, ElectroweakMassBridgeCert, HiggsYukawaBridgeCert, HiggsObservableSkeletonCert, LongitudinalVectorScatteringCert).
why it matters
This declaration completes the top-level master certificate for the Recognition Science to Standard Model EFT bridge that Anil requested. It surfaces the open subproblems listed in the module audit table (NormalizationHypothesis, OPEN_RUNG_MAP, LOOP_LEVEL_OPEN) and implements the framework goal of exposing auditable surfaces for the phi-forced constants, eight-tick octave, and mass ladder. No downstream theorems yet depend on it.
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