WeakForceCert
plain-language theorem explainer
A certificate structure bundles three facts required for deriving the weak nuclear force in Recognition Science: exactly five decay channels, the relation phi to the tenth power equals fifty-five phi plus thirty-four, and the bound phi to the tenth exceeds one hundred. Researchers computing the Fermi constant from the phi-ladder would cite these bundled facts. The declaration aggregates the statements as a plain structure with no embedded proof.
Claim. A certificate that the weak nuclear force has five decay types, that $phi^{10} = 55 phi + 34$, and that $phi^{10} > 100$.
background
The module derives the weak force from Recognition Science by relating the Fermi constant to the inverse tenth power of phi. WeakDecayType is the inductive enumeration of beta-minus decay, beta-plus decay, electron capture, muon decay, and tau decay. The structure collects the fact that this type has cardinality five. The phi identity phi to the tenth equals fifty-five phi plus thirty-four follows from Fibonacci numbers. The inequality phi to the tenth greater than one hundred provides the necessary scale. This local setting assumes the RS-native units where c equals one.
proof idea
The declaration is a structure with three fields, each a direct equality or inequality statement. It wraps the cardinality computation for the decay type inductive, the Fibonacci-derived equality for phi to the tenth, and the numerical bound check. No lemmas or tactics appear inside the structure itself.
why it matters
The certificate is instantiated in the downstream definition weakForceCert to supply the inputs for the weak force formula. It connects the five decay types to the RS forcing chain step for D equals three and the phi self-similar fixed point. The module confirms a complete path with no axioms or sorrys for this sector of the Standard Model derivation.
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