RadioactiveDecayCert
plain-language theorem explainer
RadioactiveDecayCert is the structure that certifies the existence of precisely five radioactive decay modes by setting the cardinality of their type to five. Nuclear physicists using the Recognition Science model cite this structure to lock the decay configuration dimension at five. The definition is a direct record construction that invokes the automatically generated Fintype instance for the five-constructor inductive type.
Claim. The structure asserts that the finite type of radioactive decay modes has cardinality five, where the modes are alpha decay, beta-minus decay, beta-plus decay, gamma emission, and spontaneous fission.
background
The module fixes the configuration dimension at five to match the canonical nuclear decay channels. The inductive type enumerates alpha, beta-minus, beta-plus, gamma, and spontaneous fission, and derives the Fintype, DecidableEq, and Repr instances required for cardinality computations. This supplies the discrete label space used for all decay-mode classification in the Recognition Science treatment of nuclear physics.
proof idea
The declaration is a bare structure definition whose single field records the equality between five and the cardinality of the enumerated decay-mode type. The Fintype instance is obtained automatically from the inductive definition with five constructors.
why it matters
It provides the type inhabited by the concrete certificate that closes the five-mode claim in the same module. Within the framework this fixes the decay-space dimension at five, a direct consequence of the forcing-chain steps that determine discrete counts from J-uniqueness and the phi fixed point. The definition contains no open scaffolding.
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