DecayMode
plain-language theorem explainer
The inductive enumeration of radioactive decay modes lists five canonical channels corresponding to config dimension five in the Recognition Science framework. Nuclear physicists applying the phi-ladder to nuclear stability would reference this list when certifying complete decay channels. The declaration is a direct inductive construction that derives finite type and equality instances automatically.
Claim. The radioactive decay modes are defined inductively by the five cases: alpha decay, beta-minus decay, beta-plus decay, gamma decay, and spontaneous fission.
background
The module sets five canonical radioactive-decay modes equal to configDim D = 5. These comprise alpha decay, beta-minus decay, beta-plus decay, gamma decay, and spontaneous fission. Upstream constants supply the fine-structure constant as the reciprocal of its inverse and the Euler-Mascheroni constant as the limit of harmonic numbers minus natural log. The local setting derives nuclear physics depth from the single functional equation of Recognition Science.
proof idea
The declaration is the inductive definition itself. The deriving clause automatically generates the DecidableEq, Repr, BEq, and Fintype instances with no separate proof steps required.
why it matters
It supplies the type for the theorem decayMode_count that proves cardinality five and for the RadioactiveDecayCert structure. This completes the nuclear-physics assignment of five modes to configDim, consistent with the forcing chain T0-T8 that yields spatial dimension three and the fine-structure constant band.
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