nuclearStructureCategoryCount
plain-language theorem explainer
The declaration proves that the nuclear structure categories total exactly five. Nuclear physicists modeling binding energies or magic numbers via the phi-ladder would cite this to fix configDim D = 5. The proof is a one-line decision procedure on the finite inductive type.
Claim. The cardinality of the set of nuclear structure categories is five: $|$single-particle, collective, rotation, vibration, cluster$| = 5$.
background
The Nuclear Physics Depth from RS module classifies nuclear structure into five categories: single-particle, collective, rotation, vibration, and cluster. This set equals configDim D = 5 and sits inside the broader claim of five canonical nuclear force carriers. The inductive type NuclearStructureCategory enumerates these five cases and derives Fintype, Repr, and DecidableEq to support direct cardinality computation.
proof idea
The proof is a one-line wrapper that applies the decide tactic. NuclearStructureCategory is an inductive type with five constructors that derives Fintype, so decide computes Fintype.card directly as 5 without further lemmas.
why it matters
This supplies the five_categories field inside nuclearPhysicsDepthCert, closing the nuclear structure count for the B7 Nuclear section. It aligns with the module's five force carriers and supports configDim D = 5 in the Recognition framework. No open questions remain in the supplied results.
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