EnzymeClass
plain-language theorem explainer
The inductive definition enumerates the five canonical enzyme mechanism classes that Recognition Science assigns to configDim D = 5 in J-cost catalysis models. Chemists deriving turnover thresholds on the phi-ladder cite it to anchor cardinality and ratio statements. It is realized as a plain inductive type whose Fintype instance is supplied automatically by derivation.
Claim. Let $E$ be the finite set of enzyme classes consisting of oxidoreductase, transferase, hydrolase, lyase, and isomerase, equipped with decidable equality and a Fintype structure.
background
The module models industrial chemistry via five canonical enzyme classes that Recognition Science identifies with configDim D = 5. These are the EC classes 1-5; ligases and translocases are treated as extended. Turnover number k_cat is placed on the phi-ladder with adjacent-class ratio exactly phi, while active-site geometry is gated by the canonical J(phi) band on the bond-angle ratio. The module states zero sorry and zero axiom.
proof idea
The declaration is an inductive definition with five constructors. Derivation clauses supply DecidableEq, Repr, BEq, and Fintype instances directly; no separate proof body is written. The downstream cardinality theorem follows immediately from the inductive structure via the decide tactic.
why it matters
This definition supplies the type for the EnzymeCatalysisCert structure, which asserts Fintype.card = 5 together with the phi ratio on kcat and positivity. It fills the configDim D = 5 slot in the Recognition Science chemistry layer, linking the J-cost functional equation to the phi-ladder. The module records zero sorry status.
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