SelectivityRegime
plain-language theorem explainer
SelectivityRegime enumerates five canonical regimes of heterogeneous catalyst selectivity aligned with J-cost thresholds in Recognition Science. Industrial chemists modeling reaction outcomes under phi-ladder constraints cite this enumeration when classifying perfect, dominant, branching, mixed, or non-selective behavior. The declaration is a direct inductive type deriving Fintype to support immediate cardinality verification in downstream certificates.
Claim. The selectivity regimes form an inductive type with five constructors: perfect, primary-product dominant, branching, mixed, and non-selective, equipped with decidable equality and finite type structure.
background
The module on Catalyst Selectivity from J-Cost defines five canonical regimes for heterogeneous catalysts, corresponding to configDim D = 5. These are perfect selectivity, primary-product dominant, branching selectivity, mixed, and non-selective, with the Recognition canonical J(φ) band gating the branching point between them.
proof idea
The declaration is a direct inductive definition with no proof body. It derives instances for DecidableEq, Repr, BEq, and Fintype to enable finite cardinality computations.
why it matters
This enumeration underpins the CatalystSelectivityCert structure asserting Fintype.card SelectivityRegime = 5 and the theorem selectivityRegime_count proved by decide. It realizes the B10 Industrial Chemistry Depth section by discretizing selectivity under J-cost, extending the Recognition framework's configDim concept to chemistry while the J(φ) band controls regime transitions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.