Chemistry Catalyst Selectivity From Jcost Catalyst Selectivity Cert

The selectivity certificate

In heterogeneous catalysis, a catalyst can steer a reaction toward different products. Chemists often sort the outcomes into broad classes: a catalyst that makes almost only the desired product, one that favors the primary product but with some side products, one that branches into comparable amounts of several products, a mixed case, and one that shows little preference. These five classes are a standard way to talk about selectivity.

The Recognition Science framework models this classification with a formal certificate. Its machine-checked library of formal theorems defines an inductive type with exactly those five regimes: perfect, primary-dominant, branching, mixed, and non-selective. A theorem in the library proves that the type has exactly five elements. The certificate itself is a structure that carries this count as its only field. In plain terms, it establishes that the framework's language can express the five-regime classification and that the count is machine-checked.

What the certificate does not do is just as important. It does not say which regime a given catalyst falls into, nor does it derive any property of a real chemical system. It only asserts that the five-regime classification is internally consistent. The certificate is a definitional scaffold, not a predictive model.

inductive SelectivityRegime where
  | perfect
  | primaryDominant
  | branching
  | mixed
  | nonSelective
  deriving DecidableEq, Repr, BEq, Fintype

theorem selectivityRegime_count :
    Fintype.card SelectivityRegime = 5 := by decide

structure CatalystSelectivityCert where
  five_regimes : Fintype.card SelectivityRegime = 5

What this page does not claim

This answer does not claim that the certificate predicts which regime a real catalyst occupies. This answer does not claim that the five regimes are the only possible classification of catalyst selectivity. This answer does not claim that the certificate has any experimental validation.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Chemistry/CatalystSelectivityFromJCost.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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