Chemistry Catalyst Selectivity From Jcost Selectivity Regime

Catalyst selectivity regimes

In industrial chemistry, a catalyst's selectivity is the measure of how strongly it favors one product over competing ones. The Recognition Science framework formalizes this as a classification of five canonical regimes: perfect selectivity, primary-product dominant, branching selectivity, mixed, and non-selective. The classification is a discrete record, a finite list of named states, not a continuous scale. The framework's machine-checked library of formal theorems proves that this list has exactly five members, a count that is verified by direct computation rather than assumed.

The five regimes are defined as an inductive type, a way of building a finite set by listing its possible values. The library also constructs a certificate, a formal object that carries the proof of the five-regime count as its only field. This certificate is the framework's way of making the classification auditable: any consumer of the definition can check that the count is correct without trusting a human author.

In Recognition Science, the five regimes are tied to the recognition cost function J(φ) = (φ + 1/φ)/2 − 1, whose band structure is said to gate the branching point between regimes. This is a definitional choice within the framework, a way of organizing catalyst behavior under a single cost function. The declaration itself does not claim that real catalysts fall into these regimes, nor does it specify which chemical reactions exhibit which regime.

The value of the classification is organizational: it gives chemists a vocabulary for describing selectivity patterns and a formal target for future work. The framework's claim is that the five regimes are exhaustive as a classification scheme, not that they are exhaustive as a description of nature. The bridge from this formal classification to measured catalytic behavior remains open.

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

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

def catalystSelectivityCert : CatalystSelectivityCert where
  five_regimes := selectivityRegime_count

What this page does not claim

No claim that any real catalyst has been measured to fall into one of the five regimes. No claim that the five regimes are the only possible classification of catalyst selectivity. No claim that the J(φ) cost function has been derived from chemical kinetics or thermodynamics.

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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