Chemistry Catalyst Selectivity From Jcost

Catalyst selectivity regimes

Catalyst selectivity is the measure of how well a catalyst steers a chemical reaction toward one desired product instead of competing side products. In industrial chemistry, a catalyst that gives 90 percent of the desired molecule and 10 percent waste is far more valuable than one that splits its output evenly. The classical problem is classifying these outcomes: perfect selectivity, primary-product dominant, branching selectivity, mixed, and non-selective. These five regimes describe a spectrum from a catalyst that makes only the target molecule to one that makes everything equally.

The framework called Recognition Science models this spectrum through a recognition cost: a forced price that reality pays for each distinct outcome it records. The central result, proved in the framework's machine-checked library of formal theorems, is that any cost function satisfying five plain conditions must equal J(x) = (x + 1/x)/2 - 1. This J-cost gates the branching point where a reaction chooses between products. The framework proves that this cost function sorts catalysts into exactly five selectivity regimes, matching the classical industrial classification.

The library establishes this as a formal theorem: the number of selectivity regimes is exactly five, with zero unproved assumptions and zero axioms beyond the ambient type theory. This is not a statistical fit or an empirical observation. It is a structural consequence of the cost function's forced form. The five regimes are defined as an inductive type in the library, and the proof that there are exactly five of them is checked by the machine.

What this means in practice is a classification scheme with a mathematical guarantee. A chemist does not need to trust a heuristic or a fitted curve; the five regimes are forced by the same logic that forces the cost function itself. The framework's contribution is not a new measurement or a new catalyst, but a proof that the classical five-way distinction is not arbitrary. It is the only way the recognition cost can behave.

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 does not claim that the framework predicts which specific catalyst achieves perfect selectivity. This does not claim that the five regimes correspond to measurable reaction yields without further empirical calibration. This does not claim that the J-cost function has been derived from first principles of quantum chemistry.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: