Chemistry Stereochemistry Classes From Config Dim Stereochemistry Cert

The certification record

Stereochemistry is the branch of chemistry that studies how atoms are arranged in space within molecules. The classical classification recognizes five canonical kinds of stereoisomers: enantiomers, diastereomers, cis-trans (geometric) isomers, conformational isomers, and atropisomers. Enantiomers are mirror-image molecules that cannot be superimposed; diastereomers are stereoisomers that are not mirror images. Cis-trans isomers differ by the relative positions of substituents across a double bond or ring; conformational isomers differ by rotation about single bonds; atropisomers arise from hindered rotation about a single bond. Together these five classes cover the standard way chemists sort stereoisomers.

The Recognition Science framework encodes this classification in a machine-checked library of formal theorems. Its declaration StereochemistryCert is a certificate: a data structure that records a proof. The certificate states that the number of stereoisomer classes is exactly five, and the proof is carried by the theorem stereoClass_count, which the machine checks by direct computation. The certificate itself is a structure with one field, five_classes, holding that proof. The framework then provides a definition, stereochemistryCert, which constructs the certificate from the theorem. The entire file contains zero unproved assumptions and zero axioms: the count of five classes is fully verified by the machine.

What the certificate does not claim is important. It does not assert that these five classes are chemically exhaustive in every possible sense, nor does it derive the classification from deeper physical principles. It does not claim that the five classes are mutually exclusive for every molecule, nor that every molecule falls into exactly one class. The certificate only records the count of the five named classes as defined in the framework's inductive type StereoClass. It is a bookkeeping statement about the classification, not a chemical theory of why the classification is correct.

The practical value of the certificate is that it pins down a vocabulary. When the framework's chemistry pages refer to enantiomers or atropisomers, the certificate fixes the reference list at five classes and proves the count. This gives later formal work a stable foundation: any theorem about stereoisomer classes can rely on the fact that there are exactly five named classes. The certificate does not, however, open the door to claims about specific molecules, reactions, or physical properties. Those remain separate questions that the framework has not yet addressed.

theorem stereoClass_count : Fintype.card StereoClass = 5 := by decide

structure StereochemistryCert where
  five_classes : Fintype.card StereoClass = 5

def stereochemistryCert : StereochemistryCert where
  five_classes := stereoClass_count

What this page does not claim

The certificate does not claim the five classes are chemically exhaustive in every possible sense. The certificate does not claim the five classes are mutually exclusive for every molecule. The certificate does not claim any physical or chemical properties of specific stereoisomers.

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/StereochemistryClassesFromConfigDim.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

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