Chemistry Stereochemistry Classes From Config Dim Stereo Class Count

The five classes

Stereochemistry is the study of how atoms in a molecule are arranged in space, not just which atoms are bonded to which. The classical families that describe these arrangements are five: enantiomers, diastereomers, cis-trans (geometric) isomers, conformational isomers, and atropisomers. Enantiomers are mirror-image pairs that cannot be superimposed, like left and right hands. Diastereomers are stereoisomers that are not mirror images. Cis-trans isomers differ by the relative position of substituents across a double bond or ring. Conformational isomers differ by rotation about single bonds. Atropisomers arise from restricted rotation about a single bond, creating stable chiral shapes.

The Recognition Science framework models this classical classification with a formal object. Its machine-checked library of formal theorems defines an inductive type called StereoClass whose five constructors are exactly those five families. The declaration stereoClass_count is a theorem stating that the number of elements of this type equals five. The proof is by direct computation, and the library reports zero unproved axioms and zero admitted theorems. In plain language: the framework has encoded the standard five-class scheme as a finite mathematical structure and verified that it has exactly five members.

What the declaration does not do is create new chemistry. It does not prove that every real molecule falls into one of these five classes, nor does it derive the classes from physical first principles. The classification is a definitional choice, a model of how chemists already organize stereochemical relationships. The theorem only certifies the internal count of that model. It says nothing about the relative energy of conformers, the barrier height for atropisomer interconversion, or whether a particular molecule is best described as one class or another. Those questions belong to experimental measurement and quantum chemistry, not to this counting theorem.

What the result changes is the epistemic status of the count. A working chemist already knows there are five classical stereoisomer classes; the framework now supplies a formal certificate that its own encoding of that knowledge is internally consistent. The practical lesson for a reader is that the five-class scheme is not arbitrary: it is a finite, decidable, machine-verified structure. The next step, which remains a target, is to connect this formal count to the configurational dimension D = 5 that the declaration's filename references, and to show how the five classes arise from that dimension rather than being merely enumerated.

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

inductive StereoClass where
  | enantiomers
  | diastereomers
  | cisTransGeometric
  | conformational
  | atropisomers
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

The theorem does not prove that every real molecule falls into exactly one of the five classes. It does not derive the classification from physical or chemical first principles. It says nothing about molecular energies, barrier heights, or experimental assignment.

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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