Chemistry Reaction Mechanisms From Config Dim Reaction Mechanisms Cert

Five canonical mechanisms

Organic chemistry classically recognizes a small set of core reaction mechanisms that explain how bonds break and form. The five canonical ones are SN1 (unimolecular substitution, where a leaving group departs before the nucleophile attacks), SN2 (bimolecular substitution, a single concerted step), E1 (unimolecular elimination), E2 (bimolecular elimination), and pericyclic reactions (concerted processes controlled by orbital symmetry). These five appear in every standard textbook as the foundational vocabulary for thinking about reactivity.

The Recognition Science framework's machine-checked library of formal theorems contains a certificate named ReactionMechanismsCert. The certificate establishes one precise fact: it counts the five mechanisms listed above and proves, by direct computation, that the count is exactly five. The proof is a ledger, a discrete record of formal steps, that the machine checks end to end with no unproved assumptions. This is a theorem about a definition: the framework defines a type called ReactionMechanism with exactly those five constructors, and the certificate verifies the cardinality of that type.

What the certificate does not claim is broader. It does not prove that these five mechanisms are the only possible ones in chemistry, nor that real reactions always fit neatly into one of these categories. It does not assert that the list is complete for all of organic chemistry, nor that the mechanisms themselves are physically correct descriptions of every reaction. The certificate is a statement about a formal object the framework chose to define, not a discovery about the empirical world. The choice of these five mechanisms is a definitional one, and the theorem merely records the count of that definition.

The practical value is modest but real: anyone working with the framework's chemistry module can rely on the fact that the type has exactly five members, so code and proofs that pattern-match on all five constructors are exhaustive. The certificate is a small piece of plumbing that makes larger formal developments safer. It is not a theory of organic reactivity, and it makes no prediction about any specific chemical reaction.

theorem reactionMechanism_count :
    Fintype.card ReactionMechanism = 5 := by decide

inductive ReactionMechanism where
  | sn1
  | sn2
  | e1
  | e2
  | pericyclic
  deriving DecidableEq, Repr, BEq, Fintype

def reactionMechanismsCert : ReactionMechanismsCert where
  five_mechanisms := reactionMechanism_count

What this page does not claim

The certificate does not prove these five mechanisms are the only ones possible in chemistry. It does not assert the mechanisms are physically correct descriptions of every reaction. It makes no prediction about any specific chemical reaction.

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/ReactionMechanismsFromConfigDim.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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