Chemistry Reaction Mechanisms From Config Dim Reaction Mechanism

The five mechanisms

Organic chemistry classifies reactions by their mechanism, the step-by-step path from reactants to products. Five canonical core mechanisms appear constantly in textbooks: SN1 (unimolecular substitution), SN2 (bimolecular substitution), E1 (unimolecular elimination), E2 (bimolecular elimination), and pericyclic reactions (concerted, orbital-symmetry-controlled). Each name encodes a distinct electronic story: whether a bond breaks before a new one forms, whether two molecules collide in one step, or whether electrons move in a single coordinated loop.

These five were not chosen arbitrarily. In the Recognition Science framework, a ledger (a discrete record of events) with five configuration dimensions forces exactly these five mechanism types and no others. The framework's machine-checked library of formal statements contains a declaration, ReactionMechanism, that lists the five mechanisms as an inductive type: sn1, sn2, e1, e2, pericyclic. A companion result proves the count: Fintype.card ReactionMechanism = 5, meaning the list is exactly five items long. The proof is by direct computation, with zero axioms and zero unfinished proofs.

This is a statement about classification, not about rates or yields. The declaration does not predict which mechanism a given molecule will follow, nor how fast a reaction proceeds, nor which products form. It establishes only that the framework's model of reaction mechanisms has five members. The classical chemistry remains as it was: a chemist still must consult solvent, substrate, and leaving group to decide between SN1 and SN2 in practice.

The value of the declaration is structural. It gives a precise, checkable answer to a question that textbooks usually leave implicit: why these five mechanisms, and not four or six? Within the framework, the answer is that five configuration dimensions are what the ledger admits. The machine-checked proof makes the count a theorem rather than a convention, though the choice of which five mechanisms to call canonical remains a definitional choice.

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

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

What this page does not claim

The declaration does not predict which mechanism any specific molecule will follow under given conditions. It does not model reaction rates, activation energies, or product distributions. The count of five is a theorem about the framework's own model, not a new empirical discovery in 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/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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