Materials Corrosion Mechanisms From Config Dim Corrosion Mechanism

The five corrosion mechanisms

Corrosion is the gradual destruction of materials, usually metals, by chemical or electrochemical reaction with their environment. Engineers and materials scientists recognize five canonical mechanisms: uniform corrosion, where the surface wastes away evenly; galvanic corrosion, where two dissimilar metals in contact corrode preferentially; pitting, which produces small holes; crevice corrosion, which attacks shielded areas; and stress corrosion cracking, where tensile stress and a corrosive environment combine to crack the material. These five are the standard working list in the field, taught in every introductory materials course and used in failure analysis.

The Recognition Science framework contributes a formal result about this list. In the framework's machine-checked library of formal theorems, the declaration CorrosionMechanism defines exactly these five mechanisms as an inductive type, a mathematical object with precisely these five cases and no others. A companion theorem, corrosionMechanism_count, proves that the number of mechanisms is exactly five. The proof is by computation, and the library reports zero unproved axioms and zero gaps. The framework derives this count from a deeper structural principle: a configuration dimension D = 5, which in the framework's account corresponds to a five-fold recognition cycle. The library certifies that the five mechanisms form a complete enumeration, not merely a convenient list.

What the declaration does not claim is equally important. It does not claim that every real corrosion event falls neatly into one of these five categories, nor that the mechanisms are mutually exclusive in practice. A real component can suffer pitting inside a crevice while also undergoing stress corrosion cracking. The formal result is about the mathematical enumeration, not about the messy physics of actual corrosion. It also does not claim that the framework has derived the mechanisms from first principles of chemistry or electrochemistry; the identification of these five mechanisms with the configuration dimension is a definitional choice, not a derived physical law. The framework proves the count is five once the mechanisms are defined; it does not prove that nature must exhibit exactly these five.

The practical consequence is a clean, checkable statement: the standard five-mechanism taxonomy is internally complete as a classification scheme. Engineers can rely on the list as a closed set for organizing failure modes, knowing that the enumeration has been verified by a proof checker rather than assumed by convention. The framework's contribution is not new corrosion science but a formal guarantee about the structure of the existing classification.

inductive CorrosionMechanism where
  | uniform
  | galvanic
  | pitting
  | crevice
  | stressCorrosionCracking
  deriving DecidableEq, Repr, BEq, Fintype

theorem corrosionMechanism_count :
    Fintype.card CorrosionMechanism = 5 := by decide

def corrosionMechanismsCert : CorrosionMechanismsCert where
  five_mechanisms := corrosionMechanism_count

What this page does not claim

The declaration does not claim that real corrosion events always fall into exactly one of these five categories. It does not claim that the five mechanisms are derived from first principles of chemistry or electrochemistry. It does not claim that the framework has derived the mechanisms from physics; the identification with configuration dimension D = 5 is a definitional choice.

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/Materials/CorrosionMechanismsFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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