Materials Composite Failure Modes From Config Dim Composite Failure Modes Cert

Five failure modes

Fiber-reinforced composites, the materials used in aircraft wings and wind-turbine blades, fail through five recognized damage channels: fiber fracture, matrix cracking, delamination, fiber pull-out, and interfacial debonding. These are the standard categories that materials scientists use when inspecting a broken composite part and deciding which loading condition caused the damage.

The Recognition Science framework's machine-checked library of formal theorems contains a certificate, named CompositeFailureModesCert, that records exactly this fact: the set of these five failure modes has exactly five members. The certificate is a small formal object, a structure holding one proof that the count is five. It is verified by direct computation, with no unproven assumptions and no axioms beyond the ambient type theory's standard three. The framework derives the number five from its configDim parameter, which in this materials context takes the value D = 5.

What the certificate does not do is more interesting than what it does. It does not prove that these are the only possible failure modes, nor that real composites always fail through one of these five channels. It does not predict which mode will occur under a given load, and it does not assign probabilities or strengths to any mode. The certificate merely states a counting fact about a named list: the list has five entries. A materials engineer reading the certificate learns nothing about crack growth rates or fracture toughness; those questions remain entirely outside its scope.

The value of such a certificate is precision, not prediction. When the framework's library refers to composite failure modes in later theorems, it can point to this certificate and know that the vocabulary is fixed: five modes, with these exact names, in this exact set. The certificate is a definitional anchor, not an empirical claim about materials behavior.

inductive CompositeFailureMode where
  | fiberFracture
  | matrixCracking
  | delamination
  | fiberPullout
  | interfacialDebonding
  deriving DecidableEq, Repr, BEq, Fintype

theorem compositeFailureMode_count : Fintype.card CompositeFailureMode = 5 := by decide

def compositeFailureModesCert : CompositeFailureModesCert where
  five_modes := compositeFailureMode_count

What this page does not claim

The certificate does not prove that these five modes are exhaustive for all real composite materials. The certificate does not predict which failure mode occurs under a specific mechanical load. The certificate assigns no numerical properties, such as fracture energy or crack growth rate, to any failure mode.

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/CompositeFailureModesFromConfigDim.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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