Materials Additive Manufacturing Defects From Config Dim Additive Defect

Five defect classes

Additive manufacturing, commonly called 3D printing, builds parts layer by layer from metal or polymer feedstock. The process is powerful but prone to defects that weaken or ruin the finished object. Engineers have long sorted these failures into five canonical classes: porosity (trapped gas pockets inside the material), lack-of-fusion (layers that fail to bond together), keyhole voids (deep vapor cavities left by an unstable melt pool), residual stress (locked-in internal forces that warp or crack a part), and surface roughness (uneven exterior texture). These five cover the main ways a printed part can fail: volumetric voids, interlayer separation, vapor-cavity defects, mechanical stress, and boundary imperfections, in both metal and polymer printing.

The Recognition Science framework has a machine-checked library of formal theorems, a collection of mathematical statements verified by computer so that no step of reasoning is missing. Within that library, a declaration named AdditiveDefect defines exactly these five classes as an inductive type, a formal list of five distinct cases. A companion theorem proves that the count is exactly five: Fintype.card AdditiveDefect = 5, verified by direct computation. A certificate structure bundles this count as a formal guarantee. The library reports zero unproven assumptions and zero axioms for this file, meaning the five-defect count rests on the same kernel-checked foundation as the rest of the framework.

What the declaration does not claim is just as important as what it proves. The five classes are a classification scheme, not a physical law. The declaration does not assert that every possible additive-manufacturing defect falls into one of these five categories, nor does it model the mechanisms by which these defects form. It does not predict when a given print will fail, nor does it quantify how much residual stress a part can tolerate. The certificate proves the count of the defined list is five; it does not prove that the list itself is the only possible taxonomy. Real parts can fail in ways that blur these categories, and the framework does not claim otherwise.

theorem additiveDefect_count : Fintype.card AdditiveDefect = 5 := by decide

inductive AdditiveDefect where
  | porosity
  | lackOfFusion
  | keyholeVoid
  | residualStress
  | surfaceRoughness
  deriving DecidableEq, Repr, BEq, Fintype

def additiveManufacturingDefectsCert : AdditiveManufacturingDefectsCert where
  five_defects := additiveDefect_count

What this page does not claim

The declaration does not claim that every possible additive-manufacturing defect falls into one of these five categories. The declaration does not model the physical mechanisms by which these defects form. The certificate proves the count of the defined list is five, not that the list itself is the only possible taxonomy.

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/AdditiveManufacturingDefectsFromConfigDim.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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