Materials Additive Manufacturing Defects From Config Dim Additive Manufacturing

A certified catalogue of defects

Additive manufacturing, commonly called 3D printing, builds parts layer by layer. Defects can appear at any stage, and engineers spend much of their time classifying them. A machine-checked library of formal theorems now certifies that five canonical classes cover the standard catalogue: porosity, lack-of-fusion, keyhole voids, residual stress, and surface roughness. The certificate is a formal structure named AdditiveManufacturingDefectsCert, and it contains exactly one fact: the count of these defect classes is five.

The five classes span the main failure modes in metal and polymer printing. Porosity describes trapped gas pockets inside the material. Lack-of-fusion occurs when layers do not bond properly. Keyhole voids are vapor cavities left behind by an unstable melt pool. Residual stress is the locked-in mechanical strain after cooling. Surface roughness captures the boundary irregularities that affect fit and fatigue life. Together they cover volumetric, interlayer, vapor-cavity, mechanical, and boundary defects.

The certificate itself is deliberately narrow. It proves a count, not a taxonomy. The five classes are chosen by definition, not derived from first principles. The declaration says nothing about how often each defect occurs, how severe any of them are, or how to detect them. It does not claim that these are the only possible defects, only that this is the canonical set of five that the framework's configuration dimension yields. The count is verified by direct computation, with no unproved assumptions in the library.

What the certificate buys is a fixed vocabulary. When a defect is named in this framework, it is one of these five. That lets later results refer to defect classes without redefining them each time. The practical value is organizational: a formal system that reasons about manufacturing quality can now state theorems about porosity or residual stress with a stable, machine-checked reference point. The certificate is the anchor, not the whole theory.

structure AdditiveManufacturingDefectsCert where
  five_defects : Fintype.card AdditiveDefect = 5

def additiveManufacturingDefectsCert : AdditiveManufacturingDefectsCert where
  five_defects := additiveDefect_count

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

What this page does not claim

The certificate does not prove that these five classes are the only possible defects in additive manufacturing. It does not assign frequencies, severities, or detection methods to any defect class. The five classes are a definitional choice, not a derived result from physical first principles.

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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: