AdditiveManufacturingDefectsCert
plain-language theorem explainer
The structure certifies that additive manufacturing admits exactly five defect classes when the configuration dimension equals 5. Materials researchers modeling 3D printing defects within Recognition Science cite it to anchor defect phenomenology to the same dimensional counting used for spatial geometry. The definition is realized directly by the inductive enumeration of the five classes together with the finite cardinality lemma.
Claim. The structure asserts that the finite set of additive manufacturing defect classes has cardinality exactly 5, where the classes are porosity, lack-of-fusion, keyhole voids, residual stress, and surface roughness.
background
Recognition Science assigns a configuration dimension of 5 to additive manufacturing, producing five canonical defect classes that cover volumetric, interlayer, vapor-cavity, mechanical, and boundary phenomena in metal and polymer printing. The inductive type enumerates these classes explicitly and derives decidable equality plus finite type structure from the five constructors. This local setting sits inside the broader framework in which spatial dimension is fixed at 3 while material-specific configuration dimensions vary.
proof idea
The declaration is a structure definition whose single field records the cardinality equality. It is witnessed by the downstream construction that applies the finite cardinality result to the inductive defect type.
why it matters
The structure supplies the certification required by the additive manufacturing defects theorem in the same module. It closes the link between configuration dimension 5 and the enumerated defect classes, feeding the Recognition Science claim that defect counts follow from the same forcing chain that yields spatial dimension 3. No open questions remain inside this module.
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