polymerMorphologyCert
plain-language theorem explainer
The declaration supplies a concrete certificate asserting that the finite type of block-copolymer morphologies has cardinality exactly five when the configuration dimension is five. Soft-matter physicists and materials modelers cite it to fix the canonical set of spherical, cylindrical, gyroid, lamellar and inverse phases on the phi-ladder. The definition is a one-line wrapper that inserts the decidable cardinality theorem directly into the structure field.
Claim. Let $P$ be the finite type of canonical block-copolymer morphologies. The certificate is the structure satisfying $|P|=5$.
background
The module treats five canonical block-copolymer morphologies for configuration dimension five: spherical, cylindrical, gyroid, lamellar and inverse (double gyroid or inverse cylindrical). Each phase occupies a distinct minority-block volume-fraction band on the phi-ladder. The upstream structure PolymerMorphologyCert packages the single field five_morphologies : Fintype.card PolymerMorphology = 5, while the theorem polymerMorphology_count establishes the equality by direct decision.
proof idea
The definition is a one-line wrapper that assigns the result of the cardinality theorem polymerMorphology_count to the five_morphologies field of the PolymerMorphologyCert structure.
why it matters
This definition closes the enumeration step in the chemistry module, supplying a certified count of five morphologies that aligns with configDim = 5. It supports downstream materials modeling inside the Recognition Science framework where the phi-ladder and configuration dimension appear. No open questions or scaffolding are indicated in the supplied material.
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