condensedMatterPhasesCert
plain-language theorem explainer
The declaration supplies a concrete certificate that exactly five exotic condensed-matter phases arise when the configuration dimension is fixed at five. A condensed-matter theorist would cite it to anchor the enumeration of topological and strongly-correlated states in the Recognition framework. The proof is a one-line wrapper that directly inserts the already-decided cardinality theorem into the structure constructor.
Claim. Let the certificate structure require that the finite cardinality of the type of condensed-matter phases equals five. The definition populates this field with the theorem establishing the equality.
background
The module Condensed Matter Exotic Phases from configDim introduces five canonical exotic condensed-matter phases when the configuration dimension D equals 5: quantum spin liquid, topological insulator, Weyl semimetal, Mott insulator, and fractional quantum Hall. Each phase carries a distinct topological or strong-correlation signature. The upstream theorem condensedMatterPhase_count proves by decision that the cardinality of the CondensedMatterPhase type is exactly 5, and the structure CondensedMatterPhasesCert packages this fact as a certificate.
proof idea
The definition is a one-line wrapper that applies the theorem condensedMatterPhase_count to populate the five_phases field of the CondensedMatterPhasesCert structure.
why it matters
This definition anchors the enumeration of five exotic phases in the Recognition Science treatment of condensed matter when configDim = 5. It fills the physics-depth claim in the module that links configuration dimension to phase count, consistent with the framework's derivation of spatial dimensions and self-similar fixed points. No open questions are touched; the construction is closed with zero sorry.
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