HasCubeFaceCount
plain-language theorem explainer
HasCubeFaceCount asserts that a finite type has cardinality exactly 6. Cross-domain researchers in Recognition Science cite the predicate when unifying the six quarks, six leptons, six cortical layers, six Braak stages, and six robotic degrees of freedom under the cube-face enumeration for D = 3. The definition is a direct one-line abbreviation of the Fintype.card equality.
Claim. Let $T$ be a finite type. Then $T$ has cube-face count if and only if its cardinality equals 6, i.e., $|T| = 6$.
background
The Cube-Face Universality module states that 6 equals the face count of the 3-cube via V - E + F = 8 - 12 + 6 = 2 and appears across RS domains as the face-level enumeration for spatial dimension D = 3. HasCubeFaceCount uses Mathlib's Fintype to express the finiteness and cardinality condition. The module imports Breath1024.T (fundamental periods) and Gap45.SyncMinimization.T (triangular numbers T(n) = n(n+1)/2) to support related synchronization arguments.
proof idea
This declaration is a one-line definition that directly equates the predicate to the proposition Fintype.card T = 6.
why it matters
HasCubeFaceCount supplies the common predicate for the eight downstream has_6 theorems and the CubeFaceUniversalityCert structure that aggregates the six-element instances. It realizes the C15 structural claim that 6 = 2·3 with D_cube = 2 and D_spatial = 3 from forcing-chain step T8. The predicate therefore links the cross-domain enumerations to the Recognition Science derivation of three spatial dimensions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.