cubeEdges
plain-language theorem explainer
Unit cube edge count is fixed at twelve. Triangulation certifiers and particle generation models cite the value to close combinatorial identities inside FreudenthalCert and to equate total fermions with cube geometry. The declaration is a direct constant assignment.
Claim. The unit cube has $12$ edges.
background
The Freudenthal triangulation certificate records the combinatorial skeleton of the unit cube in three dimensions. Standard counts are eight vertices, twelve edges, and six faces. These enter the structure that verifies six tetrahedra meet along the body diagonal with total angle summing to a full turn, as stated in the module doc-comment on the Beltracchi response.
proof idea
Direct constant definition. The integer twelve is assigned outright to match the geometric edge count of the unit cube.
why it matters
It populates the cube_data field inside FreudenthalCert and supplies the cube_edge_match inside GenerationCert. The count thereby supports the combinatorial closure of the zero-deficit certificate and the identification of three fermion generations with cube geometry. This anchors the three-dimensional spatial structure required by the Recognition framework.
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