q3Chromatic_bipartite
plain-language theorem explainer
The 3-cube graph Q₃ has chromatic number exactly 2. Recognition Science researchers cite this to confirm that the canonical recognition lattice is bipartite and satisfies the five-theorem count for configDim D = 5. The proof is a one-line reflexivity that matches the constant definition of q3ChromaticNumber.
Claim. The chromatic number of the three-dimensional cube graph equals 2.
background
The module treats Q₃ as the canonical recognition lattice with 8 vertices, 12 edges, and 6 faces. Its Euler characteristic equals 2, matching χ(S²). The definition q3ChromaticNumber : ℕ := 2 is imported from both the local module and GraphTheoryFromRS, where it is introduced as the chromatic number of Q₃.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition q3ChromaticNumber := 2.
why it matters
This supplies the chromatic_q3 field inside graphTheoryDepthCert, which packages the five graph theorems (handshaking, Euler, Kuratowski, four-color, Ramsey) required for configDim D = 5. It anchors the bipartiteness of the recognition lattice in the RS framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.