Q3_faces
plain-language theorem explainer
The three-dimensional binary cube has exactly six faces. Researchers deriving the Standard Model gauge group and three fermion generations from Recognition Science cite this combinatorial count. The proof evaluates the face-counting function at dimension three through a native decision procedure.
Claim. The binary cube in three dimensions has six faces.
background
The Spectral Emergence module starts from the forced datum D = 3 and constructs the binary cube Q₃ = {0,1}³ with eight vertices. This geometry simultaneously encodes the gauge group dimensions 3 + 2 + 1 and three generations via face-pair counts, together with the total of 48 chiral fermionic states matching the cube automorphism order.
proof idea
The proof is a one-line wrapper that applies the native_decide tactic to evaluate the face-counting expression at dimension three and confirm the value six.
why it matters
This supplies the cube_faces component required by the AlphaFrameworkCert structure that collects all elements for δ₂ computation. It advances the module program that extracts SU(3) × SU(2) × U(1) and three generations from Q₃ symmetry, resting on T8 forcing of D = 3 and the eight-tick octave.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.