Q3_vertices
plain-language theorem explainer
The three-dimensional binary cube has exactly eight vertices. Derivations of Standard Model gauge content and fermion counts from the Recognition Science forcing chain cite this count as the starting combinatorial datum. The proof is a one-line normalization that specializes the vertex function definition to dimension three.
Claim. The vertex count of the three-dimensional binary cube satisfies $V(3)=8$.
background
The Spectral Emergence module starts from the forced spatial dimension D=3 and introduces the binary cube Q3 whose vertices are counted by the function V. By definition V(D) equals 2^D, so the three-dimensional case is immediate. Upstream results in Constants.AlphaHigherOrder, LambdaRecDerivation and Physics.CubeSpectrum record the same count as 8 and link it to the eight-tick octave and curvature packets distributed over the vertices.
proof idea
This is a one-line wrapper that applies norm_num to the definition V(D) := 2^D, specializing directly at D=3.
why it matters
The result supplies the initial vertex count for the self-consistency loop that derives SU(3) x SU(2) x U(1) gauge dimensions, three generations from face pairs, and 48 chiral states matching |Aut(Q3)|. It feeds GDerivationChain (which balances J_curv against J_bit to obtain lambda_rec and G) and the AlphaHigherOrder and PlanckScaleMatching modules. The declaration realizes the T8 to Q3 step of the forcing chain and the key numerical identity |Aut(Q3)| = 48 that equals the Standard Model chiral fermion count.
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