Q3_simplex_vertices_eq
plain-language theorem explainer
The equality fixes the critical simplex vertex count for the three-dimensional hypercube at exactly four. Researchers computing the η₁ correction in Recognition Science mass formulas cite this constant when fixing D=3. The proof is a one-line unfolding of the definition Q3_simplex_vertices := Q3_degree + 1 followed by an arithmetic check.
Claim. The critical simplex vertex count for the three-dimensional hypercube graph satisfies $Q_3^simplex = 4$.
background
The module formalizes combinatorial and spectral properties of the three-dimensional hypercube graph Q₃, whose Laplacian eigenvalues are {0, 2, 2, 2, 4, 4, 4, 6} with multiplicities {1, 3, 3, 1}. This graph underpins critical exponent corrections in Recognition Science. The definition Q3_simplex_vertices is given by Q3_degree + 1 and represents the structural number D + 1 that appears in the η₁ correction for D = 3.
proof idea
The proof is a one-line term that unfolds the definitions of Q3_simplex_vertices and Q3_degree, reducing the goal to the arithmetic equality 3 + 1 = 4, which the omega tactic discharges.
why it matters
This supplies the vertex count used inside the certification q3Cert. It instantiates the spatial dimension D = 3 forced by the eight-tick octave (T8) in the UnifiedForcingChain and provides the input required for the η₁ term in the Recognition Science mass formula on the phi-ladder.
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