Q3_faces_eq
plain-language theorem explainer
The declaration proves that the three-dimensional cube Q₃ has exactly six faces. Workers on the Recognition Science derivation of α⁻¹ cite it when certifying the geometric inputs for the higher-order voxel-seam series. The proof is a one-line reflexivity that evaluates the explicit definition 2 * 3 directly to 6.
Claim. The number of faces of the three-dimensional cube $Q_3$ equals 6.
background
In the AlphaHigherOrder module the three-dimensional cube Q₃ supplies the combinatorial skeleton for voxel-seam corrections to the fine-structure constant. The sibling definition Q3_faces counts these faces as twice the number of spatial dimensions. Upstream results in PlanckScaleMatching and LambdaRecDerivation establish the same count via direct enumeration or Euler characteristic of the bounding sphere, while SpectralEmergence records it as F₂ 3 = 6.
proof idea
The proof is a one-line term that applies reflexivity to the definition Q3_faces := 2 * 3, which computes immediately to 6.
why it matters
This result populates the cube_faces field inside the alphaFramework certificate that assembles all combinatorial inputs for the α⁻¹ series α_seed − f_gap + Σ δ_n. It closes the geometric seed portion of the D = 3 spatial structure forced by the unified chain and leaves the explicit computation of δ₂ and higher terms as the remaining open deliverable.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.