Q3_faces_eq
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not compute any higher-order correction δ_n for n > 1.
- Does not establish convergence of the full α series.
- Does not relate the face count to the tick time quantum or RS-native units.
- Does not resolve the residual discrepancy with the CODATA value.
Lean usage
def cert : AlphaFrameworkCert := alphaFrameworkformal statement (Lean)
68theorem Q3_faces_eq : Q3_faces = 6 := rfl
proof body
Term-mode proof.
69
70/-- Active edges per tick. -/