Q3_edges
plain-language theorem explainer
Q3_edges supplies the edge count of the three-cube as twelve. Researchers on the Recognition Science derivation of the fine-structure constant cite this count when assembling combinatorial inputs for the series corrections to alpha inverse. The declaration is introduced as a direct arithmetic definition matching the general edge formula for the n-cube.
Claim. The number of edges of the three-cube satisfies $E(3) = 3 × 2^{2}$.
background
The module AlphaHigherOrder develops higher-order voxel-seam corrections to alpha inverse using the combinatorics of the three-cube Q3. The series is alpha inverse equals alpha seed minus f gap plus sum delta n, where each delta n is a finite sum over n-fold face-wallpaper configurations on Q3 weighted by the Z2^5 measure. Upstream results from SpectralEmergence prove E(3) equals twelve via norm_num on the general edge function, while CubeSpectrum defines the same value directly.
proof idea
This is a one-line definition that directly encodes the edge count of the three-cube via the arithmetic expression three multiplied by two to the power two.
why it matters
Q3_edges enters the AlphaFrameworkCert structure that certifies all elements are in place for the delta two computation. It appears in the numerological summary theorem, which states that the key numbers of the Standard Model are cube numbers including twelve edges as gauge generators. The declaration supports the spectral emergence master theorem that derives the entire Standard Model structure from D equals three spatial dimensions. It touches the open question of computing delta two explicitly.
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