Q3_edges_eq
plain-language theorem explainer
The equality establishes that the three-dimensional cube has exactly twelve edges in the Recognition Science voxel model. Researchers assembling higher-order corrections to the fine-structure constant cite this result when populating the alphaFramework certificate. The proof proceeds by direct reflexivity on the definition that sets the edge count to three times four.
Claim. The edge count of the three-dimensional cube satisfies $|E(Q_3)| = 12$.
background
The module develops higher-order voxel-seam corrections to α^{-1} using the combinatorial structure of the three-cube Q_3. Q3_edges is defined as three times two to the power two, which evaluates to twelve. This count enters the series α^{-1} = α_seed - f_gap + sum δ_n where each δ_n is a sum over n-fold face-wallpaper pairs on Q_3. Upstream results include the theorem in SpectralEmergence that proves the edge function E applied to three equals twelve by normalization.
proof idea
The proof is a one-line reflexivity that equates the definition Q3_edges := 3 * 2^2 to the constant twelve.
why it matters
This supplies the cube_edges component of the alphaFramework certificate that certifies the combinatorial inputs for the δ_n series. It completes the proved cube combinatorics section of the module, which targets the residual discrepancy between the RS prediction and the CODATA value of α^{-1}. The open question of evaluating the second-order term δ_2 remains.
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