curvature_numerator_eq
plain-language theorem explainer
The equality establishes that the curvature numerator on the Q3 cube equals 103. Researchers assembling the first-order voxel-seam correction to the inverse fine-structure constant in Recognition Science would cite this result when evaluating delta_1. The proof is a direct reflexivity reduction from the definition of the numerator as the sum of face-wallpaper pairs plus active edges.
Claim. The curvature numerator, defined as the sum of the number of face-wallpaper pairs and active edges on the three-dimensional cube, equals 103.
background
The module develops higher-order voxel-seam corrections to alpha inverse, building on the RS derivation with geometric seed alpha_seed = 4 pi times 11, gap weight f_gap = w_8 ln phi, and curvature correction delta_1 = -103 over 102 pi to the fifth. The full series is alpha inverse equals alpha_seed minus f_gap plus sum delta_n, where each delta_n is a combinatorial sum over n-fold face-wallpaper configurations on Q3 weighted by the Z_2^5 half-period measure. The upstream definition states that the curvature numerator equals face_wallpaper_pairs plus active_edges and counts the Euler closure contribution.
proof idea
The proof is a one-line reflexivity wrapper that reduces the defined curvature_numerator directly to the constant 103.
why it matters
This supplies the integer 103 that enters the first-order correction delta_1 within the series for alpha inverse. It is invoked by the alphaFramework certificate and by the delta_1_numerator theorem. In the Recognition Science framework it closes the combinatorial count for the curvature term inside the alpha band derivation, addressing the residual discrepancy with CODATA while leaving delta_2 computation open.
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