reduced_configs
plain-language theorem explainer
Symmetry-reduced configuration count (upper bound) for n-fold face-wallpaper configurations on the 3-cube. Researchers computing higher-order voxel-seam corrections to the fine-structure constant would cite this when bounding the combinatorial size of series terms δ_n. The definition performs integer division of the n-fold count by the automorphism group order of 48 and adds one.
Claim. The upper bound on the number of symmetry-reduced n-fold face-wallpaper configurations on the 3-cube is given by $102^n / 48 + 1$, where 102 counts the face-wallpaper pairs and 48 is the order of the automorphism group of the 3-cube.
background
This module develops the combinatorial framework for higher-order corrections δ_n to the Recognition Science derivation of α^{-1}. The base formula combines a geometric seed of 4π × 11, a gap weight involving ln φ, and a curvature term, with the full series α^{-1} = α_seed - f_gap + Σ δ_n where each δ_n sums over n-fold configurations on Q3 weighted by the Z₂^5 measure.
proof idea
One-line definition that divides the n-fold configuration count by the Q3 automorphism order and adds one.
why it matters
It provides the bound required by the AlphaFrameworkCert structure, which assembles the cube combinatorics (6 faces, 12 edges, 11 passive edges, 17 wallpaper groups, 102 face-wallpaper pairs) to certify readiness for δ₂ computation. The explicit evaluation for n=2 yields 217 and supports the open computation of the second-order correction term. This fits the series structure addressing the 8 ppm residual in α^{-1} against CODATA, consistent with the eight-tick octave and D=3 from the forcing chain.
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