seam_denominator
plain-language theorem explainer
The seam denominator is the product of the number of faces in a d-dimensional hypercube and the seventeen wallpaper groups. Researchers deriving the fine-structure constant from cubic ledger geometry cite this quantity as the base normalization factor in the curvature fraction. The definition is realized by direct multiplication of the two constituent definitions and evaluates to 102 at d equals 3.
Claim. For a positive integer $d$, the seam denominator is defined as $2d$ times 17.
background
The module derives the fine-structure constant from the geometry of the cubic ledger in three dimensions. The number of faces in a d-dimensional hypercube equals twice d. The number of distinct two-dimensional wallpaper groups equals the crystallographic constant seventeen, established by Fedorov in 1891. This product supplies the base normalization for the denominator of the curvature fraction. Upstream results establish the face count formula independently and fix the wallpaper group count as a standard constant.
proof idea
One-line definition that multiplies the output of the cube face count by the constant wallpaper group count.
why it matters
This definition supplies the denominator for the curvature fraction used in the theorem that establishes all magic numbers from D=3 cube geometry and in the derived curvature correction term. It realizes the base normalization step yielding 102 for D=3, as required by the seam topology in the Recognition Science derivation of the inverse fine-structure constant. The quantity feeds directly into the curvature correction of minus 103 over 102 pi to the fifth.
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