curvature_fraction_den
plain-language theorem explainer
curvature_fraction_den defines the denominator of the curvature fraction as the seam denominator evaluated at the forced spatial dimension D. Researchers deriving the fine-structure constant from cubic ledger geometry cite this when normalizing the curvature term. It supplies the value 102 that enters the ratio 103/102. The definition is a direct one-line instantiation of the seam denominator function at D=3.
Claim. The denominator of the curvature fraction is the product of the number of faces of the three-dimensional cube and the number of wallpaper groups, which equals 102.
background
The Alpha Derivation module constructs the fine-structure constant from the geometry of the cubic ledger Q₃ in three spatial dimensions. D is defined as 3, the value forced by the linking requirement in the Recognition framework. seam_denominator is the base normalization given by the product of cube faces and wallpaper groups. For D=3 this product is 6×17=102, which serves as the denominator of the curvature fraction. The module doc states: 'The base normalization: faces × wallpaper groups. This is the denominator of the curvature fraction.'
proof idea
The definition is a one-line wrapper that applies seam_denominator to D.
why it matters
This definition supplies the denominator 102 used by curvature_fraction_is_103_over_102 to establish the ratio 103/102 and by curvature_term to form the curvature term -103/(102 π^5). It completes the seam count step in the alpha assembly from voxel seam topology. The construction relies on the forced D=3, the active-passive edge distinction, and the 4π·11 geometric seed in the Recognition framework.
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