curvature_fraction_num
plain-language theorem explainer
The definition sets the curvature fraction numerator to the seam numerator evaluated at the forced spatial dimension of three. Researchers assembling the geometric contribution to the fine-structure constant would cite this step when isolating the integer 103 in the term -103 over 102 pi to the fifth. It is a direct one-line wrapper applying the seam numerator function to dimension three.
Claim. The curvature fraction numerator equals the seam numerator at spatial dimension three, where the seam numerator is the base denominator plus the Euler closure term.
background
The Alpha Derivation module constructs the fine-structure constant from the cubic ledger geometry in three dimensions. The module states: 'The curvature term (103/102π⁵): Derived from voxel seam topology' and notes the geometric seed Ω(∂Q₃) = 4π times 11 passive edges. The spatial dimension is fixed at three by the linking requirement. The upstream seam numerator is defined as seam denominator d plus Euler closure, which for dimension three yields 102 plus 1 equals 103, where 102 arises from six faces times seventeen wallpaper groups.
proof idea
This definition is a one-line wrapper that applies the seam numerator function to the constant spatial dimension three.
why it matters
This supplies the numerator 103 used in the theorem establishing the curvature fraction as 103 over 102 and in the definition of the curvature term that incorporates the five-dimensional integration measure. It advances the derivation of the fine-structure constant by providing the seam count from the cubic geometry, consistent with the framework's forcing of three spatial dimensions. The module doc notes this closes the voxel seam topology into the curvature term.
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