curvature_fraction_is_103_over_102
plain-language theorem explainer
The theorem establishes that the curvature fraction in the alpha derivation equals exactly 103/102. Researchers deriving the fine-structure constant from cubic ledger geometry would cite this numerical anchor. The proof is a one-line wrapper that splits the conjunction and evaluates the seam definitions via native decision.
Claim. In the Recognition Science derivation, the curvature fraction satisfies $103/102$, where the numerator is the seam count (including Euler closure) and the denominator is the base normalization $6×17$ arising from the six faces of the cube and the seventeen wallpaper groups.
background
The module derives the fine-structure constant from the geometry of the cubic ledger Q₃. The relevant definitions are seam_numerator D (the total seam count) and seam_denominator D (the base normalization). Module documentation states: Base normalization: 6 × 17 = 102. Closure term: +1 (Euler characteristic constraint). Seam count: 103. The upstream theorem from PrimitiveDistinction reduces seven axioms to four structural conditions plus three definitional facts that underwrite the ledger construction.
proof idea
The proof is a one-line wrapper. Constructor splits the conjunction into two subgoals. Native_decide then evaluates the natural-number definitions seam_numerator D and seam_denominator D directly for D = 3.
why it matters
This supplies the exact integers for the curvature term -103/(102 π⁵) listed among the module's main results. It anchors the geometric seed 4π·11 and the voxel-seam contribution to α^{-1}. In the broader framework it realizes the D = 3 spatial dimensions and the eight-tick octave structure by fixing the normalization that feeds the alpha band (137.030, 137.039).
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