cabibbo_coefficient_from_geometry
plain-language theorem explainer
The declaration proves that the Cabibbo coefficient equals the face count of the three-cube divided by four. Researchers deriving radiative corrections to quark mixing angles cite this result to obtain the 3/2 factor in the Cabibbo term. The proof is a one-line wrapper that unfolds the two definitions and reduces the rational arithmetic.
Claim. The Cabibbo coefficient equals three-halves, obtained as the ratio of the number of faces in the three-dimensional cube to four.
background
The PMNS Radiative Correction Derivation module extracts integer coefficients for mixing-angle corrections from the topology of the three-dimensional cube. A 3-cube has six faces, twelve edges and eight vertices; the Cabibbo coefficient arises from vertex-edge duality as six faces divided by four. The cube_faces function is defined as twice the dimension, yielding six for D=3, and appears in both AlphaDerivation and PlanckScaleMatching.
proof idea
The proof is a one-line wrapper that unfolds cabibbo_coefficient and cube_faces, then applies norm_num to evaluate the resulting rational number.
why it matters
This theorem supplies the geometric source of the 3/2 coefficient used by correction_derivation_verified to certify the full set of PMNS corrections. It completes the module's derivation of the (3/2)α Cabibbo term from 3-cube topology, consistent with the Recognition framework's T8 requirement that D=3 and the eight-tick octave closure.
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