cabibbo_scaling_forced
plain-language theorem explainer
The torsion overlap on the cubic ledger minus the Cabibbo radiative correction equals phi to the minus three minus three-halves times the fine-structure constant. Researchers deriving CKM parameters in Recognition Science cite this result to anchor the geometric origin of the scaling factor. The proof is a one-line term wrapper that unfolds the two definitions and applies ring normalization.
Claim. Let $T$ be the 3-generation torsion overlap on the cubic ledger and $C$ the Cabibbo radiative correction. Then $T - C = phi^{-3} - (3/2) alpha$, where $alpha$ is the fine-structure constant.
background
The MixingGeometry module formalizes cubic voxel topology constraints that force CKM and PMNS mixing parameters. Torsion_overlap is defined as $phi^{-3}$, the delocalization of the first generation across three spatial dimensions. Cabibbo_radiative_correction is defined as $(3/2) alpha$, arising from six faces divided by four vertex-edge weights. The fine-structure constant $alpha$ is imported from Constants.Alpha as the reciprocal of its inverse, while the abstract Constants bundle from LawOfExistence supplies the overall constant structure.
proof idea
The proof is a term-mode wrapper. It unfolds torsion_overlap and cabibbo_radiative_correction, then applies the ring tactic to confirm the algebraic identity holds by direct substitution.
why it matters
This theorem establishes that the Cabibbo scaling factor is forced by the torsion overlap and face-mediated radiative corrections within the cubic geometry. It fills a required step in the mixing-matrix chain of the Recognition Science framework, connecting to the phi-ladder (T5-T8) and the alpha band. No downstream theorems are listed, leaving its use in full CKM derivations as an open extension.
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