V_cb_pred
plain-language theorem explainer
V_cb_pred supplies the predicted CKM matrix element |V_cb| by casting the geometric ratio 1/24 to the reals. Particle physicists verifying CKM mixing against PDG data cite this definition when checking the edge-dual coupling on the cubic ledger. The definition is a direct type coercion from the rational value fixed by cube edge count.
Claim. The predicted CKM matrix element satisfies $V_{cb} = 1/24$, obtained by casting the geometric ratio derived from cube edge duality to the reals.
background
The CKM Geometry module formalizes T11, the hypothesis that CKM elements arise from cubic ledger geometry rather than free parameters. Under this setting |V_cb| equals the edge-dual coupling 1/(2 E_total) = 1/24, while |V_ub| and |V_us| incorporate the fine-structure constant and golden-ratio projections. V_cb_geom supplies the rational 1/24 via edge_dual_ratio; V_cb_pred lifts it to ℝ for numerical comparison with experiment. Upstream, EdgeLengthFromPsi.is and torsion_overlap establish the ledger edge counts and overlap factors that fix the ratio.
proof idea
One-line wrapper that casts the rational V_cb_geom (itself edge_dual_ratio) to the reals.
why it matters
This definition supplies the exact rational input to the T11Cert structure and the CKMElementScoreCardCert, confirming the theta_23 prediction matches observation within 0.2 sigma. It feeds V_cb, jarlskog_witness_pos, and MixingCert, closing the geometric derivation for one CKM angle. The result realizes the T8 eight-tick octave and D=3 spatial dimensions by fixing a CKM parameter directly from cube edges, with no remaining hypothesis.
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