vcb_derived
plain-language theorem explainer
The theorem establishes that the predicted CKM element V_cb equals the edge-dual ratio 1/24 arising from cubic ledger topology. Particle physicists deriving mixing angles from Recognition Science geometry would cite this equality to replace numerical fits with a topological count of vertex-edge slots. The proof is a one-line wrapper that unfolds the two sides and reduces them by norm_num.
Claim. The predicted CKM mixing element satisfies $|V_{cb}| = 1/24$, where the right-hand side is the edge-dual ratio obtained by counting the 12 edges of the cube, each incident to two vertices, yielding 24 vertex-edge slots that mediate the face-to-vertex transition between the second and third generations.
background
Recognition Science derives CKM elements from the cubic ledger in three spatial dimensions, with the eight-tick octave fixing the overlap windows between generations. Edge-dual coupling maps the second generation (occupying faces) to the third (occupying vertices) via single-edge transitions; the ratio 1/24 follows directly from the 12 edges times two vertices per edge. Upstream results include the crystal structure inductive type (BCC, FCC, HCP) that classifies the cubic geometry and the ledger factorization structure that calibrates the underlying J-cost.
proof idea
The term proof unfolds the definitions of V_cb_pred and edge_dual_ratio, then applies norm_num to equate both sides to the concrete rational 1/24.
why it matters
This declaration supplies the V_cb entry for the mixing_verified certificate that assembles the full CKM and PMNS matrices, and it is invoked verbatim by row_vcb_eq_geometry in the CKMElementScoreCard. It completes the phase 7.2 geometric derivation of |V_cb| = 1/24 from cubic symmetry, consistent with the T7 eight-tick octave and D = 3 spatial dimensions in the forcing chain. No open scaffolding remains for this specific equality.
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