V_cb_geom
plain-language theorem explainer
V_cb_geom defines the geometric ratio for the CKM matrix element V_cb as the reciprocal of the total vertex-edge incidences on the cubic lattice, which equals the rational 1/24. Particle physicists deriving mixing angles from ledger topology cite this when connecting cubic symmetry to the observed |V_cb| value. The definition is a direct constant assignment that downstream reductions normalize to the explicit fraction.
Claim. The geometric ratio for the CKM element is defined by $|V_{cb}| = 1/24$, where the denominator equals twice the edge count of the 3-cube.
background
The CKM Geometry module formalizes the T11 hypothesis that CKM elements arise as geometric couplings on the cubic ledger. V_cb is the edge-dual coupling, obtained as the inverse of the total vertex-edge slots. Upstream structures fix the cubic lattice via simplicial edge lengths and spectral emergence, which counts 24 chiral fermion flavors from D=3 and 2^D. The edge dual ratio is the quantity 1 over the product of edge count and vertex multiplicity per edge.
proof idea
This is a one-line definition that assigns the geometric ratio directly to the edge dual ratio constant. Downstream theorems apply simp and norm_num to reduce both sides to the explicit value 1/24.
why it matters
This definition supplies the exact rational for V_cb inside the T11Cert structure and the V_cb_match theorem, which confirms the geometric origin and the sub-sigma agreement with experiment. It realizes the edge-dual coupling step of the CKM derivation from ledger topology, consistent with D=3 and the eight-tick octave in the forcing chain. It closes the purely geometric part of the mixing predictions, leaving only the alpha-dependent terms for interval arithmetic.
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