V_cb_from_cube_edges
plain-language theorem explainer
The theorem shows that the geometric CKM element V_cb_geom equals one over twice the edge count of the three-dimensional cube. Researchers deriving CKM parameters from ledger geometry would reference this exact equality. The proof reduces the statement by unfolding the definitions of V_cb_geom and cube_edges followed by numerical normalization.
Claim. The geometric CKM matrix element satisfies $V_{cb} = 1/(2 E) = 1/24$, where $E$ is the edge count of the 3-cube given by $3 · 2^{2}$.
background
In the CKM Geometry module the CKM matrix elements are derived from cubic ledger geometry. The function cube_edges computes the number of edges in a D-dimensional hypercube as D times 2 to the power of D minus one. V_cb_geom is defined as the edge dual ratio, which evaluates to one over twenty-four for three dimensions. This fits the T11 hypothesis that |V_cb| equals one over twice the total edge count, yielding the prediction 0.04167 matching observation within 0.2 sigma. The upstream result cube_edges provides the combinatorial count used here.
proof idea
The proof is a one-line wrapper that applies simplification to the definitions of V_cb_geom, edge_dual_ratio, and cube_edges, followed by numerical normalization to confirm the equality to 1/24.
why it matters
This theorem supplies the geometric origin for the T11 certificate t11_V_cb_verified. It realizes the T11 claim for V_cb as the edge-dual coupling on the cubic ledger, consistent with D=3 from the forcing chain. The result closes the exact rational derivation for this CKM element, leaving interval proofs for the alpha-dependent entries.
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