V_cb_canonical
plain-language theorem explainer
The theorem establishes that an RSBridge with edgeDual count fixed at 24 yields the CKM element V_cb exactly equal to 1/24. Researchers deriving mixing angles from ledger geometry in Recognition Science would cite this canonical case. The proof is a one-line simplification that unfolds the bridge definition and substitutes the edge-count hypothesis.
Claim. For an RSBridge $B$ satisfying $B.edgeDual = 24$, the derived CKM mixing parameter satisfies $V_{cb} = 1/24$.
background
RSBridge augments the minimal ledger bridge with geometric fields: edgeDual (default 24, counting dual edges), alphaExponent for fine-structure coupling, and phiProj for golden-ratio projection. The module derives CKM angles from these counts rather than free parameters, with V_cb specifically the inverse of the dual edge count (24 = 2 × 12 for the cube dual). Upstream, V_cb_from_bridge is defined as 1 over B.edgeDual, and ContinuumBridge supplies the Laplacian-to-area identification used in the ledger geometry.
proof idea
The proof is a one-line wrapper that applies simp to unfold V_cb_from_bridge (which returns 1 / B.edgeDual) and substitutes the hypothesis B.edgeDual = 24.
why it matters
This pins the exact canonical value of V_cb inside the RSBridge structure, completing the geometric derivation of the CKM matrix from edge counts as outlined in the module. It supports the Recognition Science program of obtaining Standard Model parameters from ledger geometry (T7 eight-tick octave and D = 3 spatial structure) rather than arbitrary inputs. No downstream theorems are listed yet, but the result closes the canonical case for the second-third generation mixing angle.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.