vertex_edge_slots_eq_24
plain-language theorem explainer
The theorem establishes that the number of vertex-edge transition slots in the three-dimensional cubic lattice equals 24. Physicists deriving CKM and PMNS mixing parameters from voxel topology would cite this to fix the normalization for single-edge contributions such as V_cb. The proof is a term-mode reduction that unfolds the slot definition via the cube-edge count and normalizes the arithmetic identity.
Claim. In the three-dimensional cubic lattice the total number of vertex-to-edge transition slots equals $24$.
background
This module supplies the geometric constraints on cubic voxel topology that determine the CKM and PMNS mixing matrices. The edge count in a D-dimensional hypercube is defined by cube_edges(D) = D * 2^(D-1), which for D = 3 yields 12 edges. Vertex-edge slots are obtained by doubling this count to register the dual-lattice transitions between face-centered (Gen 2) and vertex (Gen 3) states.
proof idea
The proof is a one-line term wrapper. It unfolds the definition of vertex_edge_slots in terms of cube_edges and then applies norm_num to reduce the resulting numerical identity.
why it matters
The result supplies the normalization factor 24 used in the downstream theorem on the geometric origin of V_cb, where the single-edge contribution is expressed as 1/24. It completes the counting step that forces the mixing parameters from cubic topology, consistent with D = 3 obtained from the forcing chain T0-T8.
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