localCoeff_face
plain-language theorem explainer
The local coefficient for face mediation in the 3-cube equals 3/2. Researchers deriving lepton mass steps from cube geometry cite this to fix the facet contribution in the μ to τ transition. The proof is a direct unfolding of cell counts and anchors per cell followed by numerical simplification.
Claim. In the 3-cube, the local coefficient for face mediation, defined as the ratio of the number of faces to the number of vertices per face, equals $3/2$.
background
Cell count records the total number of k-cells in the 3-cube (6 faces, 12 edges, 8 vertices, 1 cube). Anchors per cell records the vertices bounding each k-cell (4 per face, 2 per edge, 1 per vertex, 8 per cube). Their ratio supplies the local coefficient for each mediator type.
proof idea
The proof is a one-line wrapper that unfolds the definitions of the local coefficient, cell count, and anchors per cell, then applies numerical normalization to reduce 6/4 to 3/2.
why it matters
This supplies the concrete value 3/2 for the face-mediated coefficient and feeds the downstream uniqueness theorems showing face mediation differs from edge (value 6) and cube (value 1/8) mediation. It completes the facet term in the first-principles derivation of Δ(3) = 3/2, aligning with the D = 3 spatial dimensions forced by the eight-tick octave.
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