faceVertexRatio_D3
plain-language theorem explainer
The face-vertex ratio for a 3-dimensional hypercube equals 3/2, confirming the structural correction term Δ(3) = 3/2 in the lepton mass ladder. Physicists deriving particle generations from cube geometry would cite this as the explicit check that the facet-mediated μ→τ step produces the required dimension dependence without external fitting. The proof is a direct algebraic reduction after unfolding the face count definition.
Claim. In three spatial dimensions, the ratio of the number of faces $F = 2D$ to the number of vertices per face $V = 4$ satisfies $F/V = 3/2$.
background
The module derives the dimension-dependent correction Δ(D) = D/2 from hypercube geometry for the μ→τ lepton step. Face count is defined as F = 2D. Vertex count per face is the vertex count of a (D-1)-hypercube, which equals 4 when D = 3. This supplies the discrete analog of solid angle in the facet-mediated correction, where each facet contributes 1/V and the total correction is F/V. The local setting compares this to the edge-mediated e→μ step that uses 1/(4π).
proof idea
One-line wrapper that unfolds the definition faceCount (D) := 2*D and applies numerical normalization to verify the equality for D = 3.
why it matters
This supplies the D = 3 case for the facet-mediated correction Δ(D) = D/2 in the μ→τ lepton generation step. It closes the geometric derivation of the structural term without calibration, feeding the mass ladder and the eight-tick octave with D = 3 forced by the upstream chain. No downstream uses are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.