F
plain-language theorem explainer
Face count F is defined as six for the three-dimensional cube. Lepton generation calculations in Recognition Science cite this as the leading term in the muon-to-tau step coefficient C_τ = W + D/2. The definition is obtained by direct substitution of the spatial dimension into the hypercube face formula.
Claim. Let F denote the number of faces of the three-dimensional cube. Then F equals 6, obtained from the hypercube face count 2D with D fixed at the spatial dimension 3.
background
The module derives the tau generation step from wallpaper symmetry coupled to dimensionality. In the lepton step formula step_mu_tau = F - (2W + 3)/2 * α, the integer F supplies the base term while W counts the 17 wallpaper groups and D is the spatial dimension. Upstream results define cube_faces(d) as 2d, the number of faces in the d-hypercube, with the three-cube case yielding exactly six faces.
proof idea
One-line definition that applies the cube_faces function to the spatial dimension D.
why it matters
This supplies the leading F term in the structural derivation of the muon-to-tau coefficient, matching the paper formula (2W + 3)/2 exactly once W = 17 and D = 3 are inserted. It anchors the lepton mass ladder to the framework's D = 3 and feeds downstream results including the standard Lagrangian and RCL checks. The definition closes the question of whether the coefficient is an arbitrary fit.
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