Explanation of cellCount

(1) In plain English, cellCount is a function on the CellDim type that returns the number of cells of a given dimension inside a 3-cube model: 8 vertices, 12 edges, 6 faces, or 1 cube.

(2) It matters in Recognition Science because it supplies the combinatorial counts needed to define the local (cellwise) normalization localCoeff k = (cellCount k) / (anchorsPerCell k). This lets the module prove that only face mediation yields exactly 3/2 inside the admissible mechanism class, confirming the discrete/continuous duality for the μ→τ correction without external fitting.

(3) The formal statement is read as a pattern-match definition: def cellCount : CellDim → ℕ followed by four cases that map each constructor of the inductive CellDim (vertex, edge, face, cube) to a concrete natural number. No recursion or computation is involved; the values are hardcoded for the 3-cube.

(4) Visible dependencies and certificates appear in the same module: the definition depends on the inductive CellDim (with deriving DecidableEq) and is used by localCoeff, localCoeff_face, localCoeff_eq_three_halves_iff, localCoeff_face_ne_edge, and localCoeff_face_ne_cube. These establish uniqueness of the 3/2 value. See localCoeff_face, localCoeff_eq_three_halves_iff, and localCoeff_face_ne_edge.

(5) The declaration does not prove any physical lepton masses, the full forcing chain from the Law of Logic, or empirical agreement with PDG data; it is a finite combinatorial model illustrating normalization locality for the 3-cube only.