Counting as construction

For each generator g, the expression φ_g(n)=ρ^n(g) is not a classification of pre-existing numbers. It is the generated count itself: the n-th finite application of ρ along an orbit. Counting therefore appears first as constructive depth, not as imported ℕ, and it must be kept separate from later calculation inside earned algebraic structures. The metalanguage may index this process by n, but the τ-object is the generated orbit position.