Canonical Digital Defects Beyond Periodicity: Automatic Counting Systems, Radix Renormalization, and Finite-State Nonlinear Observables

We develop a second, genuinely nonperiodic instance of canonical arithmetic defect theory. Let $A(N)=\\rho N+E(N)$ be a radix counting function and let $P$ be a polynomial of degree $m$. For the radix branch $N\\mapsto bN+r$, the nonlinear scale defect $$P(A(bN+r))-b^mP(A(N))$$ loses its top degree on every discrepancy-transition state. If the discrepancy orbit is finite, projection onto the positive-degree part gives an anchored counterterm that is unique on every recurrent state, and the renormalized observable has an exact finite alphabet. For automatic counting systems, bounded rational discrepancy therefore yields a canonical finite-state nonlinear defect; primitive substitutions with bounded discrepancy enter through the spectral/coboundary criterion of Paquette--Son. The Thue--Morse parity count gives a complete model. For $F_k(N)=\\binom{A(N)}k$, the canonical defect has the three-symbol alphabet $$\\left\\{0,\\;(-1)^k\\frac{(2k-3)!!}{k!},\\;(-1)^{k+1}\\frac{(2k-1)!!}{k!}\\right\\},$$ with minimal integer normalization $2^{k-s_2(k)}$, while its minimal dynamic defect automaton has four states for every $k\\ge2$. After removing an explicit parity baseline, all orders share the same normalized Prouhet--Thue--Morse/Mahler carrier. In the opposite direction, we prove a growing-discrepancy obstruction and show that the Rudin--Shapiro counting function admits no finite-state polynomial renormalization at any order $k\\ge2$. Thus finite automata alone do not force finite canonical defects: bounded discrepancy is a robust sufficient mechanism, while recurrent unbounded discrepancy can survive the radix degree drop and obstruct bounded renormalization.