The Thickening Obstruction: Carry Propagation as a Qualitative Phase Transition in Polynomial Collatz Dynamics

We prove that the Lyapunov basis {deg, D, v₀, v₁} that controls the Generally Map over F₂[x] cannot certify convergence at thickening k ≥ 2, by constructing an explicit witness: two distinct polynomials on the same orbit in (Z/4Z)[x] whose feature projections coincide. The mechanism is exponential entropy collapse under carry propagation in the multiplication step. This is a no-go result for a specific class of Lyapunov approaches and provides precise characterization of why the integer Collatz conjecture resists techniques that succeed in the polynomial setting.