The Thickening Obstruction: Carry Propagation as a Qualitative Phase Transition in Polynomial Collatz Dynamics
Year: 2026
Type: preprint
Abstract: 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.
Author: Generally, Devon A.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170036493