Dynamical Analysis of the EIP-1559 Ethereum Fee Market

The paper proves (i) convergence for step sizes d in (0, d_F] and (ii) Li–Yorke chaos for some F at any fixed d>0. The convergence proof uses a Lyapunov potential with the stabilizing map g(b)=b(1+d−2dF(b)) and derives the same threshold d_F as in the candidate’s writeup; despite a sign typo in the theorem’s display of the update rule, the subsequent definitions and inequalities use the stabilizing form and the argument is sound . The chaos result is established via a constructive period‑3 configuration and Li–Yorke’s criterion and is correct . By contrast, the model’s Task A relies on an “exact recursion” q_{t+1} q_t = (1 + d t_t)^2 that is false when t_t<0; this identity is then used to deduce monotonicity and the limit q̄=1. Hence Task A is flawed, although the flip lemma is essentially right. Task B’s construction aligns with the paper’s logic but omits a needed range constraint on the anchor c to ensure α(b)=1+d−2dF(b)∈[1−d,1+d]. Therefore, the paper’s results are correct (with minor typographical issues), whereas the model’s solution contains a critical error in Task A and an incompleteness in Task B.