MEV Sharing with Dynamic Extraction Rates

The paper’s main claim (existence of Li–Yorke chaos for the λ–MEV update for every η>0 by exhibiting a period‑3 orbit) is plausible, but the provided proof contains a critical gap: it evaluates Δ(h(a)) using the linear-in-[a,b] formula while simultaneously sending b→a+, a regime in which h(a)>b so Δ(h(a)) is no longer given by that linear piece (it equals −w outside [a,b]). This makes the step Δ(h(a))=1−ηc with c→∞ invalid and the subsequent inequality forcing λ3≤λ0 unjustified . The rest of the development (definitions, set-up, and use of Li–Yorke/Sharkovsky) is standard and consistent . By contrast, the candidate solution gives a complete constructive proof: it builds a continuous, nonincreasing Δ within a pointwise corridor that guarantees h maps [0,1] into itself, forces a→b→c→a for interior points, and then realizes Δ as 1−F−wG via a monotone splitting into continuous cdfs F,G. This directly yields a least period‑3 orbit and hence Li–Yorke chaos via Li–Yorke/Sharkovsky, without the paper’s gap.