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Claim. Wang Chunjie, The arc length of the lemniscate $\lvert w^2+c\rvert=1$, Acta Math. Sci. (Chin. Ed.) 18 (1998), no. 3, 297–301, studies the arc length $s(c)$ of the lemniscate $\lvert w^2+c\rvert=1$ for $c\ge0$ and, as the English summary in its zbMATH record (Zbl 0926.31001) states, solves the case $n=2$ of the conjecture of Erdős, Herzog and Piranian, the degree-2 instance of Problem 114. Every monic quadratic becomes $w^2+c$ with $c\ge0$ after a translation and a rotation of the variable and a unimodular rescaling of the value, none of which changes the length of its lemniscate, so the case $n=2$ is the statement that $s(c)$ is largest at $c=1$, where the lemniscate is the Bernoulli lemniscate of $z^2+1$, which is $z^2-1$ up to rotation. The paper is in Chinese, and this page states its theorem as that summary gives it. It precedes the 1999 proof of the same case by Eremenko and Hayman (Eremenko–Hayman 1999), and a comment on the site's discussion thread of 2026-03-05 pointed to it.

Covers. Degree $2$ only, the same instance as Eremenko–Hayman 1999. All sufficiently large degrees are claimed, pending, by Tao 2025, and the intermediate degrees are open.

Depends on. No page of this wiki; the result rests on the refereed paper recorded above.

Acceptance. Refereed: Acta Mathematica Scientia, Series A (Chinese edition), volume 18, issue 3 (1998), a journal of Science Press, Beijing; the issue gives no month, so the page is dated to the first day of the year. The site's label is FALSIFIABLE, an open label, and its commentary does not mention the paper, so no reviewed evidence is listed. No formal proof is recorded. Nothing here is this project's own review.