Claims

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1998_01_01_wang: Wang Chunjie's 1998 paper on the arc length of the lemniscate of w squared plus c solves the degree-2 case of the conjecture a year before Eremenko and Hayman; refereed in Acta Mathematica Scientia (Chinese edition).

1999_09_01_eremenko_hayman: Eremenko and Hayman prove that among monic quadratics the lemniscate of z squared plus one, the Bernoulli lemniscate, is the longest, which settles degree 2 of the conjecture; refereed in the Michigan Mathematical Journal.

2025_12_13_tao: Tao proves that for every sufficiently large n the lemniscate of a monic degree n polynomial is at most as long as that of z to the n minus one, with equality only up to rotation and translation; an arXiv preprint, pending.

2026_03_23_mendoza: Mendoza's interval branch-and-bound search claimed the conjecture for degrees 3 to 10 and then 3 to 14; after an objection on the code repository the author conceded in October 2026 that it is a census, not a proof, for any degree.

2026_05_20_dahlke: Dahlke's 2026 Zenodo manuscript proves that among monic cubics the lemniscate of z cubed minus one is the longest, through the Eremenko–Hayman extremal reduction as Tao states it; a partial claim, pending.

2026_08_22_chatelet: Chatelet's 2026 write-up and Lean development assert that among monic cubics the lemniscate of z cubed minus one is the longest, under a domain reduction cited from Eremenko-Hayman and Tao; a partial claim, pending review.

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