Claims

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2026_03_17_ani: A forum user, working with GPT-5.4, claimed a proof that two roots are always joined by a path of length below two, by cutting it from a tree of gradient flow lines; Tao found the tree structure false and the author agreed.

2026_04_22_kasko37: A forum user posted a write-up by GPT-5.4 Thinking announcing a proof that two roots are always joined by a path of length below two; two readers found the same serious gap in a subharmonicity step, judged not easily repairable.

2026_06_23_pendyala: Pendyala claims that for a monic quartic with all zeros in the open unit disk two zeros are joined inside the lemniscate by a polygonal path of length below two; an arXiv preprint with a Lean formalization not shared, no review.

2026_09_07_ani: A forum user, working with GPT 6, claims a family of monic degree-seven polynomials with all roots in the open unit disk in which no path of length below two inside the lemniscate joins two roots; checked by two readers.

2026_09_11_cook: Cook, with a write-up by Astra and other AI tools, claims that for a monic trinomial with all zeros in the open unit disk every root is joined to the origin inside the lemniscate, so two roots are joined by a short path.

2026_09_18_borisov: Borisov claims that for a monic cubic with all roots in the open unit disk two roots are joined inside the lemniscate by a two-segment path of length below two through a critical point; a Zenodo preprint, a partial claim on the tab.

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