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Claim. For every monic $f$ with all roots in the open unit disk, two roots are joined inside $\{z:\lvert f(z)\rvert<1\}$ by a path of length less than $2$, the affirmative answer to Problem 1041. The user kasko37 posted the write-up on the site's discussion thread on 2026-04-22 as a solution announced by GPT-5.4 Thinking, without a summary of the argument. Nat Sothanaphan noted at first that the write-up avoided the gap of the earlier attempt on ani 2026 and at least had a chance against Mac Lane's winding lemniscates.

Depends on. No page of this wiki.

Standing. Rejected. Sothanaphan's AI check with GPT-5.5 (2026-04-27) found a serious gap in the proof of Lemma 6, where subharmonicity is used to bound $\lvert\phi'(r)\rvert$ by the circle average of $\lvert\phi'\rvert$, while the inequality holds for the value at the circle's center; the check judged the gap not easily repairable, and Ho Boon Suan had earlier pointed out the same gap to Sothanaphan. The thread records no repair, no proof claim was registered on the site's proof-claims tab, and the later degree-seven counterexample on ani 2026 (counterexample), if correct, shows that the claimed statement is false.