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Let with for all . Let be the radius of the largest disc which is contained in .
Determine the behaviour of . In particular, is it always true that ?
Source: erdosproblems.com/1039
A full solution has been claimed but not yet accepted. Settled in another form, for example when its parts resolve differently or the question is open-ended.
Open (the site's label OPEN; page last edited 27 December 2025). The site's commentary credits Pommerenke [Po61] with , the accepted partial claim on Pommerenke 1961, and Krishnapur, Lundberg and Ramachandran [KLR25] with , the partial claim on Krishnapur, Lundberg and Ramachandran 2025. The site's proof-claims tab carries one full proof claim with no comments and no acceptance, on Geng–Qiu 2026: an arXiv preprint with a Lean companion, registered on the tab on 2026-09-09, asserts that . Two partial claims precede it: Price 2026, posted on the thread on 2026-05-07, claims , which would answer the second question in the affirmative; it was endorsed by readers on the thread and formalized by Kitamura, and is not marked accepted by the site. Houi 2026 claims when every critical value has modulus at least . None of the 2026 claims is refereed or accepted by the site, and none has been built or audited in this wiki.