Claims

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1961_01_01_pommerenke: Pommerenke (1961) proves that the lemniscate set of a monic polynomial with zeros in the closed unit disk contains a disk of radius 1/(2e n^2) about a zero, the first lower bound for the minimal inradius; refereed.

2025_03_24_krishnapur_lundberg_ramachandran: Krishnapur, Lundberg and Ramachandran (2025) prove that the minimal inradius of a degree n lemniscate with zeros in the closed unit disk is at least a constant over n root(log n); an arXiv preprint credited by the site.

2026_03_06_houi: A forum user, working with Claude Opus 4.6, claims that a monic polynomial with roots in the closed unit disk whose critical values all have modulus at least one has a disk of radius one over 4n inside its lemniscate; no review.

2026_05_07_price: Price, working with GPT-5.5 Pro, claims that some root of any monic polynomial with roots in the closed unit disk centers a disk of radius log 2 over n inside its lemniscate; endorsed on the thread, formalized by Kitamura.

2026_09_06_geng_qiu: Geng and Qiu, with ChatGPT assistance, claim that n times the infimum of the inradius over monic degree n polynomials with roots in the closed unit disk tends to pi over two; an arXiv preprint with Lean, a claim on the site's tab.

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