Claims

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1961_01_01_pommerenke: Pommerenke's 1961 answer: for 1 < r < 2 the set where |z^n - r^n| is at most 1 has n components whose diameter tends to 0, so the answer is no; Theorem 3 gives the affirmative answer for 0 < r <= 1; refereed.

2026_01_28_alexeev: Aristotle's disproof, found from the problem statement alone and published in Lean by Boris Alexeev: every component of the set where |z^10 - 2| < 1 has diameter at most 0.2; accepted on a later revision built and audited here.

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