Claims

../

1961_01_01_pommerenke: Constructs, for every l below 4 and every k, a monic polynomial whose sublevel set has at least k components of diameter at least l, so the count of components above a fixed diameter is not bounded; refereed.

2025_09_15_huang: Constructs, for every c below 4 and every N, a monic polynomial whose sublevel set has at least N components of diameter at least c, an independent rediscovery of Pommerenke's theorem credited by the site.

---