Let $f\in \mathbb{C}[z]$ be a monic polynomial of degree $n$, all of whose roots satisfy $|z|\le 1$. Let$$E=\{z:|f(z)|\le 1\}.$$What is the shortest length of a path in $E$ joining $z=0$ to $|z|=1$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let [ \ell(f):=\inf{\text{(Euclidean) length}(\gamma):\ \gamma\subset E,\ \gamma\text{ joins }0\text{ to some point with }|z|=1}. ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.