Frid–Puzynina–Zamboni prefix palindromic-length conjecture

Let $w$ be an infinite word. A prefix of arbitrarily high palindromic length means that for every integer $M$ there is a prefix $u$ of $w$ with $\operatorname{PL}(u)\geq M$. Frid–Puzynina–Zamboni's prefix conjecture. Every non-ultimately periodic infinite word has prefixes of arbitrarily high palindromic length. This is an equivalent formulation of the bounded palindromic length conjecture; the paper states that the latter remains open in general.