Grytczuk–Kordulewski–Niewiadomski conjecture on extremal square-free words

A square-free word is a finite word over a finite alphabet that contains no factor of the form $XX$ for a nonempty word $X$. An extremal square-free word is a square-free word none of whose extensions, obtained by inserting one letter at any position, is square-free.

Grytczuk–Kordulewski–Niewiadomski conjecture. There exists no extremal square-free word over a finite alphabet of size at least $4$.

This conjecture concerns the possible existence of extremal square-free words over larger alphabets. Infinitely many ternary extremal square-free words are known, while the conjecture was open for every finite alphabet according to the authors.