The uniqueness conjecture for most frequent subwords of minimal binary words

Let $w$ be a binary word of length $n$ achieving the minimal subword entropy. Uniqueness conjecture. There are only finitely many values of $n$ for which such a word $w$ has several most frequent subwords.

The conjecture concerns the apparent eventual uniqueness of the most frequent subword among entropy-minimizing binary words. It is supported by the paper's finite computations but remains open.