Minimum critical exponent conjecture for ternary words of complexity at most $2n+1$

Let ${\mathbf G}$ be the ternary infinite word defined earlier in the paper, and let the subword complexity of an infinite word be the number of its distinct factors of each length. For a word, its critical exponent is the supremum of the exponents of its finite factors. Minimum critical exponent conjecture. Among all ternary words with subword complexity bounded above by $2n+1$, the word ${\mathbf G}$ has the lowest possible critical exponent. This is an extremal conjecture relating factor complexity to power avoidance; the source gives no resolution.