Minimum complexity conjecture for square-free ternary words

Let ${\mathbf T}$ be the ternary Thue word, the fixed point of the morphism $0\mapsto012$, $1\mapsto02$, and $2\mapsto1$. A ternary infinite word is square-free if it contains no factor of the form $uu$ with $u$ nonempty. Minimum complexity conjecture. The ternary Thue word ${\mathbf T}$ has the minimum subword complexity among all square-free ternary infinite words. This concerns the extremal factor complexity of square-free ternary words; the source presents the assertion as a conjecture and gives no resolution.