Subquadratic upper bound conjecture for the longest solvable board

Let $n\geq 3$ be odd, and let $ML(n)$ denote the maximal length of a solvable board of size $n$. The paper establishes the lower bound $ML(n)\geq 3n$ for all $n\geq 11$ and the trivial upper bound $ML(n)\leq n^2$. Subquadratic upper bound conjecture. As $n\to\infty$, $ML(n)=o(n^2)$. This is explicitly presented as a weaker conjecture than the linear upper bound conjecture and would still improve the trivial quadratic bound.