The $k=10$ fixed-distance maze nonsolvability conjecture

Let $\mathcal{M}_{10}\subseteq\mathcal{M}$ be the class of mazes whose destination is at distance $10$ from the origin. The $k=10$ conjecture. Conjecture that there exists a $k$ for which $\mathcal{M}_k$ is not solvable holds for $k=10$; equivalently, $\mathcal{M}_{10}$ is not solvable. The paper proposes this as a stronger specific form of the preceding conjecture and gives no resolution.