Solvability conjecture for mazes whose origin component is a path

Let $\mathcal{N}$ be the subset of square-lattice mazes in which the connected component of the origin is a simple, possibly infinite, path. Path-component maze solvability conjecture. There exists an algorithm that solves $\mathcal{N}$. The paper presents this as a further positive result expected to hold; no proof or resolution is supplied, so the conjecture remains open.