Non-foil free knot diagrams realize the figure-eight knot

Let $K$ be a minimal free knot diagram with at least four crossings that is not a foil or a connected sum of solely foil knots. An assignment of crossings resolves every free crossing into crossing data and produces a resultant knot. Non-foil figure-eight conjecture. There is an assignment of crossings of $K$ that produces the figure-eight knot. This is motivated by the observation that minimal braid diagrams of sufficiently large braid index contain enough free crossings to seek a figure-eight resultant, while connected sums of foils cannot produce one; the source gives no proof or resolution.