The 2n diagrams attain the upper bound on unknots

A free $2n$ knot is the free knot diagram referred to in the source, with $n+2$ crossings. A minimal free knot diagram is one with the minimum crossing number for its knot. $2n$-unknot upper-bound conjecture. The free $2n$ knots realize the upper bound on unknots for minimal free knot diagrams with $n+2$ crossings. The source derives the resultant unknot probabilities for this family and uses them to motivate the proposed extremal bound; the conjecture itself is not proved in the supplied text.