The 2n diagrams attain the lower bound on trefoils

A minimal prime algebraic free knot diagram is a minimal free knot diagram representing a prime knot and arising from an algebraic tangle. A free $2n$ knot is the family considered in the source, with $n+2$ crossings. $2n$-trefoil lower-bound conjecture. The free $2n$ knots are the lower bound for trefoils among minimal prime algebraic free knot diagrams with $n+2$ crossings. This is proposed as an extremal statement following the analysis of the $2n$ family; the source gives no proof or resolution.