Foil diagrams attain the upper bound on figure-eight descendants

A free foil diagram with $n$ crossings is a free knot diagram, and an algebraic free diagram is a free knot diagram arising from an algebraic tangle. Foil figure-eight upper-bound conjecture. The free foil diagram with $n$ crossings realizes the upper bound on figure eights for all sufficiently complicated algebraic free diagrams with $n$ and $n+1$ crossings. The claim is based on computational evidence concerning resultant unknots, trefoils, and figure-eight knots; the source gives no proof or resolution.