The 2m diagrams attain the lower trefoil and upper unknot bounds

Let a free $2m$ diagram denote the free closure of the $2m$-tangle referred to in the source. A free diagram with $m$ crossings is considered sufficiently complicated as in the source. $2m$-diagram bound conjecture. The free $2m$ diagram realizes the lower bound on trefoils and the upper bound on unknots for all sufficiently complicated free diagrams with $m$ crossings. The claim is one of the source's computationally motivated proposed bounds; the source gives no proof or resolution.