Unknotting number one for the 11 unresolved crossing-neighbor knots

Determine whether each of the 11 distinct non-alternating crossing neighbors arising from the remaining 22 alternating knots has unknotting number one, in order to resolve the corresponding candidate crossings and improve the unknotting-number bounds of the parent knots.

Background

After excluding all crossing changes to unknotting-number-one knots for 959 alternating knots, the authors identify 22 additional alternating diagrams with at least one candidate crossing. These candidates lead to 11 distinct non-alternating knots whose recorded ranges are [1,2] or [1,3]. Establishing or excluding unknotting number one for these neighbors would respectively provide matching upper bounds for, or eliminate candidate crossings from, the parent knots.