The banding refinement of McCoy's alternating-surgery conjecture

A banding of the unknot is a band surgery on the unknot that produces an alternating link. An almost alternating diagram of the unknot is an alternating diagram with one dealternation crossing. The banding refinement of McCoy's conjecture. If a banding of the unknot produces an alternating link, then there is an almost alternating diagram of the unknot in which the banding is either a smoothing of the dealternation crossing or a flat banding from the dealternation crossing to an adjacent crossing. This modification is motivated by the two strongly invertible examples discussed in the paper; the source gives no resolution evidence for the proposed statement, so it remains open.