Wink-equivalence triviality of all welded knots

Determine whether every welded knot is wink-equivalent to the unknot.

Background

The paper introduces wink-equivalence as a welded extension of classical 4-equivalence and proves that every knot obtained as the closure of an algebraic virtual tangle is wink-equivalent to the unknot.

The broader question for arbitrary welded knots is not resolved: the stated theorem provides only a partial positive answer for the subclass arising from algebraic virtual tangles.