Goussarov–Polyak–Viro conjecture for finite type invariants of knots

A finite type invariant of classical knots is an invariant filtered by finite-dimensional vector spaces. A finite type invariant of long virtual knots is defined analogously in the long virtual knot setting. Goussarov–Polyak–Viro conjecture. Every finite type invariant of classical knots can be extended to a finite type invariant of long virtual knots. This conjecture asks whether all finite type information for classical knots is captured by finite type invariants of long virtual knots; the paper studies the degree-three case.