Nonexistence conjecture for even Vassiliev invariants

An even, degree-one Vassiliev invariant is a function $V$ on virtual knots such that $V(K_+)-V(K_-)=0$ for even crossings and $V(K_+)-V(K_-) e 0$ for odd crossings. Nonexistence conjecture for even Vassiliev invariants. There are no even Vassiliev invariants. This conjecture concerns the possible strength of odd and even Vassiliev invariants in virtual knot theory; the supplied text does not establish its resolution.