Integration conjecture for virtual-knot weight systems

For virtual knots, finite type invariants are defined by the schematic difference relation

$$\text{singular crossing}\longmapsto\text{positive crossing}-\text{negative crossing}.$$

A weight system is a linear functional on virtual-knot arrow diagrams satisfying the relevant relations, and a finite type invariant has a degree (or type) defined by this difference relation. Virtual-knot integration conjecture. Every weight system for virtual knots comes from a finite type invariant of virtual knots. This is the virtual-knot analogue of the classical fact that every weight system integrates. The paper supports the conjecture by computing matching dimensions of spaces of weight systems and finite type invariants in several degrees, but the general assertion is not established in the supplied text.