Positive twist knot diagrams minimize the Casson–Vassiliev invariant

Let $D$ be a connected irreducible positive diagram with odd crossing number, and let $v_3(D)$ denote the degree-3 Vassiliev invariant of the diagram. A positive twist knot diagram is a positive diagram obtained from the standard twist-knot construction.

Positive twist-knot minimization conjecture. Positive twist knot diagrams minimize $v_3$ among all connected irreducible positive diagrams with odd crossing number.

The claim proposes that the twist-knot examples giving only quadratic growth of $v_3$ in the crossing number are extremal among such positive diagrams. The source does not provide evidence resolving this minimization problem.