  The theory of Gauss diagrams and Gauss diagram formulas provides convenient
ways to compute knot invariants, such as coefficients of the HOMFLYPT
polynomial. In \cite{4,5}, the author uses Gauss diagram formulas to find
combinatorial 1-cocycles in the moduli space of knots in the solid torus.
Evaluated on canonical loops, one can then obtain new, non trivial knot
invariants. In those books, the author conjectures that a new formula, based on
the Vassiliev invariant $v_3$ also gives a 1-cocycle. We prove that it is in
fact true by using the same methods developed by the author in those books.
