  We present a new method to produce simple formulas for 1-cocycles of knots
over the integers, inspired by Polyak-Viro's formulas for finite-type knot
invariants. We conjecture that these formulas always represent finite-type
cohomology classes in the sense of Vassiliev. An example of degree 3 is
studied, and shown to coincide over Z/2 with the Teiblum-Turchin cocycle v_3^1.
