Higher differentials in the cohomology spectral sequence for long knots

There are two cohomology spectral sequences computing invariants of families of long knots in R^3, due respectively to Goodwillie-Sinha and Vassiliev, that conjecturally agree. Rationally it is known that they both collapse at the second page. Vassiliev conjectured that this is the case over all coefficients. In order to perform explicit computations we define a small multicomplex based on the Fox Neuwirth decomposition of configuration spaces, that produces higher differentials in the Goodwillie-Sinha spectral sequence. Surprisingly this yields a nontrivial third page differential at the prime 2. This is joint work with A. Marino.