Galois symmetries of knot spaces

We exploit the Galois symmetries of little disks operads to show that many differentials in Goodwillie–Weiss spectral sequences approximating homology and homotopy knot spaces vanish at a prime $p$ . Combined with recent results on relationship between embedding calculus finite-type theory, we deduce $(n+1)$ th approximation is -local universal Vassiliev invariant degree $\leq n$ for every $n \leq p + 1$