The polylog quotient and the Goncharov quotient in computational Chabauty-Kim theory II

Building on work by Dan-Cohen–Wewers, Dan-Cohen [DC], and Brown, we push the computational boundary of our explicit motivic version of Kim’s method in the case of the thrice punctured line over an open subscheme of Spec ZZ. To do so, we develop a refined version of the algorithm of [DC] tailored specifically to this case. We also commit ourselves fully to working with the polylogarithmic quotient. This allows us to restrict our calculus with motivic iterated integrals to the so-called depth-one part of the mixed Tate Galois group studied extensively by Goncharov. An application was given in part one, where we verified Kim’s conjecture in an interesting new case.