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.

中文翻译：

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计算 Chabauty-Kim 理论中的 polylog 商和 Goncharov 商 II

在 Dan-Cohen--Wewers、Dan-Cohen [DC] 和 Brown 的工作的基础上，我们在 Spec ZZ 的开放子方案上的三次穿孔线的情况下推动了 Kim 方法的显式动机版本的计算边界。为此，我们开发了专门针对这种情况量身定制的 [DC] 算法的改进版本。我们还完全致力于使用多对数商。这使我们能够将我们的带有动机迭代积分的微积分限制在 Goncharov 广泛研究的混合泰特伽罗瓦群的所谓深度一部分。在第一部分给出了一个应用程序，我们在一个有趣的新案例中验证了 Kim 的猜想。