AI 中文总结
研究多重混合值何时处于一级的问题，利用Brown等人的下降理论，确定了深度小于四的所有非分歧动机多重混合值及一些无界深度的族，并提出关于大于三深度的非分歧MMV的猜想。
AI 中文摘要
多重混合值（MMVs）是通过将求和指标限制为固定奇偶模式而产生的多重zeta值的二级变体。一个特别有趣的问题是确定这些值何时实际上处于一级，即在多重zeta值方面可表达。由于这需要超越数论的新思想，目前我们还无法完全解决。然而，在动机层面已经取得了很大进展。之前，利用Brown等人发展的下降理论，我们已经解决了一些求和指标具有规则奇偶模式的特殊MMV类问题。在本文中，我们转向一般情况，完全确定了深度小于四的所有非分歧动机MMV以及一些无界深度的族。最后，我们将提出一些一般猜想，以描述所有大于三的深度的非分歧MMV。
英文摘要
The multiple mixed values (MMVs) are level two variants of multiple zeta values produced by restricting the summation indices to fixed parity patterns. One particularly interesting problem is to determine exactly when such values are actually in level one, namely, expressible in terms of multiple zeta values. To solve this completely is beyond our current knowledge since it calls for new ideas from transcendental number theory. However, much progress has been made on the motivic level. Previously, using the descent theory developed by Brown et al. we have tackled this problem for a few special classes of MMVs with regular parity patterns among the summation indices, including Hoffman's multiple $t$-values, Kaneko and Tsumura's multiple $T$-values, and our own multiple $S$-values. In this paper, we turn to the general case and determine completely all the unramified motivic MMVs of depth less than four as well as a few families of unbounded depths. At the end of the paper, we will present some general conjectures to describe the unramified MMVs at all depths greater than three.
Comments37 pages
