ARI, GARI, Zig 和 Zag：Ecalle 多重zeta值理论导引
ARI, GARI, Zig and Zag: An introduction to Ecalle's theory of multiple zeta values
AI总结：
本文旨在介绍 Ecalle 的模理论及其与多重 zeta 值和双洗牌理论的联系，提供关键结果的完整证明，并强调以多重 zeta 值理论为背景的易理解导引。
摘要：
本文有两个目标。第一个是介绍 Ecalle 在模理论、多重 zeta 值和双洗牌理论方面的工作，并将这些工作明确地与以通常的非交换变量术语表述的经典多重 zeta 值理论和双洗牌理论联系起来。第二个是提供他的主要结果和恒等式中那些在（非彩色）多重 zeta 值背景下严格有用的部分的完整证明。这些证明中有许多是困难、费力且不具启发性的，已被归入附录。本文的重点是提供一个易于理解的 Ecalle 语言导引，同时几乎从一开始就将其置于多重 zeta 值理论的背景中。免责声明：本文并非最终版本，也未提交发表。其意图是随着时间的推移继续补充和完善它。
英文摘要：
This text has two goals. The first is to give an introduction to Ecalle's work on mould theory, multiple zeta values and double shuffle theory and relate this work explicitly to the classical theory of multiple zeta values and double shuffle expressed in the usual terms of non-commutative variables. The second is to provide complete proofs of those of his main results and identities which are strictly useful in the context of (non-colored) multiple zeta values. Many of these proofs are difficult, laborious and not enlightening and have been relegated to appendices. The emphasis in the text is to provide an easily approachable introduction to Ecalle's language while placing it almost from the start in the context of multiple zeta value theory. Disclaimer: This text is not final and is not submitted for publication. The intention is to continue to add to and complete it over time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
