从Collatz的一个猜想到Thompson的群F，通过Girard的一个合取
From a conjecture of Collatz to Thompson's group F, via a conjunction of Girard
摘要：
著名的3x + 1问题L. Collatz不需要介绍;然而，这篇论文涉及一个鲜为人知的，但同样未解决的先驱问题：原始Collatz猜想，或OCC。我们证明了OCC的核心算术运算符，当与J. - Y. Girard从他的相互作用几何系统中，引出了R。汤普森的群F作为同余函数，在J. Conway的意义下。我们也给出了解释这一点的基本范畴论，并描述了OCC的核心算子作为一个典型的一致性同构。
英文摘要：
The famous 3x + 1 problem of L. Collatz needs no introduction; however, this paper concerns a lesser-known, but similarly unresolved, precursor problem : the Original Collatz Conjecture, or OCC. We demonstrate that the core arithmetic operator from the OCC, when combined with a conjunction of J.-Y. Girard from his Geometry of Interaction system, leads to a realisation of R. Thompson's group F as congruential functions, in the sense of J. Conway. We also give the underlying category theory that accounts for this, and describe the core operator from the OCC as a canonical coherence isomorphism.
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。
