形式化中产生的数学。 更多论文会在这里出现。
不平衡的组定理
六边形2610.00575-35页
本文中报告了这一正规化项目所产生的新的群体理论结果。 在将第一代证据正式化的同时，我们发现了一个在通往未平衡集团定理的已公布路线中使用的关闭断言的反例。 本文解释了阻碍因素，并给出了简单组案的另一种论点，该论点基于所罗门1976年的"最大二元"理论，其关键步骤是"定理2.3"，即保存简单的超过。
我们正与小组理论家合作，汇编我们在文献中发现的错误，并将在这里出版。
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在Lean正式确定的有限简易团体分类
有限简单群体的分类是数学的伟大集体成就之一。 它的第一代证据跨越了上千个期刊页，由大约一百名数学家在几十年里撰写。 显示是每个有限度的简单组群都是由质序循环，交替循环，由Lie类型，或26个零星组群中的一个。
在此，我们提出在里恩第一代证明之后，经过里恩内核检查的每一个逻辑步骤，在里恩完全正式化。 一路走来，我们在公布的关于"不平衡集团定理"的论证中发现了一个问题。 随附的论文解释了这个问题和我们的证据中使用的替代路线。 我们的博客文章讲述了整个故事。
其他撰稿人Rafael Cabral、Colin Defant *、Erik Gregory *、Aaron Hill *、Letong Hong、秦平·胡†、Dustin Jamner *、Albert Jang *、Tadeusz Jordan *、Andrak Kurghinyan *、Kenny Lau *、Jonathan Laurent *、David Liang *、Jannis Limperg *、Simon Mahns *、Brian Nugent *、Connor Olson *、Ken Ono *、Eric Paul *、Dhruv Rajan *、Karun Ram *、Charlie Ray *、Ho Chung Siu *、Ashvin A. Swaminathan *、Jesse Thorner *、Aleksey Tsaplin *、Chenkai Wang * *
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Mathematics that came out of the formalization. More papers will appear here.
The Unbalanced Group Theorem
Hexagon 2610.00575 · 35 pages
A new group theory result that came out of this formalization project is reported in this paper. While formalizing the first-generation proof, we found counterexamples to a closure assertion used in a published route to the Unbalanced Group Theorem. The paper explains the obstruction and gives an alternative argument for the simple-group case, built on Solomon’s 1976 theory of maximal 2-components, whose key step is Theorem 2.3, the preservation of simple tops.
We are working with group theorists to compile the errata we found in the literature, and will publish them here.
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The Classification of Finite Simple Groups, formalized in Lean
The classification of finite simple groups is one of the great collective achievements of mathematics. Its first-generation proof spans thousands of journal pages, written by about a hundred mathematicians over several decades. It shows that every finite simple group is cyclic of prime order, alternating, of Lie type, or one of 26 sporadic groups.
Here we present a complete formalization in Lean following the first-generation proof, with every logical step checked by Lean’s kernel. Along the way, we found an issue in a published argument for the Unbalanced Group Theorem. The accompanying paper explains the issue and the alternative route used in our proof. Our blog post tells the full story.
Other contributorsRafael Cabral†, Colin Defant*, Erik Gregory†, Aaron Hill†, Letong Hong◇, Qinheping Hu†, Dustin Jamner†, Albert Jiang†, Tadeusz Jordan†, Andranik Kurghinyan†, Kenny Lau*†, Jonathan Laurent†, David Liang†, Jannis Limperg†, Simon Mahns†, Brian Nugent*, Connor Olson†, Ken Ono*, Eric Paul†, Dhruv Rajan†, Karun Ram†, Charlie Ray†, Ho Chung Siu†, Ashvin A. Swaminathan*†, Jesse Thorner*, Aleksey Tsaplin†, Chenkai Wang†
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