What the papers state
There exist a finitely generated normal integral \CC-algebra A of Krull dimension two and a maximal ideal \m\subset A such that
\Der_{\CC}(A)\simeq A^{\oplus2},
\qquad A_{\m}\text{ is not regular}.
The release does not say which paper theorem its catalogue describes. The statement above shares the most wording with the description; the atlas has not reviewed that choice. Identifying it is listed under Questions awaiting review.
- Reported proof verification
- The release has no Lean statement for this family. The papers are available to read and assess.
Papers
Each paper opens as a reading page in the browser, with the PDF beside it. The statements each paper opens with are on its reading page.
23 September 2026, current edition.
Read it herePDF
We construct a singular normal affine complex surface whose tangent sheaf is free of rank two. This disproves the Lipman–Zariski conjecture in characteristic zero.
Lean statements
The release has no Lean statement for this family. Its papers remain available to read, and contributors can propose a formal statement of a result. Suggest a change
Independent comparisons and proof-verification reports
Does the Lean express the advertised result?
The release contains no Lean statement for this family, so there is no formal statement to compare with OpenAI’s description.
What these papers cite in the release, and what cites them
These links come from the papers’ bibliographies. A citation records that one paper cites another; how each cited result is used has not been examined here.
Papers elsewhere in the release that this family’s papers cite
This family’s papers cite no paper elsewhere in the release.
Papers elsewhere in the release that cite this family’s papers
No paper elsewhere in the release cites this family’s papers.
References outside the release
Each paper’s outside references are listed with it on its reading page, where each citation is placed. Every outside work cited in the release: References outside the release
Explain a result, compare statements or propose a correction
Atlas has no contributed explanation for this family yet. You can offer one with a GitHub account. You receive named credit and disclose any AI assistance.
What people have said
Commentary on this family by others, dated and credited. It is commentary, not a finding.
An unsigned public tier list, the OpenAI Math Tier List, classes it as a counterexample and rates its significance, if it holds up, as “Major math journal”. The page says that nothing on it is verified.
Author not stated. Source
Questions awaiting review
Each item identifies a statement, definition or report that needs further review. Its link opens a GitHub form with the source version already recorded.
Identify the theorem the catalogue describes
- Family 048 No single paper statement clearly matches OpenAI’s description by wording, and no review identifying the intended theorem is recorded. Open the form
State the result in Lean
- Family 048 The release has no Lean statement for this family. Open the form