This repository collects raw outputs produced by Rethlas, an agentic system for research-level mathematical reasoning.
AlgGeom/
AlgebraicGroups/
PAdicHodge/
Analysis/
Brezis_OpenProblems/
CommAlg/
arxiv_1606_01867/
CFFG_OpenProblems/
The current top-level areas are:
AlgGeom: algebraic geometry.Analysis: analysis.CommAlg: commutative algebra.
This directory contains raw outputs for problems concerning algebraic groups.
These results are associated with the following paper:
- Haocheng Ju et al., “Automated Conjecture Resolution with Formal Verification.” arXiv: 2604.03789
This directory contains raw outputs for problems in p-adic Hodge theory.
The corresponding paper is:
- Xiangyu Pan and Jiahong Yu, “Lift-independence problem in the (P)-adic Simpson correspondence for curves.” arXiv: 2605.29947
This directory contains raw outputs related to open problems posed by Haïm Brezis.
Problem source:
Haïm Brezis, “Some of my favorite open problems,” Rendiconti Lincei - Matematica e Applicazioni, vol. 34, 2023, pp. 307–335.
Problems represented in this directory:
- Problem 5.1
- Problem 5.3
The corresponding paper is:
- Xu’an Dou and Zeyu Jin, “Degenerate constants in degree inequalities for Sobolev circle maps: on some problems posed by Brezis.” arXiv: 2605.24626
This directory contains raw outputs related to questions from Boij–Söderberg theory.
Problem source:
Daniel Erman and Steven V. Sam, “Questions about Boij-Soderberg theory,” in Izzet Coskun, Tommaso de Fernex, and Angela Gibney (eds.), Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, vol. 95, American Mathematical Society, Providence, RI, 2017, pp. 285–304. DOI: 10.1090/pspum/095/01635. arXiv: 1606.01867. ISBN: 978-1-4704-3557-8.
Questions represented in this directory:
- Question 6.1
- Question 6.2
The corresponding paper is:
- Jiedong Jiang et al., “On some open problems in commutative algebra resolved by Rethlas.” arXiv: 2605.25259
This directory contains raw outputs related to open problems in commutative ring theory.
Problem source:
Paul-Jean Cahen, Marco Fontana, Sophie Frisch, and Sarah Glaz, “Open Problems in Commutative Ring Theory,” in Marco Fontana, Sophie Frisch, and Sarah Glaz (eds.), Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions, Springer, New York, 2014, pp. 353–375. DOI: 10.1007/978-1-4939-0925-4_20. ISBN: 978-1-4939-0924-7.
Problems represented in this directory:
- Problem 4a-i
- Problem 4a-ii
- Problem 8a
- Problem 21
- Problem 35
- Problem 37b
The corresponding paper is:
- Jiedong Jiang et al., “On some open problems in commutative algebra resolved by Rethlas.” arXiv: 2605.25259
Rethlas has also been used to solve or assist with mathematical research problems appearing in the following papers.
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“Boundedness of total Cartier indices for rational singularities in families.” arXiv: 2605.22782
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“Shokurov's global index conjecture for threefold foliations.” arXiv: 2605.22735
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“Optimal bend-and-break for foliations.” arXiv: 2605.20754
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“A question on klt type varieties of Han and Jiang.” arXiv: 2605.22250
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“On a question of Mauri and Moraga.” arXiv: 2605.22052
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“An example of a very non-movable effective divisor.” arXiv: 2605.20594
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“On a question of Kollár and Kovács.” arXiv: 2605.20585
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“Non-projective complete log canonical surfaces.” arXiv: 2606.05881
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“A Counterexample to Bhatt-Lurie's Cohomological Dimension Conjecture.” arXiv: 2606.05260
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“An Integrally Closed Reduced Ring with McCoy Localizations That Is Neither McCoy nor Locally a Domain.” arXiv: 2604.07465
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“A Counterexample to Problem 19 on Integer-valued Polynomial Rings.” arXiv: 2604.05922