Pseudo-Formalization for Automatic Proof Verification
Paper • 2605.20531 • Published
arxiv_id stringlengths 10 10 | version stringclasses 2
values | url stringlengths 32 32 | v1_date timestamp[s]date 2025-01-02 22:35:26 2025-05-26 23:23:38 | category stringlengths 5 7 | category_name_readable stringlengths 5 30 | comments stringlengths 43 395 | Location of Error stringlengths 7 37 | Liscence stringclasses 4
values | title_extracted_from_tex stringlengths 23 127 |
|---|---|---|---|---|---|---|---|---|---|
2501.01561 | v1 | https://arxiv.org/abs/2501.01561 | 2025-01-02T22:35:26 | math.FA | Functional Analysis | 45 pages. Various improvements of the presentation, and an error in the proof of Theorem 19 is corrected | Theorem 19 | CC 4.0 | On coarse geometry of separable dual Banach spaces |
2501.04482 | v2 | https://arxiv.org/abs/2501.04482 | 2025-01-08T13:06:44 | math.LO | Logic | In this version, the erroneous Proposition 6.10 is corrected | Proposition 6.10 | arXiv.org - Non-exclusive license to distribute | Categories of orthosets and adjointable maps |
2501.05996 | v1 | https://arxiv.org/abs/2501.05996 | 2025-01-10T14:28:41 | math.AT | Algebraic Topology | 43 pages, 4 figures. Corrected an error in the proof of Theorem B. Moved the section on interval decomposability to another preprint. Some terminology has been renamed. Other minor changes | Theorem B | CC BY-SA 4.0 | Poset functor cocalculus and applications to topological data analysis |
2501.08877 | v1 | https://arxiv.org/abs/2501.08877 | 2025-01-15T15:48:33 | math.AP | Analysis of PDEs | Corrected a major error in the proof of Theorem 3.1 and revised other flawed proofs | Theorem 3.1 | arXiv.org - Non-exclusive license to distribute | Connecting SPDE to SGMs |
2501.08692 | v2 | https://arxiv.org/abs/2501.08692 | 2025-01-15T09:55:08 | math.GR | Group Theory | 19 pages. Fixes a mistake in the proof of Theorem 1.2, by refining the definition of balanced Artin groups | Theorem 1.2 | CC 4.0 | On the $\Sigma^1$ and $\Sigma^2$-invariants of Artin groups |
2501.17504 | v1 | https://arxiv.org/abs/2501.17504 | 2025-01-29T09:21:36 | math.AC | Commutative Algebra | Removed redundant and incorrect proof of Lemma 2.3, updated introduction | Lemma 2.3 | arXiv.org - Non-exclusive license to distribute | Rational Invariants of even degree polynomials under the orthogonal group |
2501.13445 | v2 | https://arxiv.org/abs/2501.13445 | 2025-01-23T07:52:28 | math.OC | Optimization and Control | We find a counterexample to illustrate that Theorem 5 (iii) and (iv) are incorrect | Theorem 5 | arXiv.org - Non-exclusive license to distribute | Comments and extensions on ``State-equivalent form and minimum-order compensator design for rectangular descriptor systems'' |
2501.05489 | v1 | https://arxiv.org/abs/2501.05489 | 2025-01-09T06:01:52 | math.DG | Differential Geometry | I find that there is a mistake in the proof of Theorem 2.2, I give a new proof in this version | Theorem 2.2 | arXiv.org - Non-exclusive license to distribute | Singularity of mean curvature flow with bounded mean curvature and Morse index |
2501.04321 | v2 | https://arxiv.org/abs/2501.04321 | 2025-01-08T07:35:49 | math.CO | Combinatorics | I thank Nathan Bowler for pointing out a critical mistake at the end of my claimed proof of Theorem 2.1. The set ${^*}A \cap {^*}\mathbb{I}$ is not necessarily contained in its internal star extension as it was claimed in the last line of that proof. The purported proofs of both conjectures had this issue. An expositor... | Theorem 2.1 | arXiv.org - Non-exclusive license to distribute | Matroid intersection and packing/covering conjectures are true in the class of finitary matroids |
2502.02254 | v1 | https://arxiv.org/abs/2502.02254 | 2025-02-04T12:02:47 | math.NT | Number Theory | Fixed proof of Lemma 8, other minor changes | Lemma 8 | CC 4.0 | Non-isomorphic abelian varieties with the same arithmetic |
2502.10278 | v1 | https://arxiv.org/abs/2502.10278 | 2025-02-14T16:36:38 | math.GR | Group Theory | 25 pages, comments welcome; version 2 includes the addition of a section on Dedekind domains and the correction of an error in Proposition 5.1 of version 1 | Proposition 5.1 | CC 4.0 | Profinite Rigidity over Noetherian Domains |
2502.00898 | v1 | https://arxiv.org/abs/2502.00898 | 2025-02-02T20:16:50 | math.DS | Dynamical Systems | Lemma 4.1 has been corrected after N. Tedesco pointed out a mistake in the calculations. The main results are unchanged | Lemma 4.1 | CC 4.0 | Finite codimension stability of invariant surfaces |
2502.10890 | v1 | https://arxiv.org/abs/2502.10890 | 2025-02-15T19:46:27 | cs.DS | Data Structures and Algorithms | Appeared at ICALP 2025. Fixed small mistake in Lemma 20 | Lemma 20 | arXiv.org - Non-exclusive license to distribute | Light Edge Fault Tolerant Graph Spanners |
2502.17415 | v1 | https://arxiv.org/abs/2502.17415 | 2025-02-24T18:48:44 | math.AT | Algebraic Topology | Version 2: fixed statement and proof of Lemma 3.5. 33 pages, 10 figures. Comments are welcome! | Lemma 3.5 | arXiv.org - Non-exclusive license to distribute | Rectification of dendroidal left fibrations |
2502.05831 | v1 | https://arxiv.org/abs/2502.05831 | 2025-02-09T09:39:50 | math.GR | Group Theory | An inaccuracy in the proof of Theorem 5.1 (6) has been fixed | Theorem 5.1 | arXiv.org - Non-exclusive license to distribute | Equationally separable classes of groups |
2503.00849 | v2 | https://arxiv.org/abs/2503.00849 | 2025-03-02T10:53:27 | math.PR | Probability | Correction of the speed of convergence in Theorem 4.5 | Theorem 4.5 | arXiv.org - Non-exclusive license to distribute | Empirical distribution of ancestral lineages in populations with density-dependent interactions |
2503.21136 | v1 | https://arxiv.org/abs/2503.21136 | 2025-03-27T03:55:53 | math.NT | Number Theory | 14 pages, 1 figure, Minor corrections to Theorem 1.5 and Lemma 2.1 | Theorem 1.5, Lemma 2.1 | arXiv.org - Non-exclusive license to distribute | Power-free palindromes and reversed primes |
2503.06267 | v1 | https://arxiv.org/abs/2503.06267 | 2025-03-08T16:26:04 | math.KT | K-Theory and Homology | 73 pages. Proposition 3.3 was corrected and references were added | Proposition 3.3 | CC 4.0 | magnetic Equivariant K-theory |
2503.10313 | v1 | https://arxiv.org/abs/2503.10313 | 2025-03-13T12:47:45 | math.RA | Rings and Algebras | 29 pages, 1 table. Corrected Theorem 4.8, added Corollary 4.9, added Table 1, added Proposition 7.12 and modified remarks in the last section. Many other typo corrected | Theorem 4.8 | CC 4.0 | Central series' and ($n$)-isoclinism of skew left braces |
2503.08957 | v2 | https://arxiv.org/abs/2503.08957 | 2025-03-11T23:20:33 | math.CV | Complex Variables | The proof of Lemma 5 is incorrect: we do not have $H(M_\mathcal S)\subset M_\infty$ since $M_\infty$ is defined by 2 equations and $Im(w)=0$ has not be considered in the proof. This affects the main result, and we do not know whether it is true | Lemma 5 | CC 4.0 | real algebraic surfaces biholomorphically equivalent but not algebraically equivalent |
2503.02340 | v1 | https://arxiv.org/abs/2503.02340 | 2025-03-04T07:02:49 | math.AP | Analysis of PDEs | 21 Pages. Corrected a statement in Lemma 2.2 to address a minor gap in the proof from the previous version | Lemma 2.2 | CC 4.0 | Sharp stability for critical points of the Sobolev inequality in the absence of bubbling |
2504.10302 | v1 | https://arxiv.org/abs/2504.10302 | 2025-04-14T15:11:12 | math.CO | Combinatorics | 16 pages, corrected version with substantial modifications, Theorem 1.2 in the former version was not correct and has changed, new coauthor | Theorem 1.2 | arXiv.org - Non-exclusive license to distribute | Nonnegativity of signomials with Newton simplex over convex sets |
2504.02276 | v1 | https://arxiv.org/abs/2504.02276 | 2025-04-03T04:50:47 | math.MG | Metric Geometry | 9 pages; substantial revisions throughout, including removing Lemma 4.3, which was in error, adding Theorem 1.3, and correcting the bounds in the main theorem | Lemma 4.3, main theorem | arXiv.org - Non-exclusive license to distribute | DISTORTION FROM SPHERES INTO EUCLIDEAN SPACE |
2504.19891 | v1 | https://arxiv.org/abs/2504.19891 | 2025-04-28T15:24:55 | math.GT | Geometric Topology | 14 pages, 1 figure, comments are welcome! v2 : corrected gap in proof of Proposition 4.3, updated reference to recent preprint by C. Lecuire (arXiv:2510.07087) | Proposition 4.3 | CC 4.0 | Bending parameterization of one-sided degenerated Kleinian surface groups |
2504.08090 | v1 | https://arxiv.org/abs/2504.08090 | 2025-04-10T19:36:16 | math.NT | Number Theory | The previous proof of proposition 3 was incorrect, the hypotheses of proposition 3 (ii) have been narrowed to allow a correct proof. It does not change the conclusions we draw of the proposition. The introduction was reformulated in a (hopefully) clearer way | Proposition 3 | arXiv.org - Non-exclusive license to distribute | Regular version of the inverse Galois problem for skew fields |
2504.15000 | v1 | https://arxiv.org/abs/2504.15000 | 2025-04-21T10:00:07 | math.AP | Analysis of PDEs | We have corrected the statement and argument of Proposition 4.1(b). Comments are welcome | Proposition 4.1(b) | arXiv.org - Non-exclusive license to distribute | Quasilinear problems with mixed local-nonlocal operator and concave-critical nonlinearities: Multiplicity of positive solutions |
2504.03243 | v1 | https://arxiv.org/abs/2504.03243 | 2025-04-04T07:46:53 | math.AG | Algebraic Geometry | 76 pages. I have corrected the errors in the version 1. Theorem 3.4 and Corollary 3.5 were not true as they are. There is a counterexample to Corollary 3.5 with $p=q=0,$ given by the harmonic function $r^{2-2n}.$ Also Lemma 6.5 was not really proved | Theorem 3.4, Corollary 3.5, Lemma 6.5 | Deformations of Compact Calabi--Yau Conifolds | |
2504.06686 | v1 | https://arxiv.org/abs/2504.06686 | 2025-04-09T08:46:05 | math.PR | Probability | We fix a gap in the proofs of Theorem 2.3 and 2.4 by imposing an additional technical assumption, 18 pages | Theorem 2.3, Theorem 2.4 | arXiv.org - Non-exclusive license to distribute | Quantitative Halmos-Savage theorems and robust large financial markets |
2504.08105 | v1 | https://arxiv.org/abs/2504.08105 | 2025-04-10T20:02:39 | math.DG | Differential Geometry | 47 pages. Comments are welcome. There is a mistake in Lemma 5.7 of the previous version, which implies that the energy reduction result holds only for manifolds that are both non-umbilic. Consequently, we can establish an energy reduction criterion that may help prevent topology loss, rather than a non-existence result | Lemma 5.7 | CC 4.0 | Non-existance of minimizers for Fourth order Willmore energy |
2505.20576 | v2 | https://arxiv.org/abs/2505.20576 | 2025-05-26T23:23:38 | math.DG | Differential Geometry | 29 pages. v3 is a substantial rewrite of the paper. Versions 1 and 2 contain a fatal error in Lemma 3.11 (old numbering), so the main claims of those versions are invalid as stated. This version gives a revised symmetry result and includes results for expanders | Lemma 3.11 | CC 4.0 | Uniqueness of asymptotically cylindrical steady gradient Ricci solitons |
2505.10683 | v2 | https://arxiv.org/abs/2505.10683 | 2025-05-15T19:59:22 | math.RT | Representation Theory | Clarified the notion of cuts vs. gradings. Removed the incorrect Proposition 2.15 (v2) and adapted affected proofs. 28 pages. Comments welcome! | Proposition 2.15 | arXiv.org - Non-exclusive license to distribute | $2$-representation infinite algebras from non-abelian subgroups of $\SL_3$ \text{Part I: Extensions of abelian groups} |
2505.15159 | v1 | https://arxiv.org/abs/2505.15159 | 2025-05-21T06:24:34 | math.AG | Algebraic Geometry | 22 pages; V2: corrected a mistake in Lemma 4.1 of v1; definitive version, to appear in Forum of Mathematics Sigma | Lemma 4.1 | CC 4.0 | Rank jumps and Multisections of elliptic fibrations on K3 surfaces |
2505.08549 | v2 | https://arxiv.org/abs/2505.08549 | 2025-05-13T13:21:39 | math.NT | Number Theory | 10 pages; The statement and proof of Lemma 8 have been revised and corrected, Proof of Theorem 1 is rewritten | Lemma 8 | CC 4.0 | A generalization of Dumas irreducibility criterion |
2505.04296 | v1 | https://arxiv.org/abs/2505.04296 | 2025-05-07T10:08:03 | math.GR | Group Theory | In this version, Theorem 2 and its proof have been corrected | Theorem 2 | CC 4.0 | $n$-Valued Groups, Kronecker Sums, and Wendt's $(x, y, z)$-Matrices |
2505.01716 | v1 | https://arxiv.org/abs/2505.01716 | 2025-05-03T06:59:21 | math.AG | Algebraic Geometry | Lemma 4.2 in v1 is wrong. We modify the proof of Theorem 4.1 | Lemma 4.2 | arXiv.org - Non-exclusive license to distribute | Variation of Tannaka groups of perverse sheaves in family |
ArxivMathGradingBench
A benchmark of 35 arXiv mathematics papers that contained an error later corrected by the authors in a subsequent version, each annotated with the location of the error. Introduced in Pseudo-Formalization for Automatic Proof Verification to evaluate LLM proof verifiers on real research-level mathematics.
Downloading the papers
This dataset provides the paper metadata and error annotations. To download the paper PDFs, follow the instructions in the code repository:
https://github.com/Slim205/pseudo-formalization
Columns
| column | description |
|---|---|
arxiv_id |
arXiv identifier (e.g. 2501.04482) |
version |
paper version used by the benchmark (e.g. v1 / v2) |
url |
arXiv abstract URL |
v1_date |
date of the first arXiv version |
category |
arXiv subject class (e.g. math.FA) |
category_name_readable |
human-readable subject name |
comments |
the author's revision comment (often describing the fix) |
Location of Error |
ground-truth error location(s), e.g. Theorem 19 |
Liscence |
the paper's license as recorded on arXiv |
title_extracted_from_tex |
paper title |
Citation
@article{barkallah2026pseudo,
title={Pseudo-Formalization for Automatic Proof Verification},
author={Barkallah, Slim and Bailey, Luke and Wen, Kaiyue and Abouzaid, Mohammed and Ma, Tengyu},
journal={arXiv preprint arXiv:2605.20531},
year={2026}
}
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