MathAudit

Paper metadata

Original submission
January 27, 2010
Latest revision
December 5, 2011 · version 2
Claimed MSC
37A17, 11J13
arXiv categories
math.DS, math.NT
Comments
37 pages, a revised version

Abstract

We prove a conjecture of G.A. Margulis on the abundance of certain exceptional orbits of partially hyperbolic flows on homogeneous spaces by utilizing a theory of modified Schmidt games, which are modifications of (α,β)(α,β)-games introduced by W. Schmidt in mid-1960s.

AI-generated audit

Audit summary

Audited against arXiv v2

Not a correctness certificate. A “Correct” result may include yellow typos or minor formal corrections that do not affect substantive soundness. It means this audit found no unresolved substantive error under the stated criteria; it does not replace expert scrutiny or formal verification.

Current report

Detailed mathematical audit

Generated August 19, 2026
01Statements2 reported findingsCorrect

The modified-game winning results for bounded and orbit-avoidance sets on homogeneous spaces, and the resulting thickness statement related to Margulis's conjecture, are correct.

Theorems 1.1 and 1.2Correct

The unstable-horospherical winning statements are correct

Pages 3–4 and 8–22 · Theorems 1.1–1.2 · arXiv:1001.5017v2

The admissible expanding region supplies a modified Schmidt game on the unstable subgroup. Quantitative non-divergence and the local product structure yield strategies for bounded forward orbits and for avoiding a prescribed countable collection of submanifolds.

Full paper, version 2 ↗
Corollary 1.3 and Theorem 1.4Correct

The global thickness consequences follow from the slice results

Pages 4–5 and 22–33 · global consequences · arXiv:1001.5017v2

Winning gives full dimension on unstable leaves, while stable and neutral directions are restored through local product coordinates and a slicing theorem. The hypotheses on the centralizer and the orbit-closure obstruction are exactly those used in this passage.

02Proofs2 reported findingsCorrect

The modified-game, non-divergence, and local-product arguments are correct and complete.

Theorem 4.2Correct and complete

The bounded-orbit game strategy is complete

Pages 11–20 · Theorem 4.2 and proof · arXiv:1001.5017v2

At every game scale quantitative non-divergence bounds the dangerous cusp set, and the expanding subgroup action leaves a legal translate outside it. Iterating over a compact exhaustion yields a uniformly bounded trajectory.

Sections 6–8Correct and complete

Orbit avoidance and the Margulis application close

Pages 21–33 · Theorem 6.1 and final applications · arXiv:1001.5017v2

Transversality controls the intersections with forbidden submanifolds, countable intersections preserve winning, and local product coordinates transfer the leafwise dimension to the full homogeneous space without losing a dimension.

03Novelty0 reported findingsNo non-novelty findings

No non-novelty findings.

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Paper
arXiv:1001.5017v2
Authors listed
Dmitry Kleinbock, Barak Weiss
Audit date
August 19, 2026
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  2. 02Submit evidenceIdentify the finding and give a formal mathematical response.
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