MathAudit

Paper metadata

Original submission
April 2, 2003
Claimed MSC
37D50, 37D40, 32G15
arXiv categories
math.DS
Comments
10 pages, LaTeX
Journal reference
IMRN 2004, no. 30, 1551-1560

Abstract

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories.The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.

AI-generated audit

Audit summary

Audited against arXiv v1

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 thickness of the set of quadratic differentials with bounded Teichmuller geodesic, including the stated directional refinements, is correct.

Theorem 1.1Correct

Bounded geodesics form a thick set

Pages 2–3 · Theorem 1.1 · arXiv:math/0304029v1

The local stable and unstable coordinates identify bounded forward trajectories with a winning avoidance condition. Winning sets have full Hausdorff dimension in every open chart, and the local-to-global passage preserves thickness.

Full paper, version 1 ↗
Directional refinementsCorrect

The slice statements use the correct orbit directions

Pages 3–5 · refined statements · arXiv:math/0304029v1

The horocyclic and rotational slices are matched to the corresponding stable or transverse coordinates, so the full-dimension conclusions occur in the dimensions claimed and do not interchange forward and two-sided boundedness.

02Proofs2 reported findingsCorrect

The Schmidt-game construction and its transfer through moduli-space coordinates are correct and complete.

Game constructionCorrect and complete

The strategy avoids every short saddle connection

Pages 5–8 · Schmidt-game argument · arXiv:math/0304029v1

At each scale the strategy removes the finitely relevant resonant directions, and the separation estimate ensures that one legal move avoids all of them. The surviving point therefore has a uniform lower bound on saddle-connection lengths along the required geodesic.

Local-coordinate reductionCorrect and complete

Winning and dimension are transferred without a missing case

Pages 8–10 · completion of the main theorem · arXiv:math/0304029v1

The coordinate maps are locally bi-Lipschitz on the compact pieces used in the argument, so winning full dimension passes to the relevant slices and then to arbitrary open subsets of the stratum.

03Novelty0 reported findingsNo non-novelty findings

No non-novelty findings.

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Paper
arXiv:math/0304029v1
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.
  3. 03Re-evaluateA separate agent checks the response and records a disposition.
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