Published paper
Role in dependence graphs
Proof-critical source
Winning property of counterexamples to Uniform Littlewood's Conjecture
This paper is included only for the following marked statement:
- Proposition 3.5 · arXiv:1311.1560v1, PDF p. 7HAW subsets of a manifold have the required thickness, countable-intersection, and diffeomorphism properties.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
arXiv:1311.1560v1 · explicit public counterpart of the Contemporary Mathematics chapter
Dmitry Kleinbock and Barak Weiss. Values of binary quadratic forms at integer points and Schmidt games. In Recent Trends in Ergodic Theory and Dynamical Systems, Contemporary Mathematics 631 (2015), 77–92.
The exact AMS chapter PDF was not publicly downloadable during this audit. The sole arXiv version was reviewed as the explicit proof-bearing counterpart; no publisher-file inspection is claimed.
Open audited source ↗01Statements1 reported findingNo statement issues found
The selected manifold hyperplane-absolute-winning closure statement is correct.
Proposition 3.5No issue found
HAW subsets of a manifold have the three advertised closure properties
arXiv:1311.1560v1, PDF p. 7 · Proposition 3.5
The proposition states that HAW subsets of a manifold are thick, are closed under countable intersections, and remain HAW under diffeomorphisms. These are exactly the properties imported by Wu–Yang.
02Proofs1 reported findingNo proof issues found
Proposition 3.5 is a direct chartwise consequence of the Euclidean HAW properties and the preceding atlas-independence argument.
Proof of Proposition 3.5No issue found in the reviewed proof
The chart reduction preserves all three conclusions
arXiv:1311.1560v1, PDF pp. 5–7 · Propositions 3.1, 3.3–3.5
Proposition 3.1 supplies the Euclidean properties. Propositions 3.3 and 3.4 show that HAW is checked chartwise and does not depend on a compatible atlas. Applying those statements in each chart proves Proposition 3.5 without an omitted geometric step.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.