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 statements:
- Lemma 3.1 · arXiv:1204.3610v2, PDF p. 3Every rational point admits a primitive rational line with weighted coefficient bounds.
- Corollary 4.2 · arXiv:1204.3610v2, PDF pp. 9–10; cited as Lemma 4.2 from an older version in NS14Dangerous rational points in the relevant partition block lie on one rational line.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
arXiv:1204.3610v2 · explicit fallback for the inaccessible Duke version of record
Jinpeng An. Two-dimensional badly approximable vectors and Schmidt's game. Duke Mathematical Journal 165 (2016), no. 2, 267–284. Reviewed in final arXiv:1204.3610v2 because the publisher PDF was inaccessible.
The Duke and Project Euclid routes returned an HTML access page rather than a PDF. The final public arXiv v2 was reviewed; this report does not claim inspection of the version of record.
Open audited source ↗01Statements2 reported findingsNo statement issues found
The two selected rational-line statements used in the recursive graph are correct.
Lemma 3.1No issue found
Every rational point admits a weighted small-coefficient rational line
arXiv:1204.3610v2, PDF p. 3 · Lemma 3.1
For , the lemma gives integers , not both zero, with , , and . This is exactly the form used in Wu–Yang Lemma 3.1.
Corollary 4.2No issue found
Dangerous rational rectangles meeting a tree square lie in one strip
arXiv:1204.3610v2, PDF pp. 9–10 · Corollary 4.2
Current v2 labels the common-strip conclusion Corollary 4.2. NS14 cites an older version where the same selected result was numbered Lemma 4.2; this is a version-locator change, not a source mismatch.
02Proofs2 reported findingsNo proof issues found
The selected conclusions are fully supported by the displayed determinant argument and the cited elementary pigeonhole lemma.
Lemma 3.1 source expansionNo issue found in the reviewed proof
BPV Lemma 1 supplies the omitted baby lemma
arXiv:1204.3610v2, PDF p. 3; BPV11 VOR pp. 1854–1855
An calls Lemma 3.1 a baby version of BPV Lemma 1 and does not repeat the proof. BPV's first pigeonhole step already proves precisely the weaker conclusion: choose two integer pairs in the weighted box with the same residue modulo and subtract. The extra BPV argument forcing a positive coefficient is not needed here.
Corollary 4.2No issue found in the reviewed proof
The common-strip conclusion follows from the internally proved common-line lemma
arXiv:1204.3610v2, PDF pp. 6–10 · Lemma 4.1 and Corollary 4.2
Lemma 4.1 proves constancy of the associated line on each relevant rational class by determinant and height estimates. Corollary 4.2 then enlarges the rational rectangles by the stated coefficient bounds and obtains the displayed strip width. The constants and indices align.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.