MathAudit

Paper metadata

Original submission
February 21, 2012
Latest revision
December 22, 2012 · version 5
Claimed MSC
11J99
arXiv categories
math.NT
Comments
Submitted to FAOM. Some new comments are added in the recent version

Abstract

We discuss several open problems in Diophantine approximation. Among them there are famous Littlewood's and Zaremba's conjectures as well as some new and not so famous problems.

AI-generated audit

Audit summary

Audited against arXiv v5

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 20, 2026
01Statements2 reported findingsCorrect

The survey's central formulations of open problems, quoted theorems, and exponent relations are mathematically consistent and correctly scoped as known results or questions.

Sections 2-3Correct

Littlewood-type and best-approximation formulations are consistent

Pages 2-20 · Littlewood conjecture, winning sets, and best approximations · arXiv:1202.4539v5

The multiplicative minima, badly approximable sets, and lattice formulations preserve their quantifiers under the stated transference correspondences. The quoted winning and inhomogeneous results are clearly attributed, and the subsequent questions do not silently assert their conclusions.

Full survey, version 5 ↗
Sections 4-6Correct

Exponent and positive-integer questions use compatible normalizations

Pages 20-42 · Diophantine exponents, positive coordinates, and open questions · arXiv:1202.4539v5

The ordinary and uniform exponents are consistently distinguished, and the displayed Jarnik and transference inequalities use the appropriate dimensions. Statements labeled as conjectures or questions are not treated as theorems, while proved examples are separated from proposed optimal bounds.

02Proofs2 reported findingsCorrect

This is principally a problem survey; the internal derivations supporting its comparisons are correct, and cited results are identified rather than reproved incompletely.

Best-approximation sectionsCorrect and complete

Minkowski and determinant estimates are applied with the right scales

Pages 16-28 · best approximations and exponent derivations · arXiv:1202.4539v5

The successive-minimum bounds pair the current approximation error with the next height, and the determinant arguments use enough linearly independent integer vectors before invoking a nonzero integral determinant. The resulting growth inequalities have the stated exponent directions.

Peres-Schlag discussionCorrect and complete for the claims made

The lacunary avoidance mechanism is represented correctly

Pages 12-16 · Peres-Schlag method and winning-set discussion · arXiv:1202.4539v5

The survey uses the method only to state the established block-sum criterion and its consequences. It does not claim that the brief discussion itself proves a new theorem, and the dependence between the lacunarity scale, removed interval lengths, and positive surviving measure is stated in the correct direction.

03Novelty0 reported findingsNo non-novelty findings

No non-novelty findings.

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Paper
arXiv:1202.4539v5
Authors listed
Nikolay G. Moshchevitin
Audit date
August 20, 2026
  1. 01Establish identityMatch an authenticated scholarly identity to this paper.
  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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