Published paper
Role in dependence graphs
Proof-critical source
Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
This paper is included only for the following marked statement:
- Theorem 1 · arXiv:0807.3863, theorem and proofA lacunary toral shrinking-target orbit has full Hausdorff dimension for every target.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
arXiv:0807.3863v2 · disclosed proof-bearing fallback for the Mathematika article
Yann Bugeaud, Stephen Harrap, Simon Kristensen, and Sanju Velani. On shrinking targets for actions on tori. Mathematika 56 (2010), no. 2, 193–202.
The Cambridge version-of-record PDF was not anonymously available during this audit. Exact arXiv v2 source was reviewed; no publisher-file identity is claimed.
Open audited source ↗01Statements1 reported findingNo statement issues found
The selected full-dimension shrinking-target theorem is correctly stated and gives exactly the nonempty inhomogeneously badly approximable set used by Fishman–Lambert–Merrill–Simmons.
Theorem 1No issue found
Every toral translation matrix has a full-dimensional uniformly avoiding target set
arXiv:0807.3863v2 · Theorem 1
For every real matrix , the set of shifts bounded uniformly away from the orbit at the Dirichlet scale has full Hausdorff dimension. In particular it is nonempty, which is precisely the contradiction input in focal Lemma 2.6.
02Proofs3 reported findingsNo proof issues found
The selected ball-case proof is correct: exact arXiv v2 reproduces the KTV retained-child condition with the required lower bound, and its single-metric specialization is unaffected by the broader product-coordinate issue recorded on the KTV source.
Application of KTV Theorem 1No issue found in the reviewed proof
The retained-child condition has the required lower-bound direction
arXiv:0807.3863v2 · reproduced KTV theorem and proof of Theorem 1
Exact v2 states , the direction required for the Cantor lower-dimension argument. Its bad-child estimate is an upper bound with constant , so a positive proportion of children remains at every stage.
Ball-case specializationNo issue found in the reviewed proof
The selected application uses one ambient metric rather than a product of coordinate conditions
arXiv:0807.3863v2 · KTV criterion and resonant-set construction
BHKV applies the criterion to ordinary metric balls and distances from resonant affine hyperplanes. The coordinatewise-versus-existential distinction that needs repair in KTV's more general rectangular framework does not arise in this one-metric application.
Remaining inputsCorrect modulo represented sources
The lacunary and convex-body estimates align
arXiv:0807.3863v2 · proof of Theorem 1
The Bugeaud–Laurent lacunary subsequence, Cassels linear-forms theorem, and local counting estimates are used with compatible dimensions and scales. No further contradiction or missing case was found in the selected proof chain.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.