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:
- Theorems (a) and (b) · Journal d'Analyse Mathématique 69 (1996), 25–54; exact statements restated in EKL06Unipotent invariance and homogeneous measure classification close EKL's algebraic-measure step.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Related Annals version of record · explicit fallback for inaccessible target article
Manfred Einsiedler, Anatole Katok, and Elon Lindenstrauss. Invariant measures and the set of exceptions to Littlewood's conjecture. Annals of Mathematics 164 (2006), no. 2, 513–560. Reviewed only as an exact restatement and application witness for Margulis–Tomanov (1996).
Every retrieved payload for the exact Margulis–Tomanov article was an HTML access or challenge page, not a proof-bearing PDF. The exact EKL06 Annals version of record restates the two needed theorems and checks their hypotheses. This report therefore verifies only those statements and their applicability; it does not claim inspection of the original Margulis–Tomanov proofs.
Open audited source ↗01Statements1 reported findingNo statement issues found
The two measure-rigidity statements used by EKL06 are correctly restated in the exact related version of record, and EKL verifies their applicability.
Theorems (a) and (b) as restated in EKL06Statement and applicability verified
The homogeneous-measure conclusions match EKL's application
EKL06 VOR, measure-classification section; MT96 DOI 10.1007/BF02787100
EKL states the MT96 results for invariant ergodic measures under subgroups generated by unipotents and class- elements. It then verifies connectedness, discreteness of the lattice, generation assumptions, and invariance for the subgroup it constructs. No scope mismatch appears. The exact MT96 wording remains uninspected.
02Proofs1 reported findingFurther proof verification needed
No proof-bearing copy of the exact 1996 article was accessible.
Proofs of Theorems (a) and (b)Not independently verified
Publisher access gates prevent independent proof audit
Journal d'Analyse Mathématique 69 (1996), 25–54
The retrieved publisher and repository payloads were HTML challenge pages despite .pdf filenames, and Poppler correctly rejected them. EKL's restatement is enough to verify the logical fit of the citation but not the original proof. No correctness defect is alleged.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.