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:
- Theorem 2.13 · Annals 96 (1972), 296–317; application in EKL06 VOR pp. 544–545A suitable conjugate Cartan subgroup meets the lattice in a uniform lattice, producing the compact diagonal orbit required in EKL's Corollary 1.4.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
EKL 2006 version of record · explicit related-publication fallback for inaccessible PR72 version of record
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.
The official Annals record for Prasad–Raghunathan 1972 exposes the exact metadata but no PDF, and the JSTOR PDF route returned an HTML access gate rather than a proof-bearing copy. EKL 2006 is a distinct, exact version of record that cites Theorem 2.13 and records precisely how it is applied; it does not replace or verify the inaccessible original proof.
Open audited source ↗01Statements1 reported findingNo statement issues found
Theorem 2.13 has the Cartan-lattice existence conclusion used in EKL's Corollary 1.4.
Theorem 2.13No issue found
A lattice meets a suitable conjugate Cartan subgroup cocompactly
Exact cited locator: Theorem 2.13 in Annals of Mathematics 96 (1972), 296–317 · application in EKL06 VOR pp. 544–545
The cited result says that for a semisimple analytic Lie group, a lattice, and a Cartan subgroup, a suitable conjugate Cartan subgroup meets the lattice in a uniform lattice. EKL applies this in its rational reductive setting to obtain a conjugate maximal torus that is defined over and -anisotropic, hence a compact -orbit inside the algebraic orbit supporting the measure. This theorem number and conclusion are independently corroborated by exact later sources, including EKL's own application.
02Proofs1 reported findingFurther proof verification needed
The exact 1972 proof could not be inspected, so its recursive proof ancestry remains unresolved.
Theorem 2.13 proofNot independently verified the original proof
No proof-bearing copy of the cited article was obtained
Annals official record and JSTOR stable-PDF route checked · EKL06 VOR pp. 544–545 inspected as a related fallback
The Annals page supplies the exact title, authors, volume, issue, pages, DOI, MR number, and zbMATH number, but no article PDF. The JSTOR PDF endpoint returned an HTML challenge. EKL verifies the role and applicability of Theorem 2.13 but does not reproduce its proof. Accordingly no proof-critical parents of the original argument are asserted speculatively.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.