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–B · Duke 63 (1991), 235–280; LW01 manuscript p. 5, Theorem 3.3; Ratner 1994 survey VOR pp. 239–240, Theorems 3–4 and 6Orbit closures of unipotent-generated actions are homogeneous finite-volume orbits, with the one-parameter distribution conclusion.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Ratner 1994 survey version of record · explicit related-publication fallback for inaccessible Ratner 1991 version of record
Marina Ratner. Invariant measures and orbit closures for unipotent actions on homogeneous spaces. Geometric and Functional Analysis 4 (1994), no. 2, 236–257.
The Project Euclid download route for Ratner's 1991 Duke article returned an HTML access gate rather than the proof-bearing version of record. Ratner's exact 1994 GAFA survey is a distinct version of record that restates the orbit-closure and uniform-distribution results, but it does not reproduce or verify the inaccessible 1991 proof.
Open audited source ↗01Statements1 reported findingNo statement issues found
Ratner's orbit-closure and equidistribution conclusions are the exact results used in Lindenstrauss–Weiss's homogeneous-orbit reduction.
Theorems A–BNo issue found
Unipotent orbit closures are homogeneous and one-parameter orbits equidistribute
Exact cited locator: Theorems A–B in Duke Mathematical Journal 63 (1991), 235–280 · consumer restatement in Lindenstrauss–Weiss author manuscript p. 5, Theorem 3.3 · related Ratner survey VOR pp. 239–240, Theorems 3–4 and 6
For a connected Lie group with a lattice, Ratner's topological theorem makes the closure of an orbit of a subgroup generated by unipotent one-parameter subgroups a homogeneous finite-volume orbit. In the one-parameter case the positive-time orbit is uniformly distributed in that closure. Lindenstrauss–Weiss states the exact homogeneous-closure specialization it needs as Theorem 3.3, and Ratner's 1994 survey independently records the orbit-closure statement in Theorems 3–4 and the uniform-distribution statement in Theorem 6.
02Proofs1 reported findingFurther proof verification needed
The exact 1991 proof was inaccessible, so neither it nor its recursive proof ancestry was verified.
Theorems A–B proofsNot independently verified the original proofs
The later survey confirms the conclusions but is not a substitute proof
Project Euclid access gate checked for Duke 63 (1991), 235–280 · Ratner 1994 survey VOR pp. 239–240 inspected
The exact Duke article record and DOI were identified, but the article download yielded an HTML access gate. The related 1994 version of record states the needed results and gives only an outline and references to Ratner's proof series. It therefore supports the statement-level audit and the consumer mapping, while leaving the original proof and any proof-critical parents explicitly unverified. No surrogate proof is attributed to the survey.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.