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 statements:
- Proposition 4.1 · Duke 44 (1977), 129–155; consumer restatement Moore80 VOR p. 164Gives the homogeneous-space spectral result imported in Moore's Theorem 5.1.
- Proposition 5.1 · Duke 44 (1977), 129–155; consumer restatement Moore80 VOR pp. 164–165Gives the absolute-continuity reduction imported in Moore's Theorem 5.2.
AI-generated audit
Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Moore 1980 version of record · explicit related-publication fallback for inaccessible Dani 1977 version of record
Calvin C. Moore. The Mautner phenomenon for general unitary representations. Pacific Journal of Mathematics 86 (1980), no. 1, 155–169.
The IAS record for Dani 1977 says that full text is unavailable, and the exact Project Euclid download route returned an HTML access gate rather than the proof-bearing Duke article. Moore 1980 is a distinct exact version of record that identifies Dani's Propositions 4.1 and 5.1 and states precisely how their arguments are adapted; it does not reproduce or verify the inaccessible original proofs.
Open audited source ↗01Statements2 reported findingsNo statement issues found
The spectral conclusions of Propositions 4.1 and 5.1 match the two reductions for which Moore 1980 explicitly invokes them.
Proposition 4.1Correct · verified at consumer restatement level
The nilradical quotient carries Lebesgue spectrum away from its fixed vectors
Exact cited locator: Dani 1977, Proposition 4.1, Duke Mathematical Journal 44, 129–155 · consumer restatement Moore 1980 VOR p. 164, Theorem 5.1 and proof
Moore states that Dani proves precisely the homogeneous-space version of Theorem 5.1: for the subgroup associated with the maximal nilradical subalgebra on which the relevant semisimple factor acts trivially modulo , the generator has Lebesgue spectrum on the orthogonal complement of the -fixed vectors. Moore replaces Dani's geometric preliminary Lemma 4.2 by his own Theorem 4.2 and says the remaining representation-theoretic argument carries over word for word.
Proposition 5.1Correct · verified at consumer restatement level
The remaining semisimple factor has absolutely continuous spectrum off its invariant vectors
Exact cited locator: Dani 1977, Proposition 5.1, Duke Mathematical Journal 44, 129–155 · consumer restatement Moore 1980 VOR pp. 164–165, Theorem 5.2 and proof
After the nilradical reduction, Moore invokes Dani's Proposition 5.1 to obtain absolute continuity for the generator on the orthogonal complement of the vectors invariant under the selected semisimple subgroup . This is the exact conclusion needed before factoring out in the final proof of Moore's Theorem 1.1.
02Proofs1 reported findingFurther proof verification needed
The exact Duke proofs and their recursive ancestry remain inaccessible; Moore's later adaptation verifies their role but is not a substitute proof.
Propositions 4.1 and 5.1 proofsNot independently verified the original proofs
No proof-bearing copy of the cited article was obtained
IAS item 74496 and Project Euclid DOI route checked · Moore 1980 VOR pp. 164–165 inspected as a related fallback
The IAS record supplies the exact title, author, journal, volume, issue, pages, DOI, and official Project Euclid link but explicitly reports that full text is unavailable. The Project Euclid PDF endpoint returned an HTML access gate. Moore gives the exact consumer mappings and describes the modifications, but omits Dani's underlying representation-theoretic details. Consequently the original proofs and any further proof-critical parents are left candidly unverified rather than inferred.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.