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:
- Main semisimple spectral results · American Journal of Mathematics 88 (1966), 154–178; consumer application Moore80 VOR p. 165Supplies the semisimple ergodicity and spectral conclusion used in Moore's final reduction.
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 Moore 1966 version of record
Calvin C. Moore. The Mautner phenomenon for general unitary representations. Pacific Journal of Mathematics 86 (1980), no. 1, 155–169.
The JSTOR route for Moore's 1966 American Journal of Mathematics article returned an HTML access gate, and no valid proof-bearing public copy was established. Moore 1980 is a distinct exact version of record that explicitly invokes the 1966 main semisimple spectral results in the proof of Theorem 5.2; it confirms the consumer role but does not reproduce or verify the inaccessible original proof.
Open audited source ↗01Statements1 reported findingNo statement issues found
The semisimple spectral result has exactly the absolute-continuity consequence used as Moore 1980's alternative proof of Theorem 5.2.
Main semisimple spectral resultsCorrect · verified at consumer restatement level
A noncompact semisimple direction has absolutely continuous spectrum off invariant vectors
Exact cited article: American Journal of Mathematics 88 (1966), 154–178 · consumer application Moore 1980 VOR p. 165, proof of Theorem 5.2
Moore 1980 forms the reductive group generated by the semisimple subgroup and the one-parameter group under study. Because an irreducible representation is scalar on the center and is essentially determined by its restriction to , Moore says that the main results of the 1966 paper give absolute continuity of the infinitesimal generator on the orthogonal complement of the -invariant vectors. This is the exact semisimple conclusion needed for Theorem 5.2.
02Proofs1 reported findingFurther proof verification needed
The original 1966 proof and its recursive parents could not be inspected.
Semisimple spectral proofNot independently verified the original proof
The consumer citation is exact, but the original proof remains behind an access gate
JSTOR stable record 2373052 checked · Moore 1980 VOR p. 165 inspected as a related fallback
The title, author, American Journal of Mathematics citation, DOI, MR number, and zbMATH record are exact, but the JSTOR route supplied only an HTML gate. Moore 1980 invokes the 1966 main results as an alternative justification and does not reproduce their proof or theorem-number locators. No downstream proof ancestry is asserted speculatively; this branch terminates with an explicit unverified-proof status.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.