{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SL5OPAT5ICYYMEODW4EUQHBNHR","short_pith_number":"pith:SL5OPAT5","schema_version":"1.0","canonical_sha256":"92fae7827d40b18611c3b709481c2d3c756925bb171827b88350d68af818bbb1","source":{"kind":"arxiv","id":"1102.0848","version":1},"attestation_state":"computed","paper":{"title":"Lifting mixing properties by Rokhlin cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Parreau, M. Lemanczyk","submitted_at":"2011-02-04T07:45:55Z","abstract_excerpt":"We study the problem of lifting various mixing properties from a base automorphism $T\\in {\\rm Aut}\\xbm$ to skew products of the form $\\tfs$, where $\\va:X\\to G$ is a cocycle with values in a locally compact Abelian group $G$, $\\cs=(S_g)_{g\\in G}$ is a measurable representation of $G$ in ${\\rm Aut}\\ycn$ and $\\tfs$ acts on the product space\n  $(X\\times Y,\\cb\\ot\\cc,\\mu\\ot\\nu)$ by $$\\tfs(x,y)=(Tx,S_{\\va(x)}(y)).$$ It is also shown that whenever $T$ is ergodic (mildly mixing, mixing) but $\\tfs$ is not ergodic (is not mildly mixing, not mixing), then on a non-trivial factor $\\ca\\subset\\cc$ of $\\cs$ t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.0848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-04T07:45:55Z","cross_cats_sorted":[],"title_canon_sha256":"29b6a2c7b221fa20f7cb27770158bc9746ba61634424b26531f06aea572fdf2e","abstract_canon_sha256":"f701d6d7db9a7732c1fe0bd9a181f95f00ec3c4f7a67450b258ed101e9417894"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.503297Z","signature_b64":"OJpSTpHQj+RlMmDRbMug7TH99dh0g4uQ3dstJG5BW0xYjS/LsKHipTPReuBXrGa4rG5OoKkHQHVVTGa92VWmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fae7827d40b18611c3b709481c2d3c756925bb171827b88350d68af818bbb1","last_reissued_at":"2026-05-18T04:30:03.502883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.502883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting mixing properties by Rokhlin cocycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"F. Parreau, M. Lemanczyk","submitted_at":"2011-02-04T07:45:55Z","abstract_excerpt":"We study the problem of lifting various mixing properties from a base automorphism $T\\in {\\rm Aut}\\xbm$ to skew products of the form $\\tfs$, where $\\va:X\\to G$ is a cocycle with values in a locally compact Abelian group $G$, $\\cs=(S_g)_{g\\in G}$ is a measurable representation of $G$ in ${\\rm Aut}\\ycn$ and $\\tfs$ acts on the product space\n  $(X\\times Y,\\cb\\ot\\cc,\\mu\\ot\\nu)$ by $$\\tfs(x,y)=(Tx,S_{\\va(x)}(y)).$$ It is also shown that whenever $T$ is ergodic (mildly mixing, mixing) but $\\tfs$ is not ergodic (is not mildly mixing, not mixing), then on a non-trivial factor $\\ca\\subset\\cc$ of $\\cs$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0848","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.0848","created_at":"2026-05-18T04:30:03.502941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.0848v1","created_at":"2026-05-18T04:30:03.502941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0848","created_at":"2026-05-18T04:30:03.502941+00:00"},{"alias_kind":"pith_short_12","alias_value":"SL5OPAT5ICYY","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SL5OPAT5ICYYMEOD","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SL5OPAT5","created_at":"2026-05-18T12:26:41.206345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR","json":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR.json","graph_json":"https://pith.science/api/pith-number/SL5OPAT5ICYYMEODW4EUQHBNHR/graph.json","events_json":"https://pith.science/api/pith-number/SL5OPAT5ICYYMEODW4EUQHBNHR/events.json","paper":"https://pith.science/paper/SL5OPAT5"},"agent_actions":{"view_html":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR","download_json":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR.json","view_paper":"https://pith.science/paper/SL5OPAT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.0848&json=true","fetch_graph":"https://pith.science/api/pith-number/SL5OPAT5ICYYMEODW4EUQHBNHR/graph.json","fetch_events":"https://pith.science/api/pith-number/SL5OPAT5ICYYMEODW4EUQHBNHR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR/action/storage_attestation","attest_author":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR/action/author_attestation","sign_citation":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR/action/citation_signature","submit_replication":"https://pith.science/pith/SL5OPAT5ICYYMEODW4EUQHBNHR/action/replication_record"}},"created_at":"2026-05-18T04:30:03.502941+00:00","updated_at":"2026-05-18T04:30:03.502941+00:00"}