{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WYWTZFUIR4GPFR4HNX5NGV7A7F","short_pith_number":"pith:WYWTZFUI","schema_version":"1.0","canonical_sha256":"b62d3c96888f0cf2c7876dfad357e0f971103c787c16f9350298e66bf91dda0a","source":{"kind":"arxiv","id":"1807.05905","version":3},"attestation_state":"computed","paper":{"title":"Weak mixing for nonsingular Bernoulli actions of countable amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko","submitted_at":"2018-07-16T15:00:57Z","abstract_excerpt":"Let $G$ be an amenable discrete countable infinite group,\n  $A$ a finite set, and $(\\mu_g)_{g\\in G}$ a family of probability measures on $A$ such that $\\inf_{g\\in G}\\min_{a\\in A}\\mu_g(a)>0$. It is shown (among other results) that if the Bernoulli shiftwise action of $G$ on the infinite product space $\\bigotimes_{g\\in G}(A,\\mu_g)$ is nonsingular and conservative then it is weakly mixing. This answers in positive a question by Z.~Kosloff who proved recently that the conservative Bernoulli $\\Bbb Z^d$-actions are ergodic. As a byproduct, we prove a weak version of the pointwise ratio ergodic theor"},"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":"1807.05905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-07-16T15:00:57Z","cross_cats_sorted":[],"title_canon_sha256":"29471a5cfba23c5d6ad0ecd7b7f509ab1448d382ed4cdea95d5a3614ed1f095e","abstract_canon_sha256":"033b9ba92508416a46e04a11e49a6272a186739bc227fe02661c5ad9d356ab00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:46.788347Z","signature_b64":"N8idn0oNjFi+ZLcZsnkWsiqGAJpWn4BpUZl18OE3raYaGPfg9cdVzXs3R/fjH12pYTN54sL0YPZRldGCnNA8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b62d3c96888f0cf2c7876dfad357e0f971103c787c16f9350298e66bf91dda0a","last_reissued_at":"2026-05-18T00:09:46.787643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:46.787643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak mixing for nonsingular Bernoulli actions of countable amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre I. Danilenko","submitted_at":"2018-07-16T15:00:57Z","abstract_excerpt":"Let $G$ be an amenable discrete countable infinite group,\n  $A$ a finite set, and $(\\mu_g)_{g\\in G}$ a family of probability measures on $A$ such that $\\inf_{g\\in G}\\min_{a\\in A}\\mu_g(a)>0$. It is shown (among other results) that if the Bernoulli shiftwise action of $G$ on the infinite product space $\\bigotimes_{g\\in G}(A,\\mu_g)$ is nonsingular and conservative then it is weakly mixing. This answers in positive a question by Z.~Kosloff who proved recently that the conservative Bernoulli $\\Bbb Z^d$-actions are ergodic. As a byproduct, we prove a weak version of the pointwise ratio ergodic theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05905","kind":"arxiv","version":3},"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":"1807.05905","created_at":"2026-05-18T00:09:46.787743+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.05905v3","created_at":"2026-05-18T00:09:46.787743+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05905","created_at":"2026-05-18T00:09:46.787743+00:00"},{"alias_kind":"pith_short_12","alias_value":"WYWTZFUIR4GP","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WYWTZFUIR4GPFR4H","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WYWTZFUI","created_at":"2026-05-18T12:33:01.666342+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/WYWTZFUIR4GPFR4HNX5NGV7A7F","json":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F.json","graph_json":"https://pith.science/api/pith-number/WYWTZFUIR4GPFR4HNX5NGV7A7F/graph.json","events_json":"https://pith.science/api/pith-number/WYWTZFUIR4GPFR4HNX5NGV7A7F/events.json","paper":"https://pith.science/paper/WYWTZFUI"},"agent_actions":{"view_html":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F","download_json":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F.json","view_paper":"https://pith.science/paper/WYWTZFUI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.05905&json=true","fetch_graph":"https://pith.science/api/pith-number/WYWTZFUIR4GPFR4HNX5NGV7A7F/graph.json","fetch_events":"https://pith.science/api/pith-number/WYWTZFUIR4GPFR4HNX5NGV7A7F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F/action/storage_attestation","attest_author":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F/action/author_attestation","sign_citation":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F/action/citation_signature","submit_replication":"https://pith.science/pith/WYWTZFUIR4GPFR4HNX5NGV7A7F/action/replication_record"}},"created_at":"2026-05-18T00:09:46.787743+00:00","updated_at":"2026-05-18T00:09:46.787743+00:00"}