{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:N625NBOKLKKN7SM5A4HJDVJGAU","short_pith_number":"pith:N625NBOK","schema_version":"1.0","canonical_sha256":"6fb5d685ca5a94dfc99d070e91d526052602e6f24c1e3049ef281ae6c4c246fb","source":{"kind":"arxiv","id":"1705.03528","version":3},"attestation_state":"computed","paper":{"title":"The space of stable weak equivalence classes of measure-preserving actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lewis Bowen, Robin Tucker-Drob","submitted_at":"2017-05-09T20:28:04Z","abstract_excerpt":"The concept of (stable) weak containment for measure-preserving actions of a countable group $\\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\\Gamma$ is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if $\\Gamma$ is non-amenable then there can be many different weak and stable weak equivalence classes. Our main result is that the set of stable weak equivalence classes naturally admits the structure of a Choquet simplex. For example, when $\\Gamma=\\mathbb{Z}$ this simplex has only a c"},"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":"1705.03528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-09T20:28:04Z","cross_cats_sorted":[],"title_canon_sha256":"a63924414f67535219a00817431a261e9f34cd6d71abebd6587117d6fe3c618c","abstract_canon_sha256":"e17fdf285dda5488cb21a1f947bdd3b63086ae6be1ad35d83762e0d2ce0fd0d5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:50.756032Z","signature_b64":"+39Aq8Idd1xA64FenLaB1vA1+lH9PQaDvkmhJjUekRDPbtlMm4SIl8rXjHVOTKhOhryKQmyM67BSeYoEf9SBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fb5d685ca5a94dfc99d070e91d526052602e6f24c1e3049ef281ae6c4c246fb","last_reissued_at":"2026-05-18T00:32:50.755351Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:50.755351Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The space of stable weak equivalence classes of measure-preserving actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lewis Bowen, Robin Tucker-Drob","submitted_at":"2017-05-09T20:28:04Z","abstract_excerpt":"The concept of (stable) weak containment for measure-preserving actions of a countable group $\\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\\Gamma$ is amenable then the Rokhlin lemma shows that all essentially free actions are weakly equivalent. However if $\\Gamma$ is non-amenable then there can be many different weak and stable weak equivalence classes. Our main result is that the set of stable weak equivalence classes naturally admits the structure of a Choquet simplex. For example, when $\\Gamma=\\mathbb{Z}$ this simplex has only a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03528","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":"1705.03528","created_at":"2026-05-18T00:32:50.755458+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03528v3","created_at":"2026-05-18T00:32:50.755458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03528","created_at":"2026-05-18T00:32:50.755458+00:00"},{"alias_kind":"pith_short_12","alias_value":"N625NBOKLKKN","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"N625NBOKLKKN7SM5","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"N625NBOK","created_at":"2026-05-18T12:31:31.346846+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/N625NBOKLKKN7SM5A4HJDVJGAU","json":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU.json","graph_json":"https://pith.science/api/pith-number/N625NBOKLKKN7SM5A4HJDVJGAU/graph.json","events_json":"https://pith.science/api/pith-number/N625NBOKLKKN7SM5A4HJDVJGAU/events.json","paper":"https://pith.science/paper/N625NBOK"},"agent_actions":{"view_html":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU","download_json":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU.json","view_paper":"https://pith.science/paper/N625NBOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03528&json=true","fetch_graph":"https://pith.science/api/pith-number/N625NBOKLKKN7SM5A4HJDVJGAU/graph.json","fetch_events":"https://pith.science/api/pith-number/N625NBOKLKKN7SM5A4HJDVJGAU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU/action/storage_attestation","attest_author":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU/action/author_attestation","sign_citation":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU/action/citation_signature","submit_replication":"https://pith.science/pith/N625NBOKLKKN7SM5A4HJDVJGAU/action/replication_record"}},"created_at":"2026-05-18T00:32:50.755458+00:00","updated_at":"2026-05-18T00:32:50.755458+00:00"}