{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3I7EB7TNVSWCFUI6OHTQBPQDRC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6c5c550b75950ea5c376f3614f620f56587895c99f88041f05d832c0f3db494b","cross_cats_sorted":["math.GR","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-01T07:55:12Z","title_canon_sha256":"512f5241291d476542ccbb7a08c628c932ba80844dd0f182b806c02e79a99f8c"},"schema_version":"1.0","source":{"id":"1705.00439","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00439","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00439v4","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00439","created_at":"2026-05-18T00:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"3I7EB7TNVSWC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3I7EB7TNVSWCFUI6","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3I7EB7TN","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:0c330586d8d224c344f93b1953f7f0404983c7cd044750d6b90b80190a03402b","target":"graph","created_at":"2026-05-18T00:17:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We conjecture that a countable group $G$ admits a nonsingular Bernoulli action of type III$_1$ if and only if the first $L^2$-cohomology of $G$ is nonzero. We prove this conjecture for all groups that admit at least one element of infinite order. We also give numerous explicit examples of type III$_1$ Bernoulli actions of the group of integers and the free groups, with different degrees of ergodicity.","authors_text":"Jonas Wahl, Stefaan Vaes","cross_cats":["math.GR","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-01T07:55:12Z","title":"Bernoulli actions of type III_1 and L^2-cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00439","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:73f19ec50802d5f7cde7dcfdbcd17b168161eba4fc9d0aec770dfa496ec49dbe","target":"record","created_at":"2026-05-18T00:17:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6c5c550b75950ea5c376f3614f620f56587895c99f88041f05d832c0f3db494b","cross_cats_sorted":["math.GR","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-01T07:55:12Z","title_canon_sha256":"512f5241291d476542ccbb7a08c628c932ba80844dd0f182b806c02e79a99f8c"},"schema_version":"1.0","source":{"id":"1705.00439","kind":"arxiv","version":4}},"canonical_sha256":"da3e40fe6dacac22d11e71e700be03889392b9b9063d54b4937d738e753909ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da3e40fe6dacac22d11e71e700be03889392b9b9063d54b4937d738e753909ea","first_computed_at":"2026-05-18T00:17:54.788608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:54.788608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M+DW1Dw3R1+Bvy+1rPwpHMVv2tuJb2Lcq77YLWhzyutMFBY08IZyzwgR4UfyQ8OmXGKmO+ncrLhoiTWiyxqSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:54.789227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00439","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73f19ec50802d5f7cde7dcfdbcd17b168161eba4fc9d0aec770dfa496ec49dbe","sha256:0c330586d8d224c344f93b1953f7f0404983c7cd044750d6b90b80190a03402b"],"state_sha256":"321de9211e481df7daddeef6e752cffc7cb4a5a4b8472f59a5218c98a14f6333"}