{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L7M4QUIG3G3YOSVJOGVGDCL4VG","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":"072fe94efa8883183bf74323ec2b1186dc3c6c72019dff7e527399a777095500","cross_cats_sorted":["math.GR","math.LO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-11T20:34:21Z","title_canon_sha256":"719937b02b3149367a777b905370ecb75f7a79cc4f5311a3dc80a334e896834e"},"schema_version":"1.0","source":{"id":"1109.2351","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2351","created_at":"2026-05-18T03:55:14Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2351v3","created_at":"2026-05-18T03:55:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2351","created_at":"2026-05-18T03:55:14Z"},{"alias_kind":"pith_short_12","alias_value":"L7M4QUIG3G3Y","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L7M4QUIG3G3YOSVJ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L7M4QUIG","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:e4106bc49b5a2ba9577f88a02387c24fee04497b704cd4344157d49c3128f21b","target":"graph","created_at":"2026-05-18T03:55:14Z","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 prove that for a countable discrete group $\\Gamma$ containing a copy of the free group $\\F_n$, for some $2\\leq n\\leq\\infty$, as a normal subgroup, the equivalence relations of conjugacy, orbit equivalence and von Neumann equivalence of the ergodic a.e. free actions of $\\Gamma$ are analytic non-Borel equivalence relations in the Polish space of probability measure preserving $\\Gamma$ actions. As a consequence we obtain that the isomorphism relation in the spaces of separably acting factors of type $\\II_1$, $\\II_\\infty$ and $\\III_\\lambda$, $0\\leq\\lambda\\leq 1$, are analytic and not Borel when","authors_text":"Asger Tornquist, Inessa Epstein","cross_cats":["math.GR","math.LO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-11T20:34:21Z","title":"The Borel complexity of von Neumann equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2351","kind":"arxiv","version":3},"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":"sha256:2a804064e02a69bec6ff81a048e06636de675c763048f9bbb76e03cc7a0a2c11","target":"record","created_at":"2026-05-18T03:55:14Z","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":"072fe94efa8883183bf74323ec2b1186dc3c6c72019dff7e527399a777095500","cross_cats_sorted":["math.GR","math.LO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-11T20:34:21Z","title_canon_sha256":"719937b02b3149367a777b905370ecb75f7a79cc4f5311a3dc80a334e896834e"},"schema_version":"1.0","source":{"id":"1109.2351","kind":"arxiv","version":3}},"canonical_sha256":"5fd9c85106d9b7874aa971aa61897ca982e5620d5dabd6fa169bed288655e6bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fd9c85106d9b7874aa971aa61897ca982e5620d5dabd6fa169bed288655e6bf","first_computed_at":"2026-05-18T03:55:14.135844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:14.135844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qxt6eZwOLz6HUFgIOHo2QkLMCMeEQQL1swEXInakwp/k2T82m0RO6oFBcES8Ncep7JNV5uAYDEbwd52MlvlPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:14.136351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2351","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a804064e02a69bec6ff81a048e06636de675c763048f9bbb76e03cc7a0a2c11","sha256:e4106bc49b5a2ba9577f88a02387c24fee04497b704cd4344157d49c3128f21b"],"state_sha256":"52e7f15f3cb0c017f8715f326036e6d84433c3c636c44ac6f9ad57b6040bb034"}