{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:K6CP75CT3HNNE2M2MT7YTDLC5J","short_pith_number":"pith:K6CP75CT","canonical_record":{"source":{"id":"1301.0510","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-01-03T17:10:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d6941a588a2c9b95fe842bfe199f6558b5cc39e1c96ee4bd494a24a6e97c250e","abstract_canon_sha256":"b2ba639aeaaa4b7c4494cb05a1b3116249dc96f1a8dbb4000aac102063f58bd1"},"schema_version":"1.0"},"canonical_sha256":"5784fff453d9dad2699a64ff898d62ea74842dcbbc8bb202ef7ef08a60cf130c","source":{"kind":"arxiv","id":"1301.0510","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0510","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0510v3","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0510","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"K6CP75CT3HNN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K6CP75CT3HNNE2M2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K6CP75CT","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:K6CP75CT3HNNE2M2MT7YTDLC5J","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0510","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-01-03T17:10:32Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"d6941a588a2c9b95fe842bfe199f6558b5cc39e1c96ee4bd494a24a6e97c250e","abstract_canon_sha256":"b2ba639aeaaa4b7c4494cb05a1b3116249dc96f1a8dbb4000aac102063f58bd1"},"schema_version":"1.0"},"canonical_sha256":"5784fff453d9dad2699a64ff898d62ea74842dcbbc8bb202ef7ef08a60cf130c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.745086Z","signature_b64":"jRUBZbMokww8g/Y+PyybxLUEegqkQGizhQ7ZVG2ObAxnop1KlrWOcgyojdeOtbG+ATY3lakH5p4n/0sIKmEyAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5784fff453d9dad2699a64ff898d62ea74842dcbbc8bb202ef7ef08a60cf130c","last_reissued_at":"2026-05-18T02:46:04.744588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.744588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0510","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1uhBOIW0fSbkUmkwGhjK5J9hd85+h3Q5z2ATra81zdIkG3Uqu35BYNg54caSKTIWHux+qr1BYecfJIn17SaXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:50:09.336708Z"},"content_sha256":"a15d613d7e84412759c4d93e64e34e6caa7ccbc6b0891189cb9cfffa2ad17f4f","schema_version":"1.0","event_id":"sha256:a15d613d7e84412759c4d93e64e34e6caa7ccbc6b0891189cb9cfffa2ad17f4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:K6CP75CT3HNNE2M2MT7YTDLC5J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial classification of the Baumslag-Solitar group von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Niels Meesschaert, Stefaan Vaes","submitted_at":"2013-01-03T17:10:32Z","abstract_excerpt":"We prove that the rational number |n/m| is an invariant of the group von Neumann algebra of the Baumslag-Solitar group BS(n,m). More precisely, if L(BS(n,m)) is isomorphic with L(\\BS(n',m')), then |n'/m'| = |n/m| or |m/n|. We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II_1 factor, an equivalence relation that can be of type III. In particular, we associate to L(BS(n,m)) a canonical equivalence relation of type III_|n/m|."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0510","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hUClJjCs2uO5k+dR8dV3Diu0sdN2xffSTkFOFN0OEIVPtpfuLbaSeE+1/yCOWHCqEA0CSV88hUdqRys3yFjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:50:09.337388Z"},"content_sha256":"2149b74f069c827698acd29578d84f3a59e5ea83db3242a7bc4e71432fa657c5","schema_version":"1.0","event_id":"sha256:2149b74f069c827698acd29578d84f3a59e5ea83db3242a7bc4e71432fa657c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/bundle.json","state_url":"https://pith.science/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T13:50:09Z","links":{"resolver":"https://pith.science/pith/K6CP75CT3HNNE2M2MT7YTDLC5J","bundle":"https://pith.science/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/bundle.json","state":"https://pith.science/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6CP75CT3HNNE2M2MT7YTDLC5J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K6CP75CT3HNNE2M2MT7YTDLC5J","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":"b2ba639aeaaa4b7c4494cb05a1b3116249dc96f1a8dbb4000aac102063f58bd1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-01-03T17:10:32Z","title_canon_sha256":"d6941a588a2c9b95fe842bfe199f6558b5cc39e1c96ee4bd494a24a6e97c250e"},"schema_version":"1.0","source":{"id":"1301.0510","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0510","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0510v3","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0510","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"K6CP75CT3HNN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K6CP75CT3HNNE2M2","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K6CP75CT","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:2149b74f069c827698acd29578d84f3a59e5ea83db3242a7bc4e71432fa657c5","target":"graph","created_at":"2026-05-18T02:46:04Z","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 the rational number |n/m| is an invariant of the group von Neumann algebra of the Baumslag-Solitar group BS(n,m). More precisely, if L(BS(n,m)) is isomorphic with L(\\BS(n',m')), then |n'/m'| = |n/m| or |m/n|. We obtain this result by associating to abelian, but not maximal abelian, subalgebras of a II_1 factor, an equivalence relation that can be of type III. In particular, we associate to L(BS(n,m)) a canonical equivalence relation of type III_|n/m|.","authors_text":"Niels Meesschaert, Stefaan Vaes","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-01-03T17:10:32Z","title":"Partial classification of the Baumslag-Solitar group von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0510","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:a15d613d7e84412759c4d93e64e34e6caa7ccbc6b0891189cb9cfffa2ad17f4f","target":"record","created_at":"2026-05-18T02:46:04Z","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":"b2ba639aeaaa4b7c4494cb05a1b3116249dc96f1a8dbb4000aac102063f58bd1","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-01-03T17:10:32Z","title_canon_sha256":"d6941a588a2c9b95fe842bfe199f6558b5cc39e1c96ee4bd494a24a6e97c250e"},"schema_version":"1.0","source":{"id":"1301.0510","kind":"arxiv","version":3}},"canonical_sha256":"5784fff453d9dad2699a64ff898d62ea74842dcbbc8bb202ef7ef08a60cf130c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5784fff453d9dad2699a64ff898d62ea74842dcbbc8bb202ef7ef08a60cf130c","first_computed_at":"2026-05-18T02:46:04.744588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:04.744588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jRUBZbMokww8g/Y+PyybxLUEegqkQGizhQ7ZVG2ObAxnop1KlrWOcgyojdeOtbG+ATY3lakH5p4n/0sIKmEyAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:04.745086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0510","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15d613d7e84412759c4d93e64e34e6caa7ccbc6b0891189cb9cfffa2ad17f4f","sha256:2149b74f069c827698acd29578d84f3a59e5ea83db3242a7bc4e71432fa657c5"],"state_sha256":"55c0e3386709e7c27be053df33f1a05cd695cd938578f3c4ed9af5344d31fd17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mTEJzd4C0M42vZEHHShvJjxnZz9rb+jIrABRPyi4c6tkVbLL+Ot++k5/ioRVafHfOYblHqUiI7oBGgzFjRTUAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:50:09.341610Z","bundle_sha256":"ff5e050ecd7e9cf4e7b3637d7891efeff7e11a5b102f326a3cf99af123da2b38"}}