{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NNMASJINRX3RCQOR44XAKGUTBO","short_pith_number":"pith:NNMASJIN","canonical_record":{"source":{"id":"1209.1728","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-08T15:23:22Z","cross_cats_sorted":[],"title_canon_sha256":"98ff7c0fd2eca615640e97af4e14613e31bfa93eaef56208f792b61fe3fa880b","abstract_canon_sha256":"3874acd54048ef264566c2a9e7114b968f39e4bd79eb48e428c7d0beed179c1b"},"schema_version":"1.0"},"canonical_sha256":"6b5809250d8df71141d1e72e051a930bb7d93cfe0970ed91e79f3875466ea8c8","source":{"kind":"arxiv","id":"1209.1728","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1728","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1728v3","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1728","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"NNMASJINRX3R","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNMASJINRX3RCQOR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNMASJIN","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NNMASJINRX3RCQOR44XAKGUTBO","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1728","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-08T15:23:22Z","cross_cats_sorted":[],"title_canon_sha256":"98ff7c0fd2eca615640e97af4e14613e31bfa93eaef56208f792b61fe3fa880b","abstract_canon_sha256":"3874acd54048ef264566c2a9e7114b968f39e4bd79eb48e428c7d0beed179c1b"},"schema_version":"1.0"},"canonical_sha256":"6b5809250d8df71141d1e72e051a930bb7d93cfe0970ed91e79f3875466ea8c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:11.079186Z","signature_b64":"vP8ZdiY/EvKqrJKxU+uAKkZ2oCqe1As7fSk4QCmKyJ6U8qw4MZT2dC/LORM9aVeDfkfFpOWH4KpHihIujBIPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b5809250d8df71141d1e72e051a930bb7d93cfe0970ed91e79f3875466ea8c8","last_reissued_at":"2026-05-18T03:01:11.078399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:11.078399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1728","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":"2026-05-18T03:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Qp3n5qB5KSR0u8G5/2CCfFRQ9B+p3gPDaay3mILqbLu7ZRgl4AjDgBnDCH4FjxOBV2VsmZ4REE/8VwY8ar4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:29:08.451885Z"},"content_sha256":"0b3eeec146998702a58e3a6cf332285d3a0834719e0b2ea6cd75225e81736e19","schema_version":"1.0","event_id":"sha256:0b3eeec146998702a58e3a6cf332285d3a0834719e0b2ea6cd75225e81736e19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NNMASJINRX3RCQOR44XAKGUTBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Examples of factors which have no Cartan subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Yusuke Isono","submitted_at":"2012-09-08T15:23:22Z","abstract_excerpt":"We consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\\rm II_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\\rm III_1$ factors with such a condition are semisolid as a $\\rm II_\\infty$ factor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1728","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":"2026-05-18T03:01:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iOI/siM27CD6vkPmay6DrEzbeav6WuvM3TB/9Pv0Qmo6S7ZZIx5FdMBoNcoH5HegPS4IGg9N4d+sdciyX/Y8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:29:08.452565Z"},"content_sha256":"9a21da39e3b6d377abaf56d073861cad6ed9de65a02c986f04f1447c150cb070","schema_version":"1.0","event_id":"sha256:9a21da39e3b6d377abaf56d073861cad6ed9de65a02c986f04f1447c150cb070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNMASJINRX3RCQOR44XAKGUTBO/bundle.json","state_url":"https://pith.science/pith/NNMASJINRX3RCQOR44XAKGUTBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNMASJINRX3RCQOR44XAKGUTBO/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":"2026-06-06T22:29:08Z","links":{"resolver":"https://pith.science/pith/NNMASJINRX3RCQOR44XAKGUTBO","bundle":"https://pith.science/pith/NNMASJINRX3RCQOR44XAKGUTBO/bundle.json","state":"https://pith.science/pith/NNMASJINRX3RCQOR44XAKGUTBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNMASJINRX3RCQOR44XAKGUTBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NNMASJINRX3RCQOR44XAKGUTBO","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":"3874acd54048ef264566c2a9e7114b968f39e4bd79eb48e428c7d0beed179c1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-08T15:23:22Z","title_canon_sha256":"98ff7c0fd2eca615640e97af4e14613e31bfa93eaef56208f792b61fe3fa880b"},"schema_version":"1.0","source":{"id":"1209.1728","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1728","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1728v3","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1728","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"NNMASJINRX3R","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNMASJINRX3RCQOR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNMASJIN","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:9a21da39e3b6d377abaf56d073861cad6ed9de65a02c986f04f1447c150cb070","target":"graph","created_at":"2026-05-18T03:01:11Z","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 consider some conditions similar to Ozawa's condition (AO), and prove that if a non-injective factor satisfies such a condition and has the W*CBAP, then it has no Cartan subalgebras. As a corollary, we prove that $\\rm II_1$ factors of universal orthogonal and unitary discrete quantum groups have no Cartan subalgebras. We also prove that continuous cores of type $\\rm III_1$ factors with such a condition are semisolid as a $\\rm II_\\infty$ factor.","authors_text":"Yusuke Isono","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-08T15:23:22Z","title":"Examples of factors which have no Cartan subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1728","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":"sha256:0b3eeec146998702a58e3a6cf332285d3a0834719e0b2ea6cd75225e81736e19","target":"record","created_at":"2026-05-18T03:01:11Z","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":"3874acd54048ef264566c2a9e7114b968f39e4bd79eb48e428c7d0beed179c1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-09-08T15:23:22Z","title_canon_sha256":"98ff7c0fd2eca615640e97af4e14613e31bfa93eaef56208f792b61fe3fa880b"},"schema_version":"1.0","source":{"id":"1209.1728","kind":"arxiv","version":3}},"canonical_sha256":"6b5809250d8df71141d1e72e051a930bb7d93cfe0970ed91e79f3875466ea8c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b5809250d8df71141d1e72e051a930bb7d93cfe0970ed91e79f3875466ea8c8","first_computed_at":"2026-05-18T03:01:11.078399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.078399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vP8ZdiY/EvKqrJKxU+uAKkZ2oCqe1As7fSk4QCmKyJ6U8qw4MZT2dC/LORM9aVeDfkfFpOWH4KpHihIujBIPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.079186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1728","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b3eeec146998702a58e3a6cf332285d3a0834719e0b2ea6cd75225e81736e19","sha256:9a21da39e3b6d377abaf56d073861cad6ed9de65a02c986f04f1447c150cb070"],"state_sha256":"80f2ce48cdcb1139379a8bf4d73d0bc9b98d774c459670ecb2a070dc0d70eb1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOAFfIvzm96kqpepeSr3+1rbtwuP9vJnDhLtQpN4OLa0FVe1asQMCdreXHqdHXM1TYSGeHsBHfI0IOytHQLhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:29:08.456447Z","bundle_sha256":"0c3e2a9af49dad7c8098204f78a9c4232e7ee7da74b76dd127e8ec15ac765b1e"}}