{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R4CJ623BWAVLNPU573LSAV2S4O","short_pith_number":"pith:R4CJ623B","canonical_record":{"source":{"id":"1811.10253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-26T09:52:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4d65e249caab5660fc3702daec9734d7b82650ea43685bac199e0c1543011929","abstract_canon_sha256":"742d8544908430b5d1bb5ce84067f61ef5ef4255aa32486f0204268919f1247c"},"schema_version":"1.0"},"canonical_sha256":"8f049f6b61b02ab6be9dfed7205752e393302ba06b3672ac62ac79fbbcddedd9","source":{"kind":"arxiv","id":"1811.10253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10253","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10253v2","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10253","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"R4CJ623BWAVL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R4CJ623BWAVLNPU5","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R4CJ623B","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R4CJ623BWAVLNPU573LSAV2S4O","target":"record","payload":{"canonical_record":{"source":{"id":"1811.10253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-26T09:52:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4d65e249caab5660fc3702daec9734d7b82650ea43685bac199e0c1543011929","abstract_canon_sha256":"742d8544908430b5d1bb5ce84067f61ef5ef4255aa32486f0204268919f1247c"},"schema_version":"1.0"},"canonical_sha256":"8f049f6b61b02ab6be9dfed7205752e393302ba06b3672ac62ac79fbbcddedd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:31.882914Z","signature_b64":"7NUH6OTlBYzBMb3w9WQC+A9Wopj8KtxX7jo19J3bCxesHjLZUx5snYzR6I4tBfkNVkRyCJDMccl4dznJmWEFAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f049f6b61b02ab6be9dfed7205752e393302ba06b3672ac62ac79fbbcddedd9","last_reissued_at":"2026-05-17T23:59:31.882183Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:31.882183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.10253","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwrxH/wjK4KlelbSlC7XRJ5tcqKX4rE9XBL0fCR19Oe1L4u9P8RN2Ih37TUEdpEEU3RIlyxa6YBfa5s2aUTzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:05:27.935341Z"},"content_sha256":"fabd07c341bc056dd2e2b8cdf7f89436f8245a9adf0679a659f094fdbf62237f","schema_version":"1.0","event_id":"sha256:fabd07c341bc056dd2e2b8cdf7f89436f8245a9adf0679a659f094fdbf62237f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R4CJ623BWAVLNPU573LSAV2S4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full factors, bicentralizer flow and approximately inner automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.OA","authors_text":"Amine Marrakchi","submitted_at":"2018-11-26T09:52:27Z","abstract_excerpt":"We show that a factor $M$ is full if and only if the $C^*$-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type $\\mathrm{III}_1$ factor is always ergodic. As a consequence, for any type $\\mathrm{III}_1$ factor $M$ and any $\\lambda \\in ]0,1]$, there exists an irreducible AFD type $\\mathrm{III}_\\lambda$ subfactor with expectation in $M$. Moreover, any type $\\mathrm{III}_1$ factor $M$ which satisfies $M \\cong M \\otimes R_\\lambda$ for some $\\lambda \\in ]0,1[$ has trivial bicentralizer. Finally, we give a coun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10253","kind":"arxiv","version":2},"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":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tB0QkEF6XFdUu96VsnHI4WSZH9ZILWqv26RAC92yJWz+MAOJI7C+FDdtr83W8I73VCMrVLApAyqT00mhFNmbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:05:27.935925Z"},"content_sha256":"20ebce6b6b1fa825e167f1cde4f7e1c80a09c022a8982e30e953b8085a22ed05","schema_version":"1.0","event_id":"sha256:20ebce6b6b1fa825e167f1cde4f7e1c80a09c022a8982e30e953b8085a22ed05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4CJ623BWAVLNPU573LSAV2S4O/bundle.json","state_url":"https://pith.science/pith/R4CJ623BWAVLNPU573LSAV2S4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4CJ623BWAVLNPU573LSAV2S4O/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":"2026-05-26T18:05:27Z","links":{"resolver":"https://pith.science/pith/R4CJ623BWAVLNPU573LSAV2S4O","bundle":"https://pith.science/pith/R4CJ623BWAVLNPU573LSAV2S4O/bundle.json","state":"https://pith.science/pith/R4CJ623BWAVLNPU573LSAV2S4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4CJ623BWAVLNPU573LSAV2S4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R4CJ623BWAVLNPU573LSAV2S4O","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":"742d8544908430b5d1bb5ce84067f61ef5ef4255aa32486f0204268919f1247c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-26T09:52:27Z","title_canon_sha256":"4d65e249caab5660fc3702daec9734d7b82650ea43685bac199e0c1543011929"},"schema_version":"1.0","source":{"id":"1811.10253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10253","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10253v2","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10253","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"R4CJ623BWAVL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R4CJ623BWAVLNPU5","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R4CJ623B","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:20ebce6b6b1fa825e167f1cde4f7e1c80a09c022a8982e30e953b8085a22ed05","target":"graph","created_at":"2026-05-17T23:59:31Z","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 show that a factor $M$ is full if and only if the $C^*$-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type $\\mathrm{III}_1$ factor is always ergodic. As a consequence, for any type $\\mathrm{III}_1$ factor $M$ and any $\\lambda \\in ]0,1]$, there exists an irreducible AFD type $\\mathrm{III}_\\lambda$ subfactor with expectation in $M$. Moreover, any type $\\mathrm{III}_1$ factor $M$ which satisfies $M \\cong M \\otimes R_\\lambda$ for some $\\lambda \\in ]0,1[$ has trivial bicentralizer. Finally, we give a coun","authors_text":"Amine Marrakchi","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-26T09:52:27Z","title":"Full factors, bicentralizer flow and approximately inner automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10253","kind":"arxiv","version":2},"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:fabd07c341bc056dd2e2b8cdf7f89436f8245a9adf0679a659f094fdbf62237f","target":"record","created_at":"2026-05-17T23:59:31Z","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":"742d8544908430b5d1bb5ce84067f61ef5ef4255aa32486f0204268919f1247c","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2018-11-26T09:52:27Z","title_canon_sha256":"4d65e249caab5660fc3702daec9734d7b82650ea43685bac199e0c1543011929"},"schema_version":"1.0","source":{"id":"1811.10253","kind":"arxiv","version":2}},"canonical_sha256":"8f049f6b61b02ab6be9dfed7205752e393302ba06b3672ac62ac79fbbcddedd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f049f6b61b02ab6be9dfed7205752e393302ba06b3672ac62ac79fbbcddedd9","first_computed_at":"2026-05-17T23:59:31.882183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:31.882183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7NUH6OTlBYzBMb3w9WQC+A9Wopj8KtxX7jo19J3bCxesHjLZUx5snYzR6I4tBfkNVkRyCJDMccl4dznJmWEFAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:31.882914Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fabd07c341bc056dd2e2b8cdf7f89436f8245a9adf0679a659f094fdbf62237f","sha256:20ebce6b6b1fa825e167f1cde4f7e1c80a09c022a8982e30e953b8085a22ed05"],"state_sha256":"30ebf0288c11fe8a99591d266dc340ea257c920581cd73410c4ff85cfda178e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MhTHH0vsOdrc4zbZM48h2OW8pEW4yHTUHqrQpS30hlsFMH1gOCHleiJ/f/RO+h2zSKYP+3cxUgmMkzGp4FmmAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:05:27.939119Z","bundle_sha256":"bf4bac6b53f820723a49f235d0a49bf68759b5651623c12e3f69c990ba0108a7"}}