{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ULTDRQ3HPJ6UVGBTDCV7Y6HCEF","short_pith_number":"pith:ULTDRQ3H","canonical_record":{"source":{"id":"2205.14053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-05-27T15:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"6b470643b2580068d03a444c84987bc011627c1c0dced2262bdded3cc133bce7","abstract_canon_sha256":"9f18e4eefee907a29c4df212cc7748f419f2bc0bb93bdfe32a12aa730a736533"},"schema_version":"1.0"},"canonical_sha256":"a2e638c3677a7d4a983318abfc78e22150788a10f3671e5b3cede5bb14af198b","source":{"kind":"arxiv","id":"2205.14053","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.14053","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"2205.14053v3","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.14053","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULTDRQ3HPJ6U","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_16","alias_value":"ULTDRQ3HPJ6UVGBT","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_8","alias_value":"ULTDRQ3H","created_at":"2026-07-05T09:26:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ULTDRQ3HPJ6UVGBTDCV7Y6HCEF","target":"record","payload":{"canonical_record":{"source":{"id":"2205.14053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-05-27T15:39:35Z","cross_cats_sorted":[],"title_canon_sha256":"6b470643b2580068d03a444c84987bc011627c1c0dced2262bdded3cc133bce7","abstract_canon_sha256":"9f18e4eefee907a29c4df212cc7748f419f2bc0bb93bdfe32a12aa730a736533"},"schema_version":"1.0"},"canonical_sha256":"a2e638c3677a7d4a983318abfc78e22150788a10f3671e5b3cede5bb14af198b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:26:54.229236Z","signature_b64":"Ap8g2YmN2sP6jgCnIthTfWyPNH369x7kKI3NpZlFqEuy9ClpJGJGqqbJQ89Oy3b8dr9ClVlRzbw+uJHlQflwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e638c3677a7d4a983318abfc78e22150788a10f3671e5b3cede5bb14af198b","last_reissued_at":"2026-07-05T09:26:54.228772Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:26:54.228772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.14053","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":"2026-07-05T09:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNBad3tDkl0GL7GT/6Bvo7DblAyTfE9Gq8S3BXIvGQLhdHii58+Ddwb8NC/p8TOtDPpK52lJrpTaiLmyhRqcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:57:58.364964Z"},"content_sha256":"692cabea8501c3cce13c9d3be68bdd6b71484b323842978ed5179c9cab936842","schema_version":"1.0","event_id":"sha256:692cabea8501c3cce13c9d3be68bdd6b71484b323842978ed5179c9cab936842"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ULTDRQ3HPJ6UVGBTDCV7Y6HCEF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inductive Limits of Noncommutative Cartan Inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ali Imad Raad, Jonathan Taylor, Ralf Meyer","submitted_at":"2022-05-27T15:39:35Z","abstract_excerpt":"We prove that an inductive limit of aperiodic noncommutative Cartan inclusions is a noncommutative Cartan inclusion whenever the connecting maps are injective, preserve normalisers and entwine conditional expectations. We show that under the additional assumption that the inductive limit Cartan subalgebra is either essentially separable, essentially simple or essentially of Type I we get an aperiodic inclusion in the limit. Consequently, we subsume the case where the building block Cartan subalgebras are commutative and provide a proof of a theorem of Xin Li without passing to twisted \\'etale "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14053","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.14053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:26:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mTpKfL0R6IS2dn7946bA6a6OZ1mx7qC7xAWCIBl4gnoiqtjmF8Bwgk1T572jTsGZ6aLj7aUL7gZJBsKxjlClBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T05:57:58.365479Z"},"content_sha256":"612ee778d7b8b2a56efabac48ab16efe4457228a69db1589797454753249ddf4","schema_version":"1.0","event_id":"sha256:612ee778d7b8b2a56efabac48ab16efe4457228a69db1589797454753249ddf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/bundle.json","state_url":"https://pith.science/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/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":"2026-08-15T05:57:58Z","links":{"resolver":"https://pith.science/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF","bundle":"https://pith.science/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/bundle.json","state":"https://pith.science/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULTDRQ3HPJ6UVGBTDCV7Y6HCEF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ULTDRQ3HPJ6UVGBTDCV7Y6HCEF","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":"9f18e4eefee907a29c4df212cc7748f419f2bc0bb93bdfe32a12aa730a736533","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-05-27T15:39:35Z","title_canon_sha256":"6b470643b2580068d03a444c84987bc011627c1c0dced2262bdded3cc133bce7"},"schema_version":"1.0","source":{"id":"2205.14053","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.14053","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"arxiv_version","alias_value":"2205.14053v3","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.14053","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULTDRQ3HPJ6U","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_16","alias_value":"ULTDRQ3HPJ6UVGBT","created_at":"2026-07-05T09:26:54Z"},{"alias_kind":"pith_short_8","alias_value":"ULTDRQ3H","created_at":"2026-07-05T09:26:54Z"}],"graph_snapshots":[{"event_id":"sha256:612ee778d7b8b2a56efabac48ab16efe4457228a69db1589797454753249ddf4","target":"graph","created_at":"2026-07-05T09:26:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2205.14053/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that an inductive limit of aperiodic noncommutative Cartan inclusions is a noncommutative Cartan inclusion whenever the connecting maps are injective, preserve normalisers and entwine conditional expectations. We show that under the additional assumption that the inductive limit Cartan subalgebra is either essentially separable, essentially simple or essentially of Type I we get an aperiodic inclusion in the limit. Consequently, we subsume the case where the building block Cartan subalgebras are commutative and provide a proof of a theorem of Xin Li without passing to twisted \\'etale ","authors_text":"Ali Imad Raad, Jonathan Taylor, Ralf Meyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-05-27T15:39:35Z","title":"Inductive Limits of Noncommutative Cartan Inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14053","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":"sha256:692cabea8501c3cce13c9d3be68bdd6b71484b323842978ed5179c9cab936842","target":"record","created_at":"2026-07-05T09:26:54Z","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":"9f18e4eefee907a29c4df212cc7748f419f2bc0bb93bdfe32a12aa730a736533","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-05-27T15:39:35Z","title_canon_sha256":"6b470643b2580068d03a444c84987bc011627c1c0dced2262bdded3cc133bce7"},"schema_version":"1.0","source":{"id":"2205.14053","kind":"arxiv","version":3}},"canonical_sha256":"a2e638c3677a7d4a983318abfc78e22150788a10f3671e5b3cede5bb14af198b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e638c3677a7d4a983318abfc78e22150788a10f3671e5b3cede5bb14af198b","first_computed_at":"2026-07-05T09:26:54.228772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:26:54.228772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ap8g2YmN2sP6jgCnIthTfWyPNH369x7kKI3NpZlFqEuy9ClpJGJGqqbJQ89Oy3b8dr9ClVlRzbw+uJHlQflwBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:26:54.229236Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.14053","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:692cabea8501c3cce13c9d3be68bdd6b71484b323842978ed5179c9cab936842","sha256:612ee778d7b8b2a56efabac48ab16efe4457228a69db1589797454753249ddf4"],"state_sha256":"a5705ea85576c445328b68243bd00f9af9bd1e96fa57eafa80a4a76229faa2a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsrplqdrOW8hmrwtNb+L0jdW3PRTUPIcKXShjsmbxlJa5eLrmxR3Ftzrg+0ulpyC5Et4tABN8n9Vd5cFmDQXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T05:57:58.369104Z","bundle_sha256":"9fd540a8e82e09ca900132c702021d31dfe53fd03e00932478e2bf23ab972a08"}}