{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:TA7NY7SSDMB4QSYX7KACC3PABI","short_pith_number":"pith:TA7NY7SS","schema_version":"1.0","canonical_sha256":"983edc7e521b03c84b17fa80216de00a0b71745beea8d8c554151966353e0f06","source":{"kind":"arxiv","id":"2211.07397","version":3},"attestation_state":"computed","paper":{"title":"Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Haotian Tian, Xiaochun Fang","submitted_at":"2022-11-11T07:53:39Z","abstract_excerpt":"In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its original algebra: (1) stable rank one; (2) real rank zero; (3) $\\beta$-comparison; (4) Winter's $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.07397","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2022-11-11T07:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"dcfaac5f17b72180decff01069076694fe85bd7669d328406416f3b37343838c","abstract_canon_sha256":"93454db73329d1faf83d5d77175f984574490a2c9556771f9d7d3ca609aa200f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:36.661286Z","signature_b64":"U5gSyj04Mx0L1D4IN10u+n/K0btGxD8G8uhQKKYYLm0VDOieQbXr8hX89P93z0+7krNufL62a8EmZ/pJdgFJBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"983edc7e521b03c84b17fa80216de00a0b71745beea8d8c554151966353e0f06","last_reissued_at":"2026-07-05T11:31:36.660806Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:36.660806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Permanence properties for crossed products by compact group actions with the tracial Rokhlin property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Haotian Tian, Xiaochun Fang","submitted_at":"2022-11-11T07:53:39Z","abstract_excerpt":"In this paper, we give some properties of the fixed point algebra and the crossed product of a unital separable simple infinite dimensional C*-algebra by an action of a second-countable compact group with the tracial Rokhlin property with comparison that could be deduced from the properties of its original algebra: (1) stable rank one; (2) real rank zero; (3) $\\beta$-comparison; (4) Winter's $n$-comparison; (5) $m$-almost divisible; (6) weakly ($m$,$n$)-divisible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07397","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/2211.07397/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.07397","created_at":"2026-07-05T11:31:36.660864+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.07397v3","created_at":"2026-07-05T11:31:36.660864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07397","created_at":"2026-07-05T11:31:36.660864+00:00"},{"alias_kind":"pith_short_12","alias_value":"TA7NY7SSDMB4","created_at":"2026-07-05T11:31:36.660864+00:00"},{"alias_kind":"pith_short_16","alias_value":"TA7NY7SSDMB4QSYX","created_at":"2026-07-05T11:31:36.660864+00:00"},{"alias_kind":"pith_short_8","alias_value":"TA7NY7SS","created_at":"2026-07-05T11:31:36.660864+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.10486","citing_title":"Uniform property $\\Gamma$ for Crossed products by group actions with the Rokhlin-type properties","ref_index":37,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI","json":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI.json","graph_json":"https://pith.science/api/pith-number/TA7NY7SSDMB4QSYX7KACC3PABI/graph.json","events_json":"https://pith.science/api/pith-number/TA7NY7SSDMB4QSYX7KACC3PABI/events.json","paper":"https://pith.science/paper/TA7NY7SS"},"agent_actions":{"view_html":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI","download_json":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI.json","view_paper":"https://pith.science/paper/TA7NY7SS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.07397&json=true","fetch_graph":"https://pith.science/api/pith-number/TA7NY7SSDMB4QSYX7KACC3PABI/graph.json","fetch_events":"https://pith.science/api/pith-number/TA7NY7SSDMB4QSYX7KACC3PABI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI/action/storage_attestation","attest_author":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI/action/author_attestation","sign_citation":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI/action/citation_signature","submit_replication":"https://pith.science/pith/TA7NY7SSDMB4QSYX7KACC3PABI/action/replication_record"}},"created_at":"2026-07-05T11:31:36.660864+00:00","updated_at":"2026-07-05T11:31:36.660864+00:00"}