{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QLZGEUISAHNMO3KY22URVEPRHB","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":"1cc9f2521bf43460e5a49971736da670bc02e7fbc8cf351bb606c54941102cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-13T13:49:21Z","title_canon_sha256":"e8f2c35f4e0a4df821b1e57888f510146b8aee0b0fdcb46f5aaef31988c3b239"},"schema_version":"1.0","source":{"id":"2412.10486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.10486","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"2412.10486v2","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.10486","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"QLZGEUISAHNM","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QLZGEUISAHNMO3KY","created_at":"2026-07-05T11:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QLZGEUIS","created_at":"2026-07-05T11:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:b9b67450ab6cde6bcabb0f4cf083af1ee1ac51d671e770bf7cfe55f4e831469b","target":"graph","created_at":"2026-07-05T11:26:01Z","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/2412.10486/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, let $A$ be a unital separable simple infinite dimensional C*-algebra which has uniform property $\\Gamma$. Let $\\alpha\\colon G\\to \\mathrm{Aut}(A)$ be an action of a finite group which has the weak tracial Rokhlin property. Then we prove that the crossed product $A\\rtimes_\\alpha G$ and fixed point algebra $A^\\alpha$ have uniform property $\\Gamma$. Let $\\alpha\\colon G\\to \\mathrm{Aut}(A)$ be an action of a second-countable compact group which has the tracial Rokhlin property with comparison. Then we prove that the crossed product $A\\rtimes_\\alpha G$ and fixed point algebra $A^\\alpha","authors_text":"Haotian Tian, Xiaochun Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-13T13:49:21Z","title":"Uniform property $\\Gamma$ for Crossed products by group actions with the Rokhlin-type properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.10486","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:e0abaed23f10acd4ebe5322cb794fec571e2c473e5a031c0813bf413ae95b46b","target":"record","created_at":"2026-07-05T11:26:01Z","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":"1cc9f2521bf43460e5a49971736da670bc02e7fbc8cf351bb606c54941102cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-13T13:49:21Z","title_canon_sha256":"e8f2c35f4e0a4df821b1e57888f510146b8aee0b0fdcb46f5aaef31988c3b239"},"schema_version":"1.0","source":{"id":"2412.10486","kind":"arxiv","version":2}},"canonical_sha256":"82f262511201dac76d58d6a91a91f1387391a6e09b772b46e4f30418f8e8068d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82f262511201dac76d58d6a91a91f1387391a6e09b772b46e4f30418f8e8068d","first_computed_at":"2026-07-05T11:26:01.884908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:01.884908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kpSi3PBFcnY9y584AVX3E2bKnjLiTBGgN8WyvGkXXjNh3XtMvPZvO+xcUx2EGPdBDKP+CKcJfkqDb7/F+6q4BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:01.885395Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.10486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0abaed23f10acd4ebe5322cb794fec571e2c473e5a031c0813bf413ae95b46b","sha256:b9b67450ab6cde6bcabb0f4cf083af1ee1ac51d671e770bf7cfe55f4e831469b"],"state_sha256":"32e2196aa8d4a9dc95a7eb25ee3240455d3519652a9bc985ded7e6f5f2d0eebe"}