{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IUGOBE2O2IYYUU2GQHGBYYI4C4","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":"46a530642b6d71bbfb53630baebda8b3806c8ea818b448fb222e520fbe0050f8","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-14T17:12:54Z","title_canon_sha256":"dd080ce4e048182913b9c7673bc7833b8583ec5707f9724f4730ed5259ac6de5"},"schema_version":"1.0","source":{"id":"1302.3476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3476","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3476v1","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3476","created_at":"2026-05-18T03:33:38Z"},{"alias_kind":"pith_short_12","alias_value":"IUGOBE2O2IYY","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IUGOBE2O2IYYUU2G","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IUGOBE2O","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:3b6ab0a25e75fbbd266b8e0a2dddd59952c3c221cc5b7e7bc6b19ff55e2a79a8","target":"graph","created_at":"2026-05-18T03:33:38Z","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 study some generalizations of the notion of regular crossed products K*G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K*G to be an n-weakly regular ring, a $\\xi^* N$-ring or a ring without nilpotent elements.","authors_text":"S. Mihovski, V. Bovdi","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-14T17:12:54Z","title":"On the regularity of crossed products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3476","kind":"arxiv","version":1},"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":"sha256:6ccee2cba09f34efbb37259beaf95d2c61dca17a00409e1e0e1c0e6fe7eee41f","target":"record","created_at":"2026-05-18T03:33:38Z","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":"46a530642b6d71bbfb53630baebda8b3806c8ea818b448fb222e520fbe0050f8","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-14T17:12:54Z","title_canon_sha256":"dd080ce4e048182913b9c7673bc7833b8583ec5707f9724f4730ed5259ac6de5"},"schema_version":"1.0","source":{"id":"1302.3476","kind":"arxiv","version":1}},"canonical_sha256":"450ce0934ed2318a534681cc1c611c173d8a3150498a1e9facf1ffd68fc7fb7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"450ce0934ed2318a534681cc1c611c173d8a3150498a1e9facf1ffd68fc7fb7d","first_computed_at":"2026-05-18T03:33:38.487613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:38.487613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ywvmo62J8dcBaLzVArnVrjwdWn/wuhCGMOU3ViGymgBDdsNrg1pNNsiajXb3a3PITHF4CqrniHixMJuHWfKLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:38.488143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ccee2cba09f34efbb37259beaf95d2c61dca17a00409e1e0e1c0e6fe7eee41f","sha256:3b6ab0a25e75fbbd266b8e0a2dddd59952c3c221cc5b7e7bc6b19ff55e2a79a8"],"state_sha256":"96efd8117323169a7c8cf0534a6e183b89df6d517993b31b26b531431a00812e"}