{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:22GG7WAZMSNUXMNBI4KZXGOKNA","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":"04730dddaaeecd49921577d544a4122d134219b5ef056be3eb5ea35a09c7f80e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-02T13:03:04Z","title_canon_sha256":"60988501f14380960b5c86e90b3c4c1302afcd75ceab8b9814470ac76a8d7aa9"},"schema_version":"1.0","source":{"id":"1001.0303","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0303","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0303v3","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0303","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"22GG7WAZMSNU","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"22GG7WAZMSNUXMNB","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"22GG7WAZ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:04299bd9f444bc5a500a9b707036683880d02b6a1ec6962c48400fa763154d38","target":"graph","created_at":"2026-05-18T03:37:09Z","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 if a groupoid graded ring has a certain nonzero ideal property, then the commutant of the center of the principal component of the ring has the ideal intersection property, that is it intersects nontrivially every nonzero ideal of the ring. Furthermore, we show that for skew groupoid algebras with commutative principal component, the principal component is maximal commutative if and only if it has the ideal intersection property.","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-02T13:03:04Z","title":"The Ideal Intersection Property for Groupoid Graded Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0303","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:bc788f6454b7042eea994ce512f8bd270db8d9fefd64f3d4033a3160af873949","target":"record","created_at":"2026-05-18T03:37:09Z","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":"04730dddaaeecd49921577d544a4122d134219b5ef056be3eb5ea35a09c7f80e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-01-02T13:03:04Z","title_canon_sha256":"60988501f14380960b5c86e90b3c4c1302afcd75ceab8b9814470ac76a8d7aa9"},"schema_version":"1.0","source":{"id":"1001.0303","kind":"arxiv","version":3}},"canonical_sha256":"d68c6fd819649b4bb1a147159b99ca68261d49c5f707be3072dc8ea9f7598b8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d68c6fd819649b4bb1a147159b99ca68261d49c5f707be3072dc8ea9f7598b8b","first_computed_at":"2026-05-18T03:37:09.468908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:09.468908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R3Cv3aY+F0x7NuGT21BD3ihQ5K4bvWtN3JCGwWTpch1jJx6ZOsCvj5no7be+ndOJWSzaK8q6AF6wsk2/wbiHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:09.469708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0303","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc788f6454b7042eea994ce512f8bd270db8d9fefd64f3d4033a3160af873949","sha256:04299bd9f444bc5a500a9b707036683880d02b6a1ec6962c48400fa763154d38"],"state_sha256":"0c80f3ddc5aa3dc36e494a595bd88b4c5c2abff1e346ca5ec77074795273eefe"}