{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XCFR7INQZFA7E7K6GMD7OM32VN","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":"faab6253a9de816cd8105129473bd921706c29bd87c14c1f88cc6c96fa6e0985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-04-29T16:47:41Z","title_canon_sha256":"68f7d1a58681bdc90d6a9dd2adf83d76c5715c365c8b656ee6631b737664e74e"},"schema_version":"1.0","source":{"id":"0904.4661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4661","created_at":"2026-07-04T15:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4661v1","created_at":"2026-07-04T15:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4661","created_at":"2026-07-04T15:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"XCFR7INQZFA7","created_at":"2026-07-04T15:41:56Z"},{"alias_kind":"pith_short_16","alias_value":"XCFR7INQZFA7E7K6","created_at":"2026-07-04T15:41:56Z"},{"alias_kind":"pith_short_8","alias_value":"XCFR7INQ","created_at":"2026-07-04T15:41:56Z"}],"graph_snapshots":[{"event_id":"sha256:91e0d7a323078e808e6a9aed316f086bbbca0daaf022c9b8450006342b9701b4","target":"graph","created_at":"2026-07-04T15:41:56Z","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/0904.4661/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we provide necessary and sufficient conditions for strongly group graded rings to be simple. For a strongly group graded ring $R = \\bigoplus_{g\\in G} R_g$ the grading group $G$ acts, in a natural way, as automorphisms of the commutant of the neutral component subring $R_e$ in $R$ and of the center of $R_e$. We show that if $R$ is a strongly $G$-graded ring where $R_e$ is maximal commutative in $R$, then $R$ is a simple ring if and only if $R_e$ is $G$-simple (i.e. there are no nontrivial $G$-invariant ideals). We also show that if $R_e$ is commutative (not necessarily maximal com","authors_text":"Johan \\\"Oinert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-04-29T16:47:41Z","title":"Simple group graded rings and maximal commutativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4661","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":"sha256:5f6f7dc9d746e3bb7cb27e0fdb9c7b035233a8661da4bebd2c9700071ef96325","target":"record","created_at":"2026-07-04T15:41:56Z","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":"faab6253a9de816cd8105129473bd921706c29bd87c14c1f88cc6c96fa6e0985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-04-29T16:47:41Z","title_canon_sha256":"68f7d1a58681bdc90d6a9dd2adf83d76c5715c365c8b656ee6631b737664e74e"},"schema_version":"1.0","source":{"id":"0904.4661","kind":"arxiv","version":1}},"canonical_sha256":"b88b1fa1b0c941f27d5e3307f7337aab5b05d816768da8636f400827e65f5e3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b88b1fa1b0c941f27d5e3307f7337aab5b05d816768da8636f400827e65f5e3b","first_computed_at":"2026-07-04T15:41:56.612748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:41:56.612748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sLngOu8n4RG3UhFWyqzn3NydQkVUNiZMM26a87NiJIZhyyj3Cwix7vWqNrolbtVmHU+mi4nqiuL0T7++Yf+Bw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:41:56.613094Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f6f7dc9d746e3bb7cb27e0fdb9c7b035233a8661da4bebd2c9700071ef96325","sha256:91e0d7a323078e808e6a9aed316f086bbbca0daaf022c9b8450006342b9701b4"],"state_sha256":"d5d5c4ab3eeaec3242b80375d4e74f3d6f326e57914ea40cb42622c0ab303872"}