{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Z4YTWZTYL6JSFIMUYIWCY573R6","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":"fd372cd3b72be2276b919969c8f3d0e55981f481e2be1e2891d2ebfb7dcaa796","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2022-11-18T13:39:26Z","title_canon_sha256":"baafdd75d30ddc18b9db88fdb6233fe5ba6a011f7898a8667365ae216cb37808"},"schema_version":"1.0","source":{"id":"2211.10233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.10233","created_at":"2026-07-05T05:21:28Z"},{"alias_kind":"arxiv_version","alias_value":"2211.10233v2","created_at":"2026-07-05T05:21:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.10233","created_at":"2026-07-05T05:21:28Z"},{"alias_kind":"pith_short_12","alias_value":"Z4YTWZTYL6JS","created_at":"2026-07-05T05:21:28Z"},{"alias_kind":"pith_short_16","alias_value":"Z4YTWZTYL6JSFIMU","created_at":"2026-07-05T05:21:28Z"},{"alias_kind":"pith_short_8","alias_value":"Z4YTWZTY","created_at":"2026-07-05T05:21:28Z"}],"graph_snapshots":[{"event_id":"sha256:3e7d23249a5d797b70ffa749b6a1a0bf7844dcbc0edcbb8f53a9391e45c0ed46","target":"graph","created_at":"2026-07-05T05:21:28Z","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/2211.10233/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple, $E^0$ has no nontrivial hereditary and saturated subset, and every cycle in $E$ has an exit. We also give a complete description of the center of a simple Leavitt path algebra.","authors_text":"Johan \\\"Oinert, Patrik Lundstr\\\"om","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2022-11-18T13:39:26Z","title":"Simplicity of Leavitt path algebras via graded ring theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.10233","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:f0dea3886410473367ad1f2e274d26ed7913a1fdc13a3d967749ca3a4522e04d","target":"record","created_at":"2026-07-05T05:21:28Z","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":"fd372cd3b72be2276b919969c8f3d0e55981f481e2be1e2891d2ebfb7dcaa796","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2022-11-18T13:39:26Z","title_canon_sha256":"baafdd75d30ddc18b9db88fdb6233fe5ba6a011f7898a8667365ae216cb37808"},"schema_version":"1.0","source":{"id":"2211.10233","kind":"arxiv","version":2}},"canonical_sha256":"cf313b66785f9322a194c22c2c77fb8f8a63eedf9a5f1629943ec590e14d0b02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf313b66785f9322a194c22c2c77fb8f8a63eedf9a5f1629943ec590e14d0b02","first_computed_at":"2026-07-05T05:21:28.513276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:21:28.513276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lHwx0xDbR0q0RoLZg1oO02ZEftDq/w3qHj7zWHl5MqiPvghYjHCWf5CNA96fDZcEaEfbhYukU8duTf9robblDA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:21:28.513660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.10233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0dea3886410473367ad1f2e274d26ed7913a1fdc13a3d967749ca3a4522e04d","sha256:3e7d23249a5d797b70ffa749b6a1a0bf7844dcbc0edcbb8f53a9391e45c0ed46"],"state_sha256":"d209d162abc3096f1742730304ea58c42707bf5fd9065a72e5cc79342e6dcde8"}