{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GKHRPU7JLKWEGVLTO3F63324AH","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":"c0b1cdd4e45c5ff786a8fa56c12af22d6eff3a2ca5ac92766ddb566e7273df8a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-26T00:44:13Z","title_canon_sha256":"6988a1aabcddcf1583c1e11c9149dd89d1cf359c931833dd31509b0539e00f42"},"schema_version":"1.0","source":{"id":"1105.5179","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5179","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5179v3","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5179","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"GKHRPU7JLKWE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKHRPU7JLKWEGVLT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKHRPU7J","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:e7e6db962efe18d791efc8f166041c4931c4756cd1df5f48e2440910a22aff7c","target":"graph","created_at":"2026-05-18T00:17:55Z","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":"A ring $R$ is called a PIR, if each ideal of $R$ is a principal ideal. An local ring $(R,\\mf{m)}$ is a artinian PIR if and only if its maximal ideal $\\mf{m}$ is principal and has finite nilpotency index. In this paper, we determine the structure of a finite local PIR.","authors_text":"Dancheng Lu, Houyi Yu, Tongsuo Wu","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-26T00:44:13Z","title":"The structure of finite local principal ideal rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5179","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":"sha256:4c70f2ecf61ffcde54627480f1c30c14b6810f1894f62954e717ff53940fdcf8","target":"record","created_at":"2026-05-18T00:17:55Z","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":"c0b1cdd4e45c5ff786a8fa56c12af22d6eff3a2ca5ac92766ddb566e7273df8a","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-26T00:44:13Z","title_canon_sha256":"6988a1aabcddcf1583c1e11c9149dd89d1cf359c931833dd31509b0539e00f42"},"schema_version":"1.0","source":{"id":"1105.5179","kind":"arxiv","version":3}},"canonical_sha256":"328f17d3e95aac43557376cbedef5c01e7f9b31bdc2e106ba1fd1f10ae248634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"328f17d3e95aac43557376cbedef5c01e7f9b31bdc2e106ba1fd1f10ae248634","first_computed_at":"2026-05-18T00:17:55.820283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:55.820283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"34Hahb1dMH7Gasssr4mzeLLx8jbx8+u6OhS6v1ePlgLijKiDpXtdv+0iq2hoOf9lPUCDxY14HbAzw62dHcFhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:55.820910Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5179","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c70f2ecf61ffcde54627480f1c30c14b6810f1894f62954e717ff53940fdcf8","sha256:e7e6db962efe18d791efc8f166041c4931c4756cd1df5f48e2440910a22aff7c"],"state_sha256":"69297ceb8732b7f7d0e5c0101a79284d8e310d7731a8de0407e473ecccd972d4"}