{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TKVZHEQYJXXBK6NP2QMKRTZX7X","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":"9a9961467f73134b0550afaa890d62a8dc88732e749f48c6da60c38d9754f376","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-19T16:02:50Z","title_canon_sha256":"4490a2a8640ad580e0253170ec39f83a23bf6e14f73de5732d3ef61e68d4de49"},"schema_version":"1.0","source":{"id":"1801.06474","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06474","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06474v2","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06474","created_at":"2026-05-18T00:12:48Z"},{"alias_kind":"pith_short_12","alias_value":"TKVZHEQYJXXB","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TKVZHEQYJXXBK6NP","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TKVZHEQY","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:9c5656d227d9aa2b02a1f6acefcc21eb6f4a483e11203ab6c326da4a2eecf3e4","target":"graph","created_at":"2026-05-18T00:12:48Z","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":"In a paper on the taxonomy of 2-primal rings, examples of various types of rings that are related to commutativity such as reduced, symmetric, duo, reversible and PS~I were given in order to show that the ring class inclusions were strict. Many of the rings given in the examples were infinite. In this paper, where possible, examples of minimal finite rings of the various types are given. Along with the rings in the previous taxonomy, NI, abelian and reflexive rings are also included.","authors_text":"Steve Szabo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-19T16:02:50Z","title":"Some Minimal Rings Related to 2-Primal Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06474","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:f1c2ce8f16ecd07d9baa7350ab5ad3e42af00c91758d3da8fe70fe33b33fce62","target":"record","created_at":"2026-05-18T00:12:48Z","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":"9a9961467f73134b0550afaa890d62a8dc88732e749f48c6da60c38d9754f376","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-01-19T16:02:50Z","title_canon_sha256":"4490a2a8640ad580e0253170ec39f83a23bf6e14f73de5732d3ef61e68d4de49"},"schema_version":"1.0","source":{"id":"1801.06474","kind":"arxiv","version":2}},"canonical_sha256":"9aab9392184dee1579afd418a8cf37fdc87b2d2dd9a3a6e97c8024d11754ae67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aab9392184dee1579afd418a8cf37fdc87b2d2dd9a3a6e97c8024d11754ae67","first_computed_at":"2026-05-18T00:12:48.442072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:48.442072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tG3DnOwTs7UQni6UWmIw9ZQZzgyzWokiK7fapixbg/fBC/4qWo/JSUYY+QStw7XNDi04sNcUxsIhiik7RUpIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:48.442620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06474","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1c2ce8f16ecd07d9baa7350ab5ad3e42af00c91758d3da8fe70fe33b33fce62","sha256:9c5656d227d9aa2b02a1f6acefcc21eb6f4a483e11203ab6c326da4a2eecf3e4"],"state_sha256":"a1379d7dba5c47eb55a9436a613b6e7fd1479089650f85bb5132a56bad044484"}