{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IQCVKO2OD5JI5MUO7LB7P6652H","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":"7bd077d1607abf29ed73500bdafbfe5d669f9216081838a4a287c1c00c5712e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-06T11:22:42Z","title_canon_sha256":"dce996c003b8bf2b11b2616a690228ff86bbb5071ec121bcd0691a97a6d70aa5"},"schema_version":"1.0","source":{"id":"1712.02133","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02133","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02133v1","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02133","created_at":"2026-05-18T00:28:39Z"},{"alias_kind":"pith_short_12","alias_value":"IQCVKO2OD5JI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IQCVKO2OD5JI5MUO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IQCVKO2O","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:a7f5f9336c6da17a8e342ab5676bdbc2462dbc3ff679bca0ace63689bb16d7bb","target":"graph","created_at":"2026-05-18T00:28:39Z","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 centrally essential ring is a ring which is an essential extension of its center (we consider the ring as a module over its center). We give several examples of noncommutative centrally essential rings and describe some properties of centrally essential rings. V.T.Markov is supported by the Russian Foundation for Basic Research, project 17-01-00895-A. A.A.Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013.","authors_text":"Askar Tuganbaev, Victor Markov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-06T11:22:42Z","title":"Rings Which Are Essential over Their Centers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02133","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":"sha256:42da7011eaf59d13290bbca353f1e450d97f7d348da22fab555af6c7bb32aa62","target":"record","created_at":"2026-05-18T00:28:39Z","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":"7bd077d1607abf29ed73500bdafbfe5d669f9216081838a4a287c1c00c5712e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-12-06T11:22:42Z","title_canon_sha256":"dce996c003b8bf2b11b2616a690228ff86bbb5071ec121bcd0691a97a6d70aa5"},"schema_version":"1.0","source":{"id":"1712.02133","kind":"arxiv","version":1}},"canonical_sha256":"4405553b4e1f528eb28efac3f7fbddd1fc620b955c55181e675bf2143bb40edf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4405553b4e1f528eb28efac3f7fbddd1fc620b955c55181e675bf2143bb40edf","first_computed_at":"2026-05-18T00:28:39.099021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:39.099021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"edjQV8jtWXQBK96sTP/bBresoBuHQsy+Fh+BTch7iL0iGiSZp058P6TkF5DP4FGnTo/RJSprx8EbP/DVUKdiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:39.099714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02133","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42da7011eaf59d13290bbca353f1e450d97f7d348da22fab555af6c7bb32aa62","sha256:a7f5f9336c6da17a8e342ab5676bdbc2462dbc3ff679bca0ace63689bb16d7bb"],"state_sha256":"f5432c20d73fdad8ce248785b115ed514127b3e91e9b53e69f4368b0e83a0001"}