{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QJADAFBTHGEPWZJ2FTDAWJU7SR","short_pith_number":"pith:QJADAFBT","schema_version":"1.0","canonical_sha256":"82403014333988fb653a2cc60b269f9466e5f2c5efd6769b20689a3905c4628c","source":{"kind":"arxiv","id":"2606.04747","version":1},"attestation_state":"computed","paper":{"title":"Extensions of Centrally Essential Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Askar Tuganbaev, Oleg Lyubimtsev","submitted_at":"2026-06-03T11:28:43Z","abstract_excerpt":"A non-zero unital ring $R$ is said to be centrally essential if for every nonzero element $a$ of $R$, there exist non-zero central elements $x$ and $y$ with $ax = y$. In the paper, almost fully prime centrally essential rings are described in terms of ideal extensions, centrally essential Dorroh extensions, and trivial extensions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.04747","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RA","submitted_at":"2026-06-03T11:28:43Z","cross_cats_sorted":[],"title_canon_sha256":"0dd561b8bd21f2ce9b4cef47198434e07c23117ea60f74f1eef4322995dd7eea","abstract_canon_sha256":"6612d0a8b07451296ae1ab907c3ad68687e462bd3f700d1f3b70eb40a31aa5ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:28.331303Z","signature_b64":"rsBB9eCBI9qIUkNVtV0oa+uzx3xCBdk/M1ELt+zraoEPN3wqBBow+BARgFC9DjEObSoSiyOt5J33A+QlKH8iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82403014333988fb653a2cc60b269f9466e5f2c5efd6769b20689a3905c4628c","last_reissued_at":"2026-06-04T01:09:28.330603Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:28.330603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of Centrally Essential Rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Askar Tuganbaev, Oleg Lyubimtsev","submitted_at":"2026-06-03T11:28:43Z","abstract_excerpt":"A non-zero unital ring $R$ is said to be centrally essential if for every nonzero element $a$ of $R$, there exist non-zero central elements $x$ and $y$ with $ax = y$. In the paper, almost fully prime centrally essential rings are described in terms of ideal extensions, centrally essential Dorroh extensions, and trivial extensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04747","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04747/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.04747","created_at":"2026-06-04T01:09:28.330715+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04747v1","created_at":"2026-06-04T01:09:28.330715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04747","created_at":"2026-06-04T01:09:28.330715+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJADAFBTHGEP","created_at":"2026-06-04T01:09:28.330715+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJADAFBTHGEPWZJ2","created_at":"2026-06-04T01:09:28.330715+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJADAFBT","created_at":"2026-06-04T01:09:28.330715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR","json":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR.json","graph_json":"https://pith.science/api/pith-number/QJADAFBTHGEPWZJ2FTDAWJU7SR/graph.json","events_json":"https://pith.science/api/pith-number/QJADAFBTHGEPWZJ2FTDAWJU7SR/events.json","paper":"https://pith.science/paper/QJADAFBT"},"agent_actions":{"view_html":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR","download_json":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR.json","view_paper":"https://pith.science/paper/QJADAFBT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04747&json=true","fetch_graph":"https://pith.science/api/pith-number/QJADAFBTHGEPWZJ2FTDAWJU7SR/graph.json","fetch_events":"https://pith.science/api/pith-number/QJADAFBTHGEPWZJ2FTDAWJU7SR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR/action/storage_attestation","attest_author":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR/action/author_attestation","sign_citation":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR/action/citation_signature","submit_replication":"https://pith.science/pith/QJADAFBTHGEPWZJ2FTDAWJU7SR/action/replication_record"}},"created_at":"2026-06-04T01:09:28.330715+00:00","updated_at":"2026-06-04T01:09:28.330715+00:00"}