{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:7DABIPIMIT6RBUYLWH63CVVHZK","short_pith_number":"pith:7DABIPIM","schema_version":"1.0","canonical_sha256":"f8c0143d0c44fd10d30bb1fdb156a7ca976e016d22a106a3af2746ccde3e34cb","source":{"kind":"arxiv","id":"2605.18356","version":1},"attestation_state":"computed","paper":{"title":"Classification of abelian Schur groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Grigory Ryabov","submitted_at":"2026-05-18T13:12:18Z","abstract_excerpt":"A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kov\\'acs, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we prove that several groups of nonpowerful order from the list are Schur groups. By that, we obtain a classification of abelian Schur groups."},"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":"2605.18356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-18T13:12:18Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"b8a1c32dbc53275c37599773a48d2ae0bab1b8be01e13e6c13cff5a8acbd6a05","abstract_canon_sha256":"0da49ec48ef95cd113a71ad89f2cf0121e386d88261c6808e0690f6e126601d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:56.845659Z","signature_b64":"81EyEl6vyQaNtjJttBDdvqnMG1JYJBvRG+gO8kuB0VANRIg96lWGvw4Jhh9bEGkFukWT3oHq7DK2eG4mV0lJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8c0143d0c44fd10d30bb1fdb156a7ca976e016d22a106a3af2746ccde3e34cb","last_reissued_at":"2026-05-20T00:05:56.844908Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:56.844908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of abelian Schur groups II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Grigory Ryabov","submitted_at":"2026-05-18T13:12:18Z","abstract_excerpt":"A finite group $G$ is called a Schur group if every Schur ring over $G$ is schurian, i.e. associated in a natural way with a subgroup of the symmetric group $Sym(G)$ that contains all right translations of $G$. The list of all possible abelian Schur groups was obtained by Evdokimov, Kov\\'acs, and Ponomarenko in 2016. In two papers, we complete a classification of abelian Schur groups. In the present paper, we prove that several groups of nonpowerful order from the list are Schur groups. By that, we obtain a classification of abelian Schur groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18356","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/2605.18356/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:31.330516Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"external_links","ran_at":"2026-05-19T23:31:54.128219Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T23:21:58.800049Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"389a579886ff5b0cbfc2401058f7a57fe3e15961fd92d76c71925eb004ecb67c"},"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":"2605.18356","created_at":"2026-05-20T00:05:56.845051+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.18356v1","created_at":"2026-05-20T00:05:56.845051+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18356","created_at":"2026-05-20T00:05:56.845051+00:00"},{"alias_kind":"pith_short_12","alias_value":"7DABIPIMIT6R","created_at":"2026-05-20T00:05:56.845051+00:00"},{"alias_kind":"pith_short_16","alias_value":"7DABIPIMIT6RBUYL","created_at":"2026-05-20T00:05:56.845051+00:00"},{"alias_kind":"pith_short_8","alias_value":"7DABIPIM","created_at":"2026-05-20T00:05:56.845051+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/7DABIPIMIT6RBUYLWH63CVVHZK","json":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK.json","graph_json":"https://pith.science/api/pith-number/7DABIPIMIT6RBUYLWH63CVVHZK/graph.json","events_json":"https://pith.science/api/pith-number/7DABIPIMIT6RBUYLWH63CVVHZK/events.json","paper":"https://pith.science/paper/7DABIPIM"},"agent_actions":{"view_html":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK","download_json":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK.json","view_paper":"https://pith.science/paper/7DABIPIM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.18356&json=true","fetch_graph":"https://pith.science/api/pith-number/7DABIPIMIT6RBUYLWH63CVVHZK/graph.json","fetch_events":"https://pith.science/api/pith-number/7DABIPIMIT6RBUYLWH63CVVHZK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK/action/storage_attestation","attest_author":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK/action/author_attestation","sign_citation":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK/action/citation_signature","submit_replication":"https://pith.science/pith/7DABIPIMIT6RBUYLWH63CVVHZK/action/replication_record"}},"created_at":"2026-05-20T00:05:56.845051+00:00","updated_at":"2026-05-20T00:05:56.845051+00:00"}