{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EVQUH75NBDDTC6Q7BJF6R5PVZI","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":"d8b2f590563f268431cadd62ebae505fc940f5cd685e0ea770e2c2401fd0722e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-30T12:48:29Z","title_canon_sha256":"7e18bfcdd34b5f2114f532773affeac337c23429a9814ad8a3ea7baa1f29aee9"},"schema_version":"1.0","source":{"id":"1710.10908","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10908","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10908v3","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10908","created_at":"2026-05-18T00:16:44Z"},{"alias_kind":"pith_short_12","alias_value":"EVQUH75NBDDT","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EVQUH75NBDDTC6Q7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EVQUH75N","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:7f4528e4b27f043a3a606b16b0fdeabf1228fc6e5c8abf05e7ba57a3c92bcb50","target":"graph","created_at":"2026-05-18T00:16:44Z","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 finite group $G$ is called a Schur group if any Schur ring over $G$ is associated in a natural way with a subgroup of $Sym(G)$ that contains all right translations. It is proved that the group $C_3\\times C_3\\times C_p$ is Schur for any prime $p$. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.","authors_text":"Grigory Ryabov, Ilia Ponomarenko","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-30T12:48:29Z","title":"Abelian Schur groups of odd order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10908","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":"sha256:8313f043fbb47359de071b702585ab2b8c5c1d4b17b860cc793120ec90c1dda4","target":"record","created_at":"2026-05-18T00:16:44Z","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":"d8b2f590563f268431cadd62ebae505fc940f5cd685e0ea770e2c2401fd0722e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-10-30T12:48:29Z","title_canon_sha256":"7e18bfcdd34b5f2114f532773affeac337c23429a9814ad8a3ea7baa1f29aee9"},"schema_version":"1.0","source":{"id":"1710.10908","kind":"arxiv","version":3}},"canonical_sha256":"256143ffad08c7317a1f0a4be8f5f5ca38c4f5434cccd387dcba3ef958f22a7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"256143ffad08c7317a1f0a4be8f5f5ca38c4f5434cccd387dcba3ef958f22a7a","first_computed_at":"2026-05-18T00:16:44.742886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:44.742886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PeXYC3vIaATQTbL8DIuujN9yzjfblRg9LkOXQzBHBeDxtMSdmW1KvqV0A+IQu5NkZC7fNiOqehp1JCZLdomDAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:44.743527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10908","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8313f043fbb47359de071b702585ab2b8c5c1d4b17b860cc793120ec90c1dda4","sha256:7f4528e4b27f043a3a606b16b0fdeabf1228fc6e5c8abf05e7ba57a3c92bcb50"],"state_sha256":"b0b5e6e5b929bd712ba3e7dc192112fbe870d187b5d7f85c02b710f2cd6f438d"}