{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AX7BH5NX3J52I2EN5RAFOB7DXJ","short_pith_number":"pith:AX7BH5NX","schema_version":"1.0","canonical_sha256":"05fe13f5b7da7ba4688dec405707e3ba7f108309363b85dbaf849614acb2dcfe","source":{"kind":"arxiv","id":"1112.1422","version":1},"attestation_state":"computed","paper":{"title":"On radical square zero rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Bao-Lin Xiong, Claus Michael Ringel","submitted_at":"2011-12-06T21:16:18Z","abstract_excerpt":"Let A be a connected left artinian ring with radical square zero and with n simple modules. If A is not self-injective, then we show that any module M with Ext^i(M,A) = 0 for 1 \\le i \\le n + 1 is projective. We also determine the structure of the artin algebras with radical square zero and n simple modules which have a non-projective module M such that Ext^i(M,A) = 0 for 1 \\le i \\le n."},"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":"1112.1422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-12-06T21:16:18Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a972ed42db1e68ea60b84770471e234a01ab1337e1fc4260dad61fa4249e9a0a","abstract_canon_sha256":"5f289f1a0fafaddae860b0814ff7522eb2544fec703fc2a7d4ba525c0150d13b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:54.559477Z","signature_b64":"qr/EmHY5BevXpgL6hT5Kf0Gg/tMdvJCMdDsKuez1QPL6+ubSRBt7zg0nJnVdSm7F/INKttNTotx5R33aWc2KBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05fe13f5b7da7ba4688dec405707e3ba7f108309363b85dbaf849614acb2dcfe","last_reissued_at":"2026-05-18T04:06:54.558987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:54.558987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On radical square zero rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Bao-Lin Xiong, Claus Michael Ringel","submitted_at":"2011-12-06T21:16:18Z","abstract_excerpt":"Let A be a connected left artinian ring with radical square zero and with n simple modules. If A is not self-injective, then we show that any module M with Ext^i(M,A) = 0 for 1 \\le i \\le n + 1 is projective. We also determine the structure of the artin algebras with radical square zero and n simple modules which have a non-projective module M such that Ext^i(M,A) = 0 for 1 \\le i \\le n."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1422","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":""},"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":"1112.1422","created_at":"2026-05-18T04:06:54.559061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1422v1","created_at":"2026-05-18T04:06:54.559061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1422","created_at":"2026-05-18T04:06:54.559061+00:00"},{"alias_kind":"pith_short_12","alias_value":"AX7BH5NX3J52","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AX7BH5NX3J52I2EN","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AX7BH5NX","created_at":"2026-05-18T12:26:24.575870+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/AX7BH5NX3J52I2EN5RAFOB7DXJ","json":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ.json","graph_json":"https://pith.science/api/pith-number/AX7BH5NX3J52I2EN5RAFOB7DXJ/graph.json","events_json":"https://pith.science/api/pith-number/AX7BH5NX3J52I2EN5RAFOB7DXJ/events.json","paper":"https://pith.science/paper/AX7BH5NX"},"agent_actions":{"view_html":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ","download_json":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ.json","view_paper":"https://pith.science/paper/AX7BH5NX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1422&json=true","fetch_graph":"https://pith.science/api/pith-number/AX7BH5NX3J52I2EN5RAFOB7DXJ/graph.json","fetch_events":"https://pith.science/api/pith-number/AX7BH5NX3J52I2EN5RAFOB7DXJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ/action/storage_attestation","attest_author":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ/action/author_attestation","sign_citation":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ/action/citation_signature","submit_replication":"https://pith.science/pith/AX7BH5NX3J52I2EN5RAFOB7DXJ/action/replication_record"}},"created_at":"2026-05-18T04:06:54.559061+00:00","updated_at":"2026-05-18T04:06:54.559061+00:00"}