{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OJQGRTUZHNPCLKZRLVRU3XN7C2","short_pith_number":"pith:OJQGRTUZ","schema_version":"1.0","canonical_sha256":"726068ce993b5e25ab315d634dddbf16b10be065051c06482752c4798138ec36","source":{"kind":"arxiv","id":"1211.2188","version":4},"attestation_state":"computed","paper":{"title":"Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Filip Najman","submitted_at":"2012-11-09T16:59:14Z","abstract_excerpt":"We classify the possible torsion structures of rational elliptic curves over cubic fields. Along the way we find a previously unknown torsion structure over a cubic field, $\\Z /21 \\Z$, which corresponds to a sporadic point on $X_1(21)$ of degree 3, which is the lowest possible degree of a sporadic point on a modular curve $X_1(n)$."},"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":"1211.2188","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2012-11-09T16:59:14Z","cross_cats_sorted":[],"title_canon_sha256":"4876835430f23c18872812d048d49b239511021f1dc2027ac975f9245d35ec15","abstract_canon_sha256":"dfca88a1a4dbbaadb1d345359b4bf6203d523c347bbab87a8fa968b123107dc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:45.661829Z","signature_b64":"UILHC3CEK9TUaxiyXFwUcW0ePMv7lbcnVVnRf1gEo6A+X3uyruZQxsCJhvYgxbFyGn4v/792sAqO1gUTCpp6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"726068ce993b5e25ab315d634dddbf16b10be065051c06482752c4798138ec36","last_reissued_at":"2026-05-18T02:43:45.661405Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:45.661405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torsion of rational elliptic curves over cubic fields and sporadic points on $X_1(n)$","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Filip Najman","submitted_at":"2012-11-09T16:59:14Z","abstract_excerpt":"We classify the possible torsion structures of rational elliptic curves over cubic fields. Along the way we find a previously unknown torsion structure over a cubic field, $\\Z /21 \\Z$, which corresponds to a sporadic point on $X_1(21)$ of degree 3, which is the lowest possible degree of a sporadic point on a modular curve $X_1(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2188","kind":"arxiv","version":4},"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":"1211.2188","created_at":"2026-05-18T02:43:45.661471+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.2188v4","created_at":"2026-05-18T02:43:45.661471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2188","created_at":"2026-05-18T02:43:45.661471+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJQGRTUZHNPC","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJQGRTUZHNPCLKZR","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJQGRTUZ","created_at":"2026-05-18T12:27:16.716162+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/OJQGRTUZHNPCLKZRLVRU3XN7C2","json":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2.json","graph_json":"https://pith.science/api/pith-number/OJQGRTUZHNPCLKZRLVRU3XN7C2/graph.json","events_json":"https://pith.science/api/pith-number/OJQGRTUZHNPCLKZRLVRU3XN7C2/events.json","paper":"https://pith.science/paper/OJQGRTUZ"},"agent_actions":{"view_html":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2","download_json":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2.json","view_paper":"https://pith.science/paper/OJQGRTUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.2188&json=true","fetch_graph":"https://pith.science/api/pith-number/OJQGRTUZHNPCLKZRLVRU3XN7C2/graph.json","fetch_events":"https://pith.science/api/pith-number/OJQGRTUZHNPCLKZRLVRU3XN7C2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2/action/storage_attestation","attest_author":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2/action/author_attestation","sign_citation":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2/action/citation_signature","submit_replication":"https://pith.science/pith/OJQGRTUZHNPCLKZRLVRU3XN7C2/action/replication_record"}},"created_at":"2026-05-18T02:43:45.661471+00:00","updated_at":"2026-05-18T02:43:45.661471+00:00"}