{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GYRQHUUBOZDXLYUYFYDIU2EN4L","short_pith_number":"pith:GYRQHUUB","schema_version":"1.0","canonical_sha256":"362303d281764775e2982e068a688de2e5b20fefc6a1f6c6b954790f1448af7f","source":{"kind":"arxiv","id":"1606.00645","version":3},"attestation_state":"computed","paper":{"title":"On the torsion of rational elliptic curves over quartic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alvaro Lozano-Robledo, Enrique Gonzalez-Jimenez","submitted_at":"2016-06-02T12:17:58Z","abstract_excerpt":"Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the associated torsion subgroup. We study, for a given G, which possible groups G <= H could appear such that H=E(K)_tors, for [K:Q]=4 and H is one of the possible torsion structures that occur infinitely often as torsion structures of elliptic curves defined over quartic number fields."},"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":"1606.00645","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T12:17:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"44fe35901996c9bb84af5a2b483212913bad4c934ae87cce841e9e3f1d7b4ae6","abstract_canon_sha256":"07d3e431f687986e538378556aad0e81f4df2a92035cff3855b55ce6b05a089d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:00.545230Z","signature_b64":"AhP/sxMYbevM4m7gf+8xqoqAe1Jnro9op65Xn/zmHPHVFiZV3oi+odn9qiGr+n7Nl1/dMjig86J4h241huQlAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"362303d281764775e2982e068a688de2e5b20fefc6a1f6c6b954790f1448af7f","last_reissued_at":"2026-05-17T23:51:00.544653Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:00.544653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the torsion of rational elliptic curves over quartic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Alvaro Lozano-Robledo, Enrique Gonzalez-Jimenez","submitted_at":"2016-06-02T12:17:58Z","abstract_excerpt":"Let E be an elliptic curve defined over Q and let G = E(Q)_tors be the associated torsion subgroup. We study, for a given G, which possible groups G <= H could appear such that H=E(K)_tors, for [K:Q]=4 and H is one of the possible torsion structures that occur infinitely often as torsion structures of elliptic curves defined over quartic number fields."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00645","kind":"arxiv","version":3},"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":"1606.00645","created_at":"2026-05-17T23:51:00.544731+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00645v3","created_at":"2026-05-17T23:51:00.544731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00645","created_at":"2026-05-17T23:51:00.544731+00:00"},{"alias_kind":"pith_short_12","alias_value":"GYRQHUUBOZDX","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GYRQHUUBOZDXLYUY","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GYRQHUUB","created_at":"2026-05-18T12:30:19.053100+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/GYRQHUUBOZDXLYUYFYDIU2EN4L","json":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L.json","graph_json":"https://pith.science/api/pith-number/GYRQHUUBOZDXLYUYFYDIU2EN4L/graph.json","events_json":"https://pith.science/api/pith-number/GYRQHUUBOZDXLYUYFYDIU2EN4L/events.json","paper":"https://pith.science/paper/GYRQHUUB"},"agent_actions":{"view_html":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L","download_json":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L.json","view_paper":"https://pith.science/paper/GYRQHUUB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00645&json=true","fetch_graph":"https://pith.science/api/pith-number/GYRQHUUBOZDXLYUYFYDIU2EN4L/graph.json","fetch_events":"https://pith.science/api/pith-number/GYRQHUUBOZDXLYUYFYDIU2EN4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L/action/storage_attestation","attest_author":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L/action/author_attestation","sign_citation":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L/action/citation_signature","submit_replication":"https://pith.science/pith/GYRQHUUBOZDXLYUYFYDIU2EN4L/action/replication_record"}},"created_at":"2026-05-17T23:51:00.544731+00:00","updated_at":"2026-05-17T23:51:00.544731+00:00"}