{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:QGZBSGQQQYDRBCYP4KFMVORE25","short_pith_number":"pith:QGZBSGQQ","schema_version":"1.0","canonical_sha256":"81b2191a108607108b0fe28acaba24d77ed3dccdb997be2c761f0ccbf9364997","source":{"kind":"arxiv","id":"1805.03484","version":2},"attestation_state":"computed","paper":{"title":"Regulators of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Pazuki, Marc Hindry, Pascal Autissier","submitted_at":"2018-05-09T12:44:39Z","abstract_excerpt":"We study the regulator of the Mordell-Weil group of elliptic curves over number fields, functions fields of characteristic zero or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank at least $4$ defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions."},"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":"1805.03484","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-09T12:44:39Z","cross_cats_sorted":[],"title_canon_sha256":"5eee54b052ac0ec67fa114e43de1e499f7b09009a1b16300569e145221dcc4c0","abstract_canon_sha256":"195671e83f60f4c079ef5ba469efadf009bb5942605f7b11a4470619d4c40b74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:34.040691Z","signature_b64":"8o2GRhJVQasn05amWtyoY0GkHkvTB54tBkDBJdL8wUt36pBVujeVu0RHPw4JMsTuY3MkNmUH3biopYlLvZbmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81b2191a108607108b0fe28acaba24d77ed3dccdb997be2c761f0ccbf9364997","last_reissued_at":"2026-05-17T23:52:34.040358Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:34.040358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regulators of elliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fabien Pazuki, Marc Hindry, Pascal Autissier","submitted_at":"2018-05-09T12:44:39Z","abstract_excerpt":"We study the regulator of the Mordell-Weil group of elliptic curves over number fields, functions fields of characteristic zero or function fields of characteristic $p>0$. We prove a new Northcott property for the regulator of elliptic curves of rank at least $4$ defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03484","kind":"arxiv","version":2},"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":"1805.03484","created_at":"2026-05-17T23:52:34.040413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.03484v2","created_at":"2026-05-17T23:52:34.040413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03484","created_at":"2026-05-17T23:52:34.040413+00:00"},{"alias_kind":"pith_short_12","alias_value":"QGZBSGQQQYDR","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_16","alias_value":"QGZBSGQQQYDRBCYP","created_at":"2026-05-18T12:32:46.962924+00:00"},{"alias_kind":"pith_short_8","alias_value":"QGZBSGQQ","created_at":"2026-05-18T12:32:46.962924+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/QGZBSGQQQYDRBCYP4KFMVORE25","json":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25.json","graph_json":"https://pith.science/api/pith-number/QGZBSGQQQYDRBCYP4KFMVORE25/graph.json","events_json":"https://pith.science/api/pith-number/QGZBSGQQQYDRBCYP4KFMVORE25/events.json","paper":"https://pith.science/paper/QGZBSGQQ"},"agent_actions":{"view_html":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25","download_json":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25.json","view_paper":"https://pith.science/paper/QGZBSGQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.03484&json=true","fetch_graph":"https://pith.science/api/pith-number/QGZBSGQQQYDRBCYP4KFMVORE25/graph.json","fetch_events":"https://pith.science/api/pith-number/QGZBSGQQQYDRBCYP4KFMVORE25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25/action/storage_attestation","attest_author":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25/action/author_attestation","sign_citation":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25/action/citation_signature","submit_replication":"https://pith.science/pith/QGZBSGQQQYDRBCYP4KFMVORE25/action/replication_record"}},"created_at":"2026-05-17T23:52:34.040413+00:00","updated_at":"2026-05-17T23:52:34.040413+00:00"}