{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:UJGRQQUMWQWSOARWTA5YTB6ML5","short_pith_number":"pith:UJGRQQUM","schema_version":"1.0","canonical_sha256":"a24d18428cb42d270236983b8987cc5f4646c8757e5d4b2b7d80f888d6fd516d","source":{"kind":"arxiv","id":"1004.4785","version":2},"attestation_state":"computed","paper":{"title":"Tabulation of cubic function fields via polynomial binary cubic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Jacobson Jr., Pieter Rozenhart, Renate Scheidler","submitted_at":"2010-04-27T12:44:07Z","abstract_excerpt":"We present a method for tabulating all cubic function fields over $\\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\\mathbb{F}_{q}^*$, up to a given bound $B$ on the degree of $D$. Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of bin"},"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":"1004.4785","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-04-27T12:44:07Z","cross_cats_sorted":[],"title_canon_sha256":"7a41bbe8132829cda59bb146ea111769e6595750e0100d5f1016d1aff90c1d75","abstract_canon_sha256":"c6415d7927d601372f7098b61d649c96da5329f2d9f102043f88ce138c70b326"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:25.156696Z","signature_b64":"dWlrZlksFN704qXNsdq8hOoX+yuNiD8xAvqnM5rYMpkKR6ABNcMABoTEPa69o4BCO+zMWLDRXn/BF4k+qPTIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a24d18428cb42d270236983b8987cc5f4646c8757e5d4b2b7d80f888d6fd516d","last_reissued_at":"2026-05-18T04:17:25.156077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:25.156077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tabulation of cubic function fields via polynomial binary cubic forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Jacobson Jr., Pieter Rozenhart, Renate Scheidler","submitted_at":"2010-04-27T12:44:07Z","abstract_excerpt":"We present a method for tabulating all cubic function fields over $\\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\\mathbb{F}_{q}^*$, up to a given bound $B$ on the degree of $D$. Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of bin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4785","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":"1004.4785","created_at":"2026-05-18T04:17:25.156158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.4785v2","created_at":"2026-05-18T04:17:25.156158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.4785","created_at":"2026-05-18T04:17:25.156158+00:00"},{"alias_kind":"pith_short_12","alias_value":"UJGRQQUMWQWS","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"UJGRQQUMWQWSOARW","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"UJGRQQUM","created_at":"2026-05-18T12:26:15.391820+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/UJGRQQUMWQWSOARWTA5YTB6ML5","json":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5.json","graph_json":"https://pith.science/api/pith-number/UJGRQQUMWQWSOARWTA5YTB6ML5/graph.json","events_json":"https://pith.science/api/pith-number/UJGRQQUMWQWSOARWTA5YTB6ML5/events.json","paper":"https://pith.science/paper/UJGRQQUM"},"agent_actions":{"view_html":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5","download_json":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5.json","view_paper":"https://pith.science/paper/UJGRQQUM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.4785&json=true","fetch_graph":"https://pith.science/api/pith-number/UJGRQQUMWQWSOARWTA5YTB6ML5/graph.json","fetch_events":"https://pith.science/api/pith-number/UJGRQQUMWQWSOARWTA5YTB6ML5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5/action/storage_attestation","attest_author":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5/action/author_attestation","sign_citation":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5/action/citation_signature","submit_replication":"https://pith.science/pith/UJGRQQUMWQWSOARWTA5YTB6ML5/action/replication_record"}},"created_at":"2026-05-18T04:17:25.156158+00:00","updated_at":"2026-05-18T04:17:25.156158+00:00"}