{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ATP2WYETFZJHINFQLZLB3RBZAD","short_pith_number":"pith:ATP2WYET","schema_version":"1.0","canonical_sha256":"04dfab60932e527434b05e561dc43900ff3736afffe8324de4cc753d7f0ac30d","source":{"kind":"arxiv","id":"1003.2563","version":1},"attestation_state":"computed","paper":{"title":"Computing in Jacobians of projective curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Peter Bruin","submitted_at":"2010-03-12T15:42:18Z","abstract_excerpt":"We give algorithms for computing with divisors on projective curves over finite fields, and with their Jacobians, using the algorithmic representation of projective curves developed by Khuri-Makdisi.  We show that many desirable operations can be done efficiently in this setting: decomposing divisors into prime divisors; computing pull-backs and push-forwards of divisors under finite morphisms, and hence Picard and Albanese maps on Jacobians; generating uniformly random divisors and points on Jacobians; computing Frobenius maps and Kummer maps; and finding a basis for the $l$-torsion of the Pi"},"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":"1003.2563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-03-12T15:42:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"30e7e90b018ac216a7a3619f83b75407404534c984c467c6a787c7547bc5b4c3","abstract_canon_sha256":"8008c85d3dbdfe1837dbbb48708c77ad6b25acba98c52ed171fe13ba358fecbe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:37.678469Z","signature_b64":"rFjuMC//gi4utmURrGkM5gb+LU1XGgujJQcO5Av//reniwcL7isjKDJsUoUcPFUmahev+WOe+MeSWqn63YMXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04dfab60932e527434b05e561dc43900ff3736afffe8324de4cc753d7f0ac30d","last_reissued_at":"2026-05-18T02:24:37.677794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:37.677794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing in Jacobians of projective curves over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Peter Bruin","submitted_at":"2010-03-12T15:42:18Z","abstract_excerpt":"We give algorithms for computing with divisors on projective curves over finite fields, and with their Jacobians, using the algorithmic representation of projective curves developed by Khuri-Makdisi.  We show that many desirable operations can be done efficiently in this setting: decomposing divisors into prime divisors; computing pull-backs and push-forwards of divisors under finite morphisms, and hence Picard and Albanese maps on Jacobians; generating uniformly random divisors and points on Jacobians; computing Frobenius maps and Kummer maps; and finding a basis for the $l$-torsion of the Pi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2563","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":"1003.2563","created_at":"2026-05-18T02:24:37.677896+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.2563v1","created_at":"2026-05-18T02:24:37.677896+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2563","created_at":"2026-05-18T02:24:37.677896+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATP2WYETFZJH","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATP2WYETFZJHINFQ","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATP2WYET","created_at":"2026-05-18T12:26:05.355336+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/ATP2WYETFZJHINFQLZLB3RBZAD","json":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD.json","graph_json":"https://pith.science/api/pith-number/ATP2WYETFZJHINFQLZLB3RBZAD/graph.json","events_json":"https://pith.science/api/pith-number/ATP2WYETFZJHINFQLZLB3RBZAD/events.json","paper":"https://pith.science/paper/ATP2WYET"},"agent_actions":{"view_html":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD","download_json":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD.json","view_paper":"https://pith.science/paper/ATP2WYET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.2563&json=true","fetch_graph":"https://pith.science/api/pith-number/ATP2WYETFZJHINFQLZLB3RBZAD/graph.json","fetch_events":"https://pith.science/api/pith-number/ATP2WYETFZJHINFQLZLB3RBZAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD/action/storage_attestation","attest_author":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD/action/author_attestation","sign_citation":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD/action/citation_signature","submit_replication":"https://pith.science/pith/ATP2WYETFZJHINFQLZLB3RBZAD/action/replication_record"}},"created_at":"2026-05-18T02:24:37.677896+00:00","updated_at":"2026-05-18T02:24:37.677896+00:00"}