{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IQ5I5I4VX4Z5AXGT6LV67LB4MZ","short_pith_number":"pith:IQ5I5I4V","schema_version":"1.0","canonical_sha256":"443a8ea395bf33d05cd3f2ebefac3c665b2eea28369cc354f6d24a672427f1b5","source":{"kind":"arxiv","id":"1011.2991","version":2},"attestation_state":"computed","paper":{"title":"Parity conjectures for elliptic curves over global fields of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Wuthrich, Fabien Trihan","submitted_at":"2010-11-12T17:17:04Z","abstract_excerpt":"We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\\ell$-parity conjecture for primes $\\ell \\neq p$."},"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":"1011.2991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-12T17:17:04Z","cross_cats_sorted":[],"title_canon_sha256":"7deff5b62404a2a5688c14eaef98baf64495d19791bee08fc45f6f00a20077f0","abstract_canon_sha256":"98c263ab06c57e1dd9d2e82e87ae498dfa8b9ed5af7049fb54eb5fdf59688c31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:19.608753Z","signature_b64":"bjtiKTrj7G5/8UFNMugUxjNdHU6IcZBkwTNbZmL9GIntJko+ajV/G00ga2mJ9xz6u3qv6N9pvMgDApRFW0q9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"443a8ea395bf33d05cd3f2ebefac3c665b2eea28369cc354f6d24a672427f1b5","last_reissued_at":"2026-05-17T23:53:19.608051Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:19.608051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parity conjectures for elliptic curves over global fields of positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Wuthrich, Fabien Trihan","submitted_at":"2010-11-12T17:17:04Z","abstract_excerpt":"We prove the $p$-parity conjecture for elliptic curves over global fields of characteristic $p > 3$. We also present partial results on the $\\ell$-parity conjecture for primes $\\ell \\neq p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2991","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":"1011.2991","created_at":"2026-05-17T23:53:19.608151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.2991v2","created_at":"2026-05-17T23:53:19.608151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2991","created_at":"2026-05-17T23:53:19.608151+00:00"},{"alias_kind":"pith_short_12","alias_value":"IQ5I5I4VX4Z5","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IQ5I5I4VX4Z5AXGT","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IQ5I5I4V","created_at":"2026-05-18T12:26:09.077623+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/IQ5I5I4VX4Z5AXGT6LV67LB4MZ","json":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ.json","graph_json":"https://pith.science/api/pith-number/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/graph.json","events_json":"https://pith.science/api/pith-number/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/events.json","paper":"https://pith.science/paper/IQ5I5I4V"},"agent_actions":{"view_html":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ","download_json":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ.json","view_paper":"https://pith.science/paper/IQ5I5I4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.2991&json=true","fetch_graph":"https://pith.science/api/pith-number/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/graph.json","fetch_events":"https://pith.science/api/pith-number/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/action/storage_attestation","attest_author":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/action/author_attestation","sign_citation":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/action/citation_signature","submit_replication":"https://pith.science/pith/IQ5I5I4VX4Z5AXGT6LV67LB4MZ/action/replication_record"}},"created_at":"2026-05-17T23:53:19.608151+00:00","updated_at":"2026-05-17T23:53:19.608151+00:00"}