{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IQ5I5I4VX4Z5AXGT6LV67LB4MZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"98c263ab06c57e1dd9d2e82e87ae498dfa8b9ed5af7049fb54eb5fdf59688c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-12T17:17:04Z","title_canon_sha256":"7deff5b62404a2a5688c14eaef98baf64495d19791bee08fc45f6f00a20077f0"},"schema_version":"1.0","source":{"id":"1011.2991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2991","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2991v2","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2991","created_at":"2026-05-17T23:53:19Z"},{"alias_kind":"pith_short_12","alias_value":"IQ5I5I4VX4Z5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IQ5I5I4VX4Z5AXGT","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IQ5I5I4V","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:32c0d36d6bbecd1cdc230e473f13e7387e2e5038a51d4aceb08cc0ef75515a98","target":"graph","created_at":"2026-05-17T23:53:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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 $\\ell \\neq p$.","authors_text":"Christian Wuthrich, Fabien Trihan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-12T17:17:04Z","title":"Parity conjectures for elliptic curves over global fields of positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2991","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c93501f95912143116ac8386f0a143aee0ac4cfb0753a6f8cdc31e7fc2011e08","target":"record","created_at":"2026-05-17T23:53:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"98c263ab06c57e1dd9d2e82e87ae498dfa8b9ed5af7049fb54eb5fdf59688c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-12T17:17:04Z","title_canon_sha256":"7deff5b62404a2a5688c14eaef98baf64495d19791bee08fc45f6f00a20077f0"},"schema_version":"1.0","source":{"id":"1011.2991","kind":"arxiv","version":2}},"canonical_sha256":"443a8ea395bf33d05cd3f2ebefac3c665b2eea28369cc354f6d24a672427f1b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"443a8ea395bf33d05cd3f2ebefac3c665b2eea28369cc354f6d24a672427f1b5","first_computed_at":"2026-05-17T23:53:19.608051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:19.608051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bjtiKTrj7G5/8UFNMugUxjNdHU6IcZBkwTNbZmL9GIntJko+ajV/G00ga2mJ9xz6u3qv6N9pvMgDApRFW0q9BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:19.608753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c93501f95912143116ac8386f0a143aee0ac4cfb0753a6f8cdc31e7fc2011e08","sha256:32c0d36d6bbecd1cdc230e473f13e7387e2e5038a51d4aceb08cc0ef75515a98"],"state_sha256":"5f0bb7b5cc1559187a7a12517fd857fcf5d7c8ed3e936852a7657ed63b552ee6"}