{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UPE47INVPWHZ7JSZGTK5OKIIMS","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":"618a1605e4834bb8c355477eb04ec1aba74d9d64ee14884b76a2f343d418d3ed","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-12T22:57:25Z","title_canon_sha256":"6ae1ffdb7bec57da521041dc613c167eafe106937ebff3a3b4c11066838a7591"},"schema_version":"1.0","source":{"id":"1302.2944","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2944","created_at":"2026-05-18T02:30:22Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2944v3","created_at":"2026-05-18T02:30:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2944","created_at":"2026-05-18T02:30:22Z"},{"alias_kind":"pith_short_12","alias_value":"UPE47INVPWHZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UPE47INVPWHZ7JSZ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UPE47INV","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:dd255ecebdcc8a67ddf82cc4a8d97d6b27d6b306b61a05b865f6afa6cd2faf7d","target":"graph","created_at":"2026-05-18T02:30:22Z","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 give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use the method in explicit computation. An important aspect of the method is that it only requires a basis of the Mordell-Weil group tensored with the rationals.","authors_text":"Amnon Besser, Jennifer S. Balakrishnan, J. Steffen M\\\"uller","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-12T22:57:25Z","title":"Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2944","kind":"arxiv","version":3},"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:a1744e7c86c996a7f9dc41d9a38e4433d0c83b66748800a3084fc1246907e353","target":"record","created_at":"2026-05-18T02:30:22Z","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":"618a1605e4834bb8c355477eb04ec1aba74d9d64ee14884b76a2f343d418d3ed","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-12T22:57:25Z","title_canon_sha256":"6ae1ffdb7bec57da521041dc613c167eafe106937ebff3a3b4c11066838a7591"},"schema_version":"1.0","source":{"id":"1302.2944","kind":"arxiv","version":3}},"canonical_sha256":"a3c9cfa1b57d8f9fa65934d5d7290864883135fd30823a45671031680a23bd2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3c9cfa1b57d8f9fa65934d5d7290864883135fd30823a45671031680a23bd2a","first_computed_at":"2026-05-18T02:30:22.974679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:22.974679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3qNtAJ2JFlD04k3mxjbUBmW/ySz7BNQanLuoSJdSGBiGXkPx3nikjlYMkyMlKtxnPomXWWNySjZyZFJXD0ZIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:22.975081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2944","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1744e7c86c996a7f9dc41d9a38e4433d0c83b66748800a3084fc1246907e353","sha256:dd255ecebdcc8a67ddf82cc4a8d97d6b27d6b306b61a05b865f6afa6cd2faf7d"],"state_sha256":"90541f41bc78dad09e5f2e21d838f463892eedbe9e3014daa1e5ee6c5544f9bc"}