{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UPE47INVPWHZ7JSZGTK5OKIIMS","short_pith_number":"pith:UPE47INV","schema_version":"1.0","canonical_sha256":"a3c9cfa1b57d8f9fa65934d5d7290864883135fd30823a45671031680a23bd2a","source":{"kind":"arxiv","id":"1302.2944","version":3},"attestation_state":"computed","paper":{"title":"Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Amnon Besser, Jennifer S. Balakrishnan, J. Steffen M\\\"uller","submitted_at":"2013-02-12T22:57:25Z","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."},"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":"1302.2944","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-02-12T22:57:25Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6ae1ffdb7bec57da521041dc613c167eafe106937ebff3a3b4c11066838a7591","abstract_canon_sha256":"618a1605e4834bb8c355477eb04ec1aba74d9d64ee14884b76a2f343d418d3ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:22.975081Z","signature_b64":"3qNtAJ2JFlD04k3mxjbUBmW/ySz7BNQanLuoSJdSGBiGXkPx3nikjlYMkyMlKtxnPomXWWNySjZyZFJXD0ZIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3c9cfa1b57d8f9fa65934d5d7290864883135fd30823a45671031680a23bd2a","last_reissued_at":"2026-05-18T02:30:22.974679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:22.974679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic Chabauty: p-adic height pairings and integral points on hyperelliptic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Amnon Besser, Jennifer S. Balakrishnan, J. Steffen M\\\"uller","submitted_at":"2013-02-12T22:57:25Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2944","kind":"arxiv","version":3},"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":"1302.2944","created_at":"2026-05-18T02:30:22.974732+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.2944v3","created_at":"2026-05-18T02:30:22.974732+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2944","created_at":"2026-05-18T02:30:22.974732+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPE47INVPWHZ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPE47INVPWHZ7JSZ","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPE47INV","created_at":"2026-05-18T12:28:02.375192+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/UPE47INVPWHZ7JSZGTK5OKIIMS","json":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS.json","graph_json":"https://pith.science/api/pith-number/UPE47INVPWHZ7JSZGTK5OKIIMS/graph.json","events_json":"https://pith.science/api/pith-number/UPE47INVPWHZ7JSZGTK5OKIIMS/events.json","paper":"https://pith.science/paper/UPE47INV"},"agent_actions":{"view_html":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS","download_json":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS.json","view_paper":"https://pith.science/paper/UPE47INV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.2944&json=true","fetch_graph":"https://pith.science/api/pith-number/UPE47INVPWHZ7JSZGTK5OKIIMS/graph.json","fetch_events":"https://pith.science/api/pith-number/UPE47INVPWHZ7JSZGTK5OKIIMS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS/action/storage_attestation","attest_author":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS/action/author_attestation","sign_citation":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS/action/citation_signature","submit_replication":"https://pith.science/pith/UPE47INVPWHZ7JSZGTK5OKIIMS/action/replication_record"}},"created_at":"2026-05-18T02:30:22.974732+00:00","updated_at":"2026-05-18T02:30:22.974732+00:00"}