{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ITWSFERPWMKY3HXYS3I36R73IN","short_pith_number":"pith:ITWSFERP","schema_version":"1.0","canonical_sha256":"44ed22922fb3158d9ef896d1bf47fb43777828141568b0457392845d2553fb55","source":{"kind":"arxiv","id":"1603.00640","version":2},"attestation_state":"computed","paper":{"title":"Canonical Heights on Genus Two Jacobians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"J. Steffen M\\\"uller, Michael Stoll","submitted_at":"2016-03-02T10:01:19Z","abstract_excerpt":"Let $K$ be a number field and let $C/K$ be a curve of genus 2 with Jacobian variety $J$. In this paper, we study the canonical height $\\hat{h} \\colon J(K) \\to \\mathbb R$. More specifically, we consider the following two problems, which are important in applications:\n  (1) for a given $P \\in J(K)$, compute $\\hat{h}(P)$ efficiently;\n  (2) for a given bound $B > 0$, find all $P \\in J(K)$ with $\\hat{h}(P) \\le B$.\n  We develop an algorithm running in polynomial time (and fast in practice) to deal with the first problem. Regarding the second problem, we show how one can tweak the naive height $h$ th"},"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":"1603.00640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-02T10:01:19Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"1e5814b7dc641bde6ff7a385bf4a64e30ecc6b484ba450184121e72d9936430e","abstract_canon_sha256":"4f454228ba8e0a906ad0bd306b0cfe1d7391acce5fa8e1a9ecda42c1fc1e1d70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:14.086654Z","signature_b64":"K8TIn/BrSgfCbupvCjjE4gK0pSVGvApjMzqsAjistLQnnryae0peJWHpWN6y17BRT0x/eulihZAK0nUqA8dGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44ed22922fb3158d9ef896d1bf47fb43777828141568b0457392845d2553fb55","last_reissued_at":"2026-05-18T00:55:14.086201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:14.086201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Canonical Heights on Genus Two Jacobians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"J. Steffen M\\\"uller, Michael Stoll","submitted_at":"2016-03-02T10:01:19Z","abstract_excerpt":"Let $K$ be a number field and let $C/K$ be a curve of genus 2 with Jacobian variety $J$. In this paper, we study the canonical height $\\hat{h} \\colon J(K) \\to \\mathbb R$. More specifically, we consider the following two problems, which are important in applications:\n  (1) for a given $P \\in J(K)$, compute $\\hat{h}(P)$ efficiently;\n  (2) for a given bound $B > 0$, find all $P \\in J(K)$ with $\\hat{h}(P) \\le B$.\n  We develop an algorithm running in polynomial time (and fast in practice) to deal with the first problem. Regarding the second problem, we show how one can tweak the naive height $h$ th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00640","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":"1603.00640","created_at":"2026-05-18T00:55:14.086276+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.00640v2","created_at":"2026-05-18T00:55:14.086276+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00640","created_at":"2026-05-18T00:55:14.086276+00:00"},{"alias_kind":"pith_short_12","alias_value":"ITWSFERPWMKY","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"ITWSFERPWMKY3HXY","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"ITWSFERP","created_at":"2026-05-18T12:30:22.444734+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/ITWSFERPWMKY3HXYS3I36R73IN","json":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN.json","graph_json":"https://pith.science/api/pith-number/ITWSFERPWMKY3HXYS3I36R73IN/graph.json","events_json":"https://pith.science/api/pith-number/ITWSFERPWMKY3HXYS3I36R73IN/events.json","paper":"https://pith.science/paper/ITWSFERP"},"agent_actions":{"view_html":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN","download_json":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN.json","view_paper":"https://pith.science/paper/ITWSFERP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.00640&json=true","fetch_graph":"https://pith.science/api/pith-number/ITWSFERPWMKY3HXYS3I36R73IN/graph.json","fetch_events":"https://pith.science/api/pith-number/ITWSFERPWMKY3HXYS3I36R73IN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN/action/storage_attestation","attest_author":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN/action/author_attestation","sign_citation":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN/action/citation_signature","submit_replication":"https://pith.science/pith/ITWSFERPWMKY3HXYS3I36R73IN/action/replication_record"}},"created_at":"2026-05-18T00:55:14.086276+00:00","updated_at":"2026-05-18T00:55:14.086276+00:00"}