{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QI7W3ETFQUIZARZ66SH4VJ5HKP","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":"39fe59a21a517100d746ff494ad7ae697468bf88a25fc0cea6f6fa9498008c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:27:04Z","title_canon_sha256":"a1b41f473423242c7649c4dd1332b6308d0fb9928325219875a7431ee0a2576a"},"schema_version":"1.0","source":{"id":"0812.2854","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2854","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2854v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2854","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"QI7W3ETFQUIZ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QI7W3ETFQUIZARZ6","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QI7W3ETF","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:5c720ea9472b0ecb642d8a56416ae9dd6d4b4c38c1ae5ea1854ed97b37b0c047","target":"graph","created_at":"2026-05-18T01:37:33Z","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":"This paper contains results concerning a conjecture made by Lang and Silverman predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition. We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curves.","authors_text":"Fabien Pazuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:27:04Z","title":"Minoration de la hauteur de Neron-Tate sur les surfaces abeliennes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2854","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":"sha256:1b6d3d6b10b6523f3920a7f8300066f821bb97ca29cd59df24f04955edc8bda3","target":"record","created_at":"2026-05-18T01:37:33Z","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":"39fe59a21a517100d746ff494ad7ae697468bf88a25fc0cea6f6fa9498008c55","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:27:04Z","title_canon_sha256":"a1b41f473423242c7649c4dd1332b6308d0fb9928325219875a7431ee0a2576a"},"schema_version":"1.0","source":{"id":"0812.2854","kind":"arxiv","version":3}},"canonical_sha256":"823f6d9265851190473ef48fcaa7a753d8df8cc5b95a7875a2d68d94915077bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823f6d9265851190473ef48fcaa7a753d8df8cc5b95a7875a2d68d94915077bc","first_computed_at":"2026-05-18T01:37:33.376070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:33.376070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VBE+gt/VF+tW9VKRK87fEGPYHvb2W1G8AAS6nXVSvFc++80jhixDTS7TpViPwN9/zLEA+ND9FZWE87kJLhppDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:33.376583Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.2854","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b6d3d6b10b6523f3920a7f8300066f821bb97ca29cd59df24f04955edc8bda3","sha256:5c720ea9472b0ecb642d8a56416ae9dd6d4b4c38c1ae5ea1854ed97b37b0c047"],"state_sha256":"1f940b8b053d141a9d09e861183fc4623b337df0c9da4dc625e004ff5870536e"}