{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7I3JKKMJRA4SD2BGJNJPA5EU66","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":"b8f912cbd7542494b835ea119adc9f01f9982bbadb54cf233c5fde1ac1e28c77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:13:57Z","title_canon_sha256":"3f8f8ac680de627473b7a1955d9b36b06a16bb6ff3b92a9619ec1be2ec861ffa"},"schema_version":"1.0","source":{"id":"0812.2849","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2849","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2849v3","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2849","created_at":"2026-05-18T01:37:33Z"},{"alias_kind":"pith_short_12","alias_value":"7I3JKKMJRA4S","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7I3JKKMJRA4SD2BG","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7I3JKKMJ","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:d682b61f900092f2a2b05438787eeb70a9a1d9b17f92b197d64b7dc4b8145124","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":"The aim of this paper is to study a conjecture predicting a lower bound on the canonical height on abelian varieties, formulated by S. Lang and generalized by J. H. Silverman. We give here an asymptotic result on the height of Heegner points on the modular jacobian $J_{0}(N)$, and we derive non-trivial remarks about the conjecture.","authors_text":"Fabien Pazuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:13:57Z","title":"Remarques sur une conjecture de Lang"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2849","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:bfd154bc410775d35387e0ddfa3de085dc9cdedc8127282fcb17b0d1dcfcdcc0","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":"b8f912cbd7542494b835ea119adc9f01f9982bbadb54cf233c5fde1ac1e28c77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2008-12-15T16:13:57Z","title_canon_sha256":"3f8f8ac680de627473b7a1955d9b36b06a16bb6ff3b92a9619ec1be2ec861ffa"},"schema_version":"1.0","source":{"id":"0812.2849","kind":"arxiv","version":3}},"canonical_sha256":"fa36952989883921e8264b52f07494f787a25dc1f0afa79c63adeab02cfbe0c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa36952989883921e8264b52f07494f787a25dc1f0afa79c63adeab02cfbe0c3","first_computed_at":"2026-05-18T01:37:33.383457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:33.383457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ur09iWU3b/fU25xcXyeifInKC6O5tgIf2srZP6ujEAlf9++FN56omc7zlQ8N/cMNmktlF6quKlUADwa4p0RkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:33.383952Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.2849","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfd154bc410775d35387e0ddfa3de085dc9cdedc8127282fcb17b0d1dcfcdcc0","sha256:d682b61f900092f2a2b05438787eeb70a9a1d9b17f92b197d64b7dc4b8145124"],"state_sha256":"f7e96cbff8f63c99801be0a4742756bb5d124898fbbb0cd52f56e78ab573e38f"}