{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RXEOZXAC5NICRBVH2PR4NSUVKV","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":"5d84422b6b96cb4a99e987e88e1ea3d076b8f813abcb00e1792d28e4695a0805","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T13:54:19Z","title_canon_sha256":"9c91406eb8472aef919ad1313dd63abad7ce6f8fbe7d5214a0ed0af057692bd1"},"schema_version":"1.0","source":{"id":"1111.2475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2475","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2475v1","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2475","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"RXEOZXAC5NIC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RXEOZXAC5NICRBVH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RXEOZXAC","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:b816be82264454dd80a8a0f1b5cef4d334d34cc633f122e70db031f37845cfde","target":"graph","created_at":"2026-05-18T04:08:34Z","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 examples of points with particularly low height on elliptic curves over quadratic fields, recovered by a search over elliptic divisibility sequences. The smallest example identified satisfies dh(P)=0.0077127...: improving on the previous smallest for curves over quadratic fields of dh(P)=0.0194426... given by Everest and Ward; and comparable with some of the examples of smallest height on curves over Q tabulated by Elkies.","authors_text":"Graeme Taylor","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T13:54:19Z","title":"Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2475","kind":"arxiv","version":1},"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:ec1fceddaf5b1d7a059ddd5d46e89a8f725a0c59498b8676d75c51ebd160fac7","target":"record","created_at":"2026-05-18T04:08:34Z","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":"5d84422b6b96cb4a99e987e88e1ea3d076b8f813abcb00e1792d28e4695a0805","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-11-10T13:54:19Z","title_canon_sha256":"9c91406eb8472aef919ad1313dd63abad7ce6f8fbe7d5214a0ed0af057692bd1"},"schema_version":"1.0","source":{"id":"1111.2475","kind":"arxiv","version":1}},"canonical_sha256":"8dc8ecdc02eb502886a7d3e3c6ca955570b5af58942d9fa70e951cf9b58093b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dc8ecdc02eb502886a7d3e3c6ca955570b5af58942d9fa70e951cf9b58093b6","first_computed_at":"2026-05-18T04:08:34.052429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:34.052429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DOvyBwRaHAOf0J1p4RYE4wlX2tQsyaRKLXw8D2/Y9XAkLkYhmxkRgNJ11lYzwgA9B+aolK3jmuemLD7B+/YhDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:34.052890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec1fceddaf5b1d7a059ddd5d46e89a8f725a0c59498b8676d75c51ebd160fac7","sha256:b816be82264454dd80a8a0f1b5cef4d334d34cc633f122e70db031f37845cfde"],"state_sha256":"c2fb84461dc66156dd7bdad14789f14bb0d71335726d422d193269c27b2b6d69"}