{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LE3YIJ5LX2PPIFNKEQCT6LQJAY","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":"8dad68c1836a7219f9011b81c88065e8874aa531b168da5ce6cc0deef276301a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-15T14:21:05Z","title_canon_sha256":"564b99b3d12af5c8faeeef307d19001e6840e0c026b796cef21080cd824dccdc"},"schema_version":"1.0","source":{"id":"2102.07573","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.07573","created_at":"2026-07-05T07:57:25Z"},{"alias_kind":"arxiv_version","alias_value":"2102.07573v2","created_at":"2026-07-05T07:57:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.07573","created_at":"2026-07-05T07:57:25Z"},{"alias_kind":"pith_short_12","alias_value":"LE3YIJ5LX2PP","created_at":"2026-07-05T07:57:25Z"},{"alias_kind":"pith_short_16","alias_value":"LE3YIJ5LX2PPIFNK","created_at":"2026-07-05T07:57:25Z"},{"alias_kind":"pith_short_8","alias_value":"LE3YIJ5L","created_at":"2026-07-05T07:57:25Z"}],"graph_snapshots":[{"event_id":"sha256:5ab0fd707d931ad1bffff22f1f955ea9f46b0efb3cf41020ed4f15f3d58c1fc1","target":"graph","created_at":"2026-07-05T07:57:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.07573/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In literature, there are two different definitions of elliptic divisibility sequences. The first one says that a sequence of integers $\\{h_n\\}_{n\\geq 0}$ is an elliptic divisibility sequence if it verifies the recurrence relation $h_{m+n}h_{m-n}h_{r}^2=h_{m+r}h_{m-r}h_{n}^2-h_{n+r}h_{n-r}h_{m}^2$ for every natural number $m\\geq n\\geq r$. The second definition says that a sequence of integers $\\{\\beta_n\\}_{n\\geq 0}$ is an elliptic divisibility sequence if it is the sequence of the square roots (chosen with an appropriate sign) of the denominators of the abscissas of the iterates of a point on a","authors_text":"Matteo Verzobio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-15T14:21:05Z","title":"A recurrence relation for elliptic divisibility sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.07573","kind":"arxiv","version":2},"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:f78269cd08ea28a4b25232973a78822b0daf26cccffaec70b2d97a9639044827","target":"record","created_at":"2026-07-05T07:57:25Z","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":"8dad68c1836a7219f9011b81c88065e8874aa531b168da5ce6cc0deef276301a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-02-15T14:21:05Z","title_canon_sha256":"564b99b3d12af5c8faeeef307d19001e6840e0c026b796cef21080cd824dccdc"},"schema_version":"1.0","source":{"id":"2102.07573","kind":"arxiv","version":2}},"canonical_sha256":"59378427abbe9ef415aa24053f2e090626faa51b4e1ce62a11e2be7af1d61062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59378427abbe9ef415aa24053f2e090626faa51b4e1ce62a11e2be7af1d61062","first_computed_at":"2026-07-05T07:57:25.335648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:57:25.335648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E15Av2hRv9ZGWAc43AJhCkkfZMnMWmwUQYNUwlaaLvXuIe/IUAQFo86IPiiOokhVn3t4vJU24ch1uqsVhbs7Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:57:25.336060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.07573","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78269cd08ea28a4b25232973a78822b0daf26cccffaec70b2d97a9639044827","sha256:5ab0fd707d931ad1bffff22f1f955ea9f46b0efb3cf41020ed4f15f3d58c1fc1"],"state_sha256":"1f6478a73e9da8bda1fb26684277473fc21b128833a67eed9425cd615ed3a1c5"}