{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XWPIKEM4TFADLXYJ65UKAUW7HS","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":"96f2ca73cdae27e2799aeac59425e807a63e05c3d7a30b2aa34fe8a2b366bcf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","title_canon_sha256":"52201bf9aee3a63c05095a253a470a7bcb2e9a755dfc584185189ae53f88170f"},"schema_version":"1.0","source":{"id":"1610.08109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08109","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08109v1","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08109","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"XWPIKEM4TFAD","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XWPIKEM4TFADLXYJ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XWPIKEM4","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:f3dc323f85a3b40627a64d28aa305c6f7b0f9ccb63b37a887b4cde8c106a4a8a","target":"graph","created_at":"2026-05-18T00:56:45Z","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":"Let $E$ be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let $P=(x_1/z_1^2,y_1/z_1^3)$ be a rational point of infinite order on $E$, where $x_1,y_1,z_1$ are coprime integers. We show that the integer sequence $(z_n)$ defined by $nP=(x_n/z_n^2,y_n/z_n^3)$ for all $n\\ge 1$ does not eventually coincide with $(u_{n^2})$ for any choice of linear recurrence sequence $(u_n)$ with integer values.","authors_text":"Florian Luca, Tom Ward","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","title":"An elliptic sequence is not a sampled linear recurrence sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08109","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":"sha256:0e1608fc383316e38ab2f8ae3b461a0234ec2515efce1be845d6d05931a713de","target":"record","created_at":"2026-05-18T00:56:45Z","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":"96f2ca73cdae27e2799aeac59425e807a63e05c3d7a30b2aa34fe8a2b366bcf8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","title_canon_sha256":"52201bf9aee3a63c05095a253a470a7bcb2e9a755dfc584185189ae53f88170f"},"schema_version":"1.0","source":{"id":"1610.08109","kind":"arxiv","version":1}},"canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","first_computed_at":"2026-05-18T00:56:45.265839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:45.265839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"94p+G0/xcWoaurqVagxLyuyssOCcA5horLNNrbm1dQ9vs3nu23gvJrdE882t4QIY781UslRmh0u1BpgtszwQDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:45.266553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e1608fc383316e38ab2f8ae3b461a0234ec2515efce1be845d6d05931a713de","sha256:f3dc323f85a3b40627a64d28aa305c6f7b0f9ccb63b37a887b4cde8c106a4a8a"],"state_sha256":"bc93ac0ba17b71d903a715cf0efc1cac4bc3c17386f8925bf59eb26d775c58da"}