{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XWPIKEM4TFADLXYJ65UKAUW7HS","short_pith_number":"pith:XWPIKEM4","canonical_record":{"source":{"id":"1610.08109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","cross_cats_sorted":[],"title_canon_sha256":"52201bf9aee3a63c05095a253a470a7bcb2e9a755dfc584185189ae53f88170f","abstract_canon_sha256":"96f2ca73cdae27e2799aeac59425e807a63e05c3d7a30b2aa34fe8a2b366bcf8"},"schema_version":"1.0"},"canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","source":{"kind":"arxiv","id":"1610.08109","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XWPIKEM4TFADLXYJ65UKAUW7HS","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-10-25T22:06:01Z","cross_cats_sorted":[],"title_canon_sha256":"52201bf9aee3a63c05095a253a470a7bcb2e9a755dfc584185189ae53f88170f","abstract_canon_sha256":"96f2ca73cdae27e2799aeac59425e807a63e05c3d7a30b2aa34fe8a2b366bcf8"},"schema_version":"1.0"},"canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.266553Z","signature_b64":"94p+G0/xcWoaurqVagxLyuyssOCcA5horLNNrbm1dQ9vs3nu23gvJrdE882t4QIY781UslRmh0u1BpgtszwQDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9e85119c994035df09f768a052df3c823a73d7aaeee8a57b53a876fcc467a5","last_reissued_at":"2026-05-18T00:56:45.265839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.265839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08109","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0L7lI1VCaYDqY4Yrk3EbTTY4uhGhsYrP/JxpZD2GhLTIqbzJvyryfA9AOWYxCIYk/nVZW+8wbE0eGsL14MrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:42:58.572983Z"},"content_sha256":"0e1608fc383316e38ab2f8ae3b461a0234ec2515efce1be845d6d05931a713de","schema_version":"1.0","event_id":"sha256:0e1608fc383316e38ab2f8ae3b461a0234ec2515efce1be845d6d05931a713de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XWPIKEM4TFADLXYJ65UKAUW7HS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An elliptic sequence is not a sampled linear recurrence sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Luca, Tom Ward","submitted_at":"2016-10-25T22:06:01Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08109","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hh6YZKw/aOzI/4ZSACQrVs4HEQJTh9AVY15/aVQAsiduRuFkRgL6V5HFxFmDzazYDsOTGeU4/axC8ufz7UQjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:42:58.573641Z"},"content_sha256":"f3dc323f85a3b40627a64d28aa305c6f7b0f9ccb63b37a887b4cde8c106a4a8a","schema_version":"1.0","event_id":"sha256:f3dc323f85a3b40627a64d28aa305c6f7b0f9ccb63b37a887b4cde8c106a4a8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/bundle.json","state_url":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T12:42:58Z","links":{"resolver":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS","bundle":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/bundle.json","state":"https://pith.science/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWPIKEM4TFADLXYJ65UKAUW7HS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"56Oiw7V9ehNxiJCSbDOn6wF0zmmDe8FtxpHxoX8qZtKSSNWw2z3LkwmqC5jRXe3sz8rzrYIMR6ITotbSSNRNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:42:58.576719Z","bundle_sha256":"72876481b6344e976b81e1ab6a3f92a783b72ef11b0cba744108ce819eef50ac"}}