{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z5RKLDOKE6TOPAY2IZ7CC6UEKF","short_pith_number":"pith:Z5RKLDOK","canonical_record":{"source":{"id":"1408.1710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-07T21:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"aa30e59e24415ab35960c9ae4195a030126e5f2ca1b34f1c384bd812baaf1546","abstract_canon_sha256":"b1023a232dd469905ee29020beefa454663a59c5abaa8e32c79de36eb2d89e7a"},"schema_version":"1.0"},"canonical_sha256":"cf62a58dca27a6e7831a467e217a84514567ea2e9301628f9b644e70b828845d","source":{"kind":"arxiv","id":"1408.1710","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1710","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1710v1","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1710","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z5RKLDOKE6TO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5RKLDOKE6TOPAY2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5RKLDOK","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z5RKLDOKE6TOPAY2IZ7CC6UEKF","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-07T21:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"aa30e59e24415ab35960c9ae4195a030126e5f2ca1b34f1c384bd812baaf1546","abstract_canon_sha256":"b1023a232dd469905ee29020beefa454663a59c5abaa8e32c79de36eb2d89e7a"},"schema_version":"1.0"},"canonical_sha256":"cf62a58dca27a6e7831a467e217a84514567ea2e9301628f9b644e70b828845d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:14.233432Z","signature_b64":"GH8Na8lKCR6BlKz6ypJhLcCyzHHzgti6yYZ8h7sA2HT1QOQyBay3P84dmC2bJss2Zp7m0x56rXVgehT4fPp7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf62a58dca27a6e7831a467e217a84514567ea2e9301628f9b644e70b828845d","last_reissued_at":"2026-05-17T23:53:14.232794Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:14.232794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1710","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":"2026-05-17T23:53:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxUL+3OkOivFm/joXNaQmtWaoCDz13W5ZvHwiI5gg0V7NyqDBg5vuWIry8nwuZZOnj6qqY6YpBR0KwVabx8jCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:23.265992Z"},"content_sha256":"f24e485be84d70eb55c6ea6954f45225a4172fd4f2a6faed31091c82fee55b20","schema_version":"1.0","event_id":"sha256:f24e485be84d70eb55c6ea6954f45225a4172fd4f2a6faed31091c82fee55b20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z5RKLDOKE6TOPAY2IZ7CC6UEKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shifted powers in binary recurrence sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Maurice Mignotte, Michael A. Bennett, Samir Siksek, Sander R. Dahmen","submitted_at":"2014-08-07T21:01:02Z","abstract_excerpt":"Let $u_k$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_k$ combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approach is the fact that the equation $u_k=x^n$ can be translated into a ternary equation of the form $a y^2=b x^{2n}+c$ (with $a$, $b$, $c \\in \\mathbb{Z}$) for which Frey curves are available. In this paper we consider shifted powers in Lucas sequences, and consequently equations of the form $u_k=x^n+c$ which do not typically correspond to ternary equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1710","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":"2026-05-17T23:53:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dyP0UOerq1hssKA3eX5i/VZMo42K64FYmSwOmYq+JyXABZbvUQMlRDYV883TheJhYcUrA8XoQOwFAlIC7AXPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:23.266347Z"},"content_sha256":"0b645bc9358a48a187c05649dd4b44e61351d4faf05d7640e676f1f45505bf1b","schema_version":"1.0","event_id":"sha256:0b645bc9358a48a187c05649dd4b44e61351d4faf05d7640e676f1f45505bf1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/bundle.json","state_url":"https://pith.science/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/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":"2026-05-28T06:16:23Z","links":{"resolver":"https://pith.science/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF","bundle":"https://pith.science/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/bundle.json","state":"https://pith.science/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5RKLDOKE6TOPAY2IZ7CC6UEKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z5RKLDOKE6TOPAY2IZ7CC6UEKF","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":"b1023a232dd469905ee29020beefa454663a59c5abaa8e32c79de36eb2d89e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-07T21:01:02Z","title_canon_sha256":"aa30e59e24415ab35960c9ae4195a030126e5f2ca1b34f1c384bd812baaf1546"},"schema_version":"1.0","source":{"id":"1408.1710","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1710","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1710v1","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1710","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z5RKLDOKE6TO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5RKLDOKE6TOPAY2","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5RKLDOK","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:0b645bc9358a48a187c05649dd4b44e61351d4faf05d7640e676f1f45505bf1b","target":"graph","created_at":"2026-05-17T23:53:14Z","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 $u_k$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_k$ combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approach is the fact that the equation $u_k=x^n$ can be translated into a ternary equation of the form $a y^2=b x^{2n}+c$ (with $a$, $b$, $c \\in \\mathbb{Z}$) for which Frey curves are available. In this paper we consider shifted powers in Lucas sequences, and consequently equations of the form $u_k=x^n+c$ which do not typically correspond to ternary equa","authors_text":"Maurice Mignotte, Michael A. Bennett, Samir Siksek, Sander R. Dahmen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-07T21:01:02Z","title":"Shifted powers in binary recurrence sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1710","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:f24e485be84d70eb55c6ea6954f45225a4172fd4f2a6faed31091c82fee55b20","target":"record","created_at":"2026-05-17T23:53:14Z","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":"b1023a232dd469905ee29020beefa454663a59c5abaa8e32c79de36eb2d89e7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-07T21:01:02Z","title_canon_sha256":"aa30e59e24415ab35960c9ae4195a030126e5f2ca1b34f1c384bd812baaf1546"},"schema_version":"1.0","source":{"id":"1408.1710","kind":"arxiv","version":1}},"canonical_sha256":"cf62a58dca27a6e7831a467e217a84514567ea2e9301628f9b644e70b828845d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf62a58dca27a6e7831a467e217a84514567ea2e9301628f9b644e70b828845d","first_computed_at":"2026-05-17T23:53:14.232794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:14.232794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GH8Na8lKCR6BlKz6ypJhLcCyzHHzgti6yYZ8h7sA2HT1QOQyBay3P84dmC2bJss2Zp7m0x56rXVgehT4fPp7Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:14.233432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1710","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f24e485be84d70eb55c6ea6954f45225a4172fd4f2a6faed31091c82fee55b20","sha256:0b645bc9358a48a187c05649dd4b44e61351d4faf05d7640e676f1f45505bf1b"],"state_sha256":"66ac8f82eea47c187a74074c98316125a3ac2a81f2797212da022d75945ac087"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1iaFbxQdCPFK/ypNKsdDfW9oXxAr69s/xur8gqPaHOfbdo3fs8s6Fzpgks6Sa6R/88rJyF/Z4bKRlJTOMo9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:16:23.268411Z","bundle_sha256":"cd22c4bf7fadc1a4df92af66affba0ac01947a39e31d522c3d25fc2fb1d7dee0"}}