{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XDFT6VC4N5EEJADZVUBTWCMVJ2","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":"15a36702ae8f5944363e50c96b78be9eab2174956d63a2e39f2e27bf6818c054","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-22T08:45:54Z","title_canon_sha256":"b8d88993295ce277d15bc77c54e8f25f32699b5b41e44030940691350d38ab7e"},"schema_version":"1.0","source":{"id":"1608.06086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06086","created_at":"2026-05-18T01:08:22Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06086v1","created_at":"2026-05-18T01:08:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06086","created_at":"2026-05-18T01:08:22Z"},{"alias_kind":"pith_short_12","alias_value":"XDFT6VC4N5EE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XDFT6VC4N5EEJADZ","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XDFT6VC4","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e9902f6eeafeae36108dcf9ebd423cd363995ba03b9bf4c5da7c8a705e2f73c9","target":"graph","created_at":"2026-05-18T01:08:22Z","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":"In this paper, we find all the solutions of the Diophantine equation $P_\\ell + P_m +P_n=2^a$, in nonnegative integer variables $(n,m,\\ell, a)$ where $P_k$ is the $k$-th term of the Pell sequence $\\{P_n\\}_{n\\ge 0}$ given by $P_0=0$, $P_1=1$ and $P_{n+1}=2P_{n}+ P_{n-1}$ for all $n\\geq 1$.","authors_text":"Bernadette Faye, Florian Luca, Jhon J. Bravo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-22T08:45:54Z","title":"Power of Two as sums of Three Pell Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06086","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":"sha256:16bc1b8a6d6709bf2dc3eb06492f6cb35d7befda194f528f5016752b674ffbad","target":"record","created_at":"2026-05-18T01:08:22Z","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":"15a36702ae8f5944363e50c96b78be9eab2174956d63a2e39f2e27bf6818c054","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-22T08:45:54Z","title_canon_sha256":"b8d88993295ce277d15bc77c54e8f25f32699b5b41e44030940691350d38ab7e"},"schema_version":"1.0","source":{"id":"1608.06086","kind":"arxiv","version":1}},"canonical_sha256":"b8cb3f545c6f48448079ad033b09954eab245fc010b532002a8f846f686919bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8cb3f545c6f48448079ad033b09954eab245fc010b532002a8f846f686919bd","first_computed_at":"2026-05-18T01:08:22.329988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:22.329988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sHlOoTXDQqtzP0Ly6u0E/rmyznDq13WA/+J5ECmyooPGXG493O+GXTteP7neJqZMa9Ljd8SgTn7CWpH29U/aBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:22.330676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16bc1b8a6d6709bf2dc3eb06492f6cb35d7befda194f528f5016752b674ffbad","sha256:e9902f6eeafeae36108dcf9ebd423cd363995ba03b9bf4c5da7c8a705e2f73c9"],"state_sha256":"f0d4bc6dd46a27c51a9d5e1bcd6dab5e7a771a228cd385bcd8a4ab0b63cee2a3"}