{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YDUABK6LQWHXETQAW63FBBEYPA","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":"6a89ce57ba26223cd3077c6ef591d7aaf696f3e59c6f1d11813f2dfe21d71288","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T17:46:07Z","title_canon_sha256":"ccac1ee2cc0d1fe2e7156b71fb74f8676580fbbe3e6cbf9c540cda80c837d548"},"schema_version":"1.0","source":{"id":"1503.00637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00637","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00637v1","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00637","created_at":"2026-05-18T02:25:49Z"},{"alias_kind":"pith_short_12","alias_value":"YDUABK6LQWHX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YDUABK6LQWHXETQA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YDUABK6L","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:cad0b231082732dab232f346ac5c50112fe9ec7f653182297d517ea8d27c0e2a","target":"graph","created_at":"2026-05-18T02:25:49Z","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":"This short paper is concerned with polynomial Pell equations \\[P^2-DQ^2=1,\\] with $P,Q,D\\in\\Bbb C[X]$ and ${deg}(D)=2$. The main result shows that the polynomials $P$ and $Q$ are closely related to Chebyshev polynomials. We then investigate the existence of such polynomials in $\\Bbb Z[X]$ specializing to fixed solutions of ordinary Pell equations over the integers.","authors_text":"Leonardo Zapponi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T17:46:07Z","title":"Parametric solutions of Pell equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00637","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":"sha256:07b65decb91f984995eabcb801e1aa1f0a77332cb895d5fc81698ecd721535ea","target":"record","created_at":"2026-05-18T02:25:49Z","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":"6a89ce57ba26223cd3077c6ef591d7aaf696f3e59c6f1d11813f2dfe21d71288","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-02T17:46:07Z","title_canon_sha256":"ccac1ee2cc0d1fe2e7156b71fb74f8676580fbbe3e6cbf9c540cda80c837d548"},"schema_version":"1.0","source":{"id":"1503.00637","kind":"arxiv","version":1}},"canonical_sha256":"c0e800abcb858f724e00b7b6508498783f80b77acd70de537582852b29fd73a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0e800abcb858f724e00b7b6508498783f80b77acd70de537582852b29fd73a4","first_computed_at":"2026-05-18T02:25:49.619394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:49.619394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eofDbXoCk5Ssf/BSwWV7b9bLb9Tnm2cZ7CyGTd/9npq6PdEJh8I0iA2q5roTsLGGLYEjD6t0d5Oa2xb2jJW0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:49.619947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07b65decb91f984995eabcb801e1aa1f0a77332cb895d5fc81698ecd721535ea","sha256:cad0b231082732dab232f346ac5c50112fe9ec7f653182297d517ea8d27c0e2a"],"state_sha256":"118c68410e734d5cf1981afced34b9ce75bb9374fc529aaea3eab1529787cd25"}