{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EEN5N23J7Z6JDKZEJX7QI6O7OZ","short_pith_number":"pith:EEN5N23J","canonical_record":{"source":{"id":"1812.10828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-27T21:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"f399ccadbb8adaf086ef59838f025cb402e71281d6d11ac3aa36850bc28f944b","abstract_canon_sha256":"f1be8ad88db73ddeed65ffcd20e7c5a5226a5b21b05c30ae6f882e2bd9a1cacf"},"schema_version":"1.0"},"canonical_sha256":"211bd6eb69fe7c91ab244dff0479df76796d4f5b0d3669e60c8ab28301d18b5d","source":{"kind":"arxiv","id":"1812.10828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10828","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10828v1","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10828","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"EEN5N23J7Z6J","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EEN5N23J7Z6JDKZE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EEN5N23J","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EEN5N23J7Z6JDKZEJX7QI6O7OZ","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10828","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-27T21:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"f399ccadbb8adaf086ef59838f025cb402e71281d6d11ac3aa36850bc28f944b","abstract_canon_sha256":"f1be8ad88db73ddeed65ffcd20e7c5a5226a5b21b05c30ae6f882e2bd9a1cacf"},"schema_version":"1.0"},"canonical_sha256":"211bd6eb69fe7c91ab244dff0479df76796d4f5b0d3669e60c8ab28301d18b5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:16.961526Z","signature_b64":"D6qanDSis1WfOSXXIjbbgjE9d6o0S/BNx98wJ5iI8B37KqWe/NlVQkmBOxwMz5qLFFqRIvDw0xVHjERJ/OR+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"211bd6eb69fe7c91ab244dff0479df76796d4f5b0d3669e60c8ab28301d18b5d","last_reissued_at":"2026-05-17T23:57:16.961053Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:16.961053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10828","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":"2026-05-17T23:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yRfZPn5lPpGaxZftbED3TLSeEjcuw5ImY2JoNKgpVgMme8dXlmlfoFcJbp2HhWHQ5t5UscmHvgM9IOvo3H6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:45:32.214498Z"},"content_sha256":"f293d395b00f87cfba5fcdb94730b343d32727bc76e86a4c3c30c2ce090fad7a","schema_version":"1.0","event_id":"sha256:f293d395b00f87cfba5fcdb94730b343d32727bc76e86a4c3c30c2ce090fad7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EEN5N23J7Z6JDKZEJX7QI6O7OZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"James Mc Laughlin","submitted_at":"2018-12-27T21:22:10Z","abstract_excerpt":"Finding polynomial solutions to Pell's equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic fields.\n  In this paper, for each triple of positive integers $(c,h,f)$ satisfying \\[c^{2}-f\\,h^{2}=1, \\] where $(c,h)$ are the smallest pair of integers satisfying this equation, several sets of polynomials $(c(t),h(t),f(t))$ which satisfy \\[c(t)^{2}-f(t)\\,h(t)^{2}=1 \\text{ and } (c(0),h(0),f(0)) = (c,h,f) \\]\n  are derived. Moreover, it is shown that the pair $(c(t),h(t))$ constitute the fundamental polynomial solution t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10828","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":"2026-05-17T23:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USbpczoYpxBXTjbqxu+h0NDprzKQk4QD4JGxYFVdaCJgCEGYfa4l2VKvb7IU2wuf5l2x9zFMtK78yamjm7PVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:45:32.215149Z"},"content_sha256":"c18cf63055d4c4cf8c22645ed4cbefdb89daa81b529a1792eb07b0267f4f9d7d","schema_version":"1.0","event_id":"sha256:c18cf63055d4c4cf8c22645ed4cbefdb89daa81b529a1792eb07b0267f4f9d7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/bundle.json","state_url":"https://pith.science/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/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":"2026-06-03T16:45:32Z","links":{"resolver":"https://pith.science/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ","bundle":"https://pith.science/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/bundle.json","state":"https://pith.science/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EEN5N23J7Z6JDKZEJX7QI6O7OZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EEN5N23J7Z6JDKZEJX7QI6O7OZ","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":"f1be8ad88db73ddeed65ffcd20e7c5a5226a5b21b05c30ae6f882e2bd9a1cacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-27T21:22:10Z","title_canon_sha256":"f399ccadbb8adaf086ef59838f025cb402e71281d6d11ac3aa36850bc28f944b"},"schema_version":"1.0","source":{"id":"1812.10828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10828","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10828v1","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10828","created_at":"2026-05-17T23:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"EEN5N23J7Z6J","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EEN5N23J7Z6JDKZE","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EEN5N23J","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:c18cf63055d4c4cf8c22645ed4cbefdb89daa81b529a1792eb07b0267f4f9d7d","target":"graph","created_at":"2026-05-17T23:57:16Z","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":"Finding polynomial solutions to Pell's equation is of interest as such solutions sometimes allow the fundamental units to be determined in an infinite class of real quadratic fields.\n  In this paper, for each triple of positive integers $(c,h,f)$ satisfying \\[c^{2}-f\\,h^{2}=1, \\] where $(c,h)$ are the smallest pair of integers satisfying this equation, several sets of polynomials $(c(t),h(t),f(t))$ which satisfy \\[c(t)^{2}-f(t)\\,h(t)^{2}=1 \\text{ and } (c(0),h(0),f(0)) = (c,h,f) \\]\n  are derived. Moreover, it is shown that the pair $(c(t),h(t))$ constitute the fundamental polynomial solution t","authors_text":"James Mc Laughlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-27T21:22:10Z","title":"Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10828","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:f293d395b00f87cfba5fcdb94730b343d32727bc76e86a4c3c30c2ce090fad7a","target":"record","created_at":"2026-05-17T23:57:16Z","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":"f1be8ad88db73ddeed65ffcd20e7c5a5226a5b21b05c30ae6f882e2bd9a1cacf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-12-27T21:22:10Z","title_canon_sha256":"f399ccadbb8adaf086ef59838f025cb402e71281d6d11ac3aa36850bc28f944b"},"schema_version":"1.0","source":{"id":"1812.10828","kind":"arxiv","version":1}},"canonical_sha256":"211bd6eb69fe7c91ab244dff0479df76796d4f5b0d3669e60c8ab28301d18b5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"211bd6eb69fe7c91ab244dff0479df76796d4f5b0d3669e60c8ab28301d18b5d","first_computed_at":"2026-05-17T23:57:16.961053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:16.961053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D6qanDSis1WfOSXXIjbbgjE9d6o0S/BNx98wJ5iI8B37KqWe/NlVQkmBOxwMz5qLFFqRIvDw0xVHjERJ/OR+Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:16.961526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f293d395b00f87cfba5fcdb94730b343d32727bc76e86a4c3c30c2ce090fad7a","sha256:c18cf63055d4c4cf8c22645ed4cbefdb89daa81b529a1792eb07b0267f4f9d7d"],"state_sha256":"1604b7db19a90744ae589cc4ca30614ccbe346cb6a93fa08b25ca0d1a854f86f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5v2PKhzOvZ5n2uKBd4DqZmRYA/r+gyfRRA/b3fyWAyBfMVWFe9SjGey0UZqX/9qkpGkrRInhkN9Tbgt/PUc9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:45:32.218192Z","bundle_sha256":"4897defa614b54da79572d3cf6b4eea5d5e5dc9cc88ef9ed5b59da4c4db1d254"}}