{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F5726XAHPZTVZGJQBTUYVG63WX","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":"08b19bc5363e1c296d84e574be800ea0ec2ebecb09ae4bc8395ae67c744531c8","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-07T18:38:35Z","title_canon_sha256":"0abbf8bb54102c79b0513033f885fcfa915c1bfe06cb974c27392bc7277ce4f3"},"schema_version":"1.0","source":{"id":"1705.02677","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02677","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02677v2","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02677","created_at":"2026-05-18T00:23:39Z"},{"alias_kind":"pith_short_12","alias_value":"F5726XAHPZTV","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F5726XAHPZTVZGJQ","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F5726XAH","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:e61b75d54900940e30a83260bd4628c5612850ca4c7237d7ff61485514af7c2e","target":"graph","created_at":"2026-05-18T00:23:39Z","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 present applications of some special numbers obtained from a difference equation of degree three, especially in the Coding Theory. As a particular case, we obtain the generalized Pell-Fibonacci-Lucas numbers, which were extended to the generalized quaternions.","authors_text":"Cristina Flaut, Diana Savin","cross_cats":["cs.IT","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-07T18:38:35Z","title":"Applications of some special numbers obtained from a difference equation of degree three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02677","kind":"arxiv","version":2},"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:c6c88f3c9595447e38b3fdf137f748510aac51e0b5c18c603473275352647364","target":"record","created_at":"2026-05-18T00:23:39Z","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":"08b19bc5363e1c296d84e574be800ea0ec2ebecb09ae4bc8395ae67c744531c8","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-05-07T18:38:35Z","title_canon_sha256":"0abbf8bb54102c79b0513033f885fcfa915c1bfe06cb974c27392bc7277ce4f3"},"schema_version":"1.0","source":{"id":"1705.02677","kind":"arxiv","version":2}},"canonical_sha256":"2f7faf5c077e675c99300ce98a9bdbb5c1d3729a048de5e2c14605f2f7973ca6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f7faf5c077e675c99300ce98a9bdbb5c1d3729a048de5e2c14605f2f7973ca6","first_computed_at":"2026-05-18T00:23:39.056097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:39.056097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6v5wzvpfu3jpQd/4LbZ2mc5iV50fV1W3pUc+dxE/q+2Hh16jaiDZWoXj9X+wHwI1sTD39vkCmfN1xNOkLNeiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:39.056889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02677","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6c88f3c9595447e38b3fdf137f748510aac51e0b5c18c603473275352647364","sha256:e61b75d54900940e30a83260bd4628c5612850ca4c7237d7ff61485514af7c2e"],"state_sha256":"28b0ae7fc62b4da663781062b007052d5bd2ec1c70e1b9efe6e82408e5ebc1b3"}