{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3WPSKNAT6HS5HNM3PNEBY4UDHR","short_pith_number":"pith:3WPSKNAT","canonical_record":{"source":{"id":"1701.00321","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-02T06:24:12Z","cross_cats_sorted":[],"title_canon_sha256":"e436d7c7938fcd4311959130bb927ceba2279df0cacab5f5725f71b65c52e6e4","abstract_canon_sha256":"93d902ffa6ab44ae252f195370a76e98d93781cbcc79088d1e065396167e837a"},"schema_version":"1.0"},"canonical_sha256":"dd9f253413f1e5d3b59b7b481c72833c5dbcab908e879619255d816324b1ce0d","source":{"kind":"arxiv","id":"1701.00321","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00321","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00321v5","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00321","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"3WPSKNAT6HS5","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WPSKNAT6HS5HNM3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WPSKNAT","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3WPSKNAT6HS5HNM3PNEBY4UDHR","target":"record","payload":{"canonical_record":{"source":{"id":"1701.00321","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-02T06:24:12Z","cross_cats_sorted":[],"title_canon_sha256":"e436d7c7938fcd4311959130bb927ceba2279df0cacab5f5725f71b65c52e6e4","abstract_canon_sha256":"93d902ffa6ab44ae252f195370a76e98d93781cbcc79088d1e065396167e837a"},"schema_version":"1.0"},"canonical_sha256":"dd9f253413f1e5d3b59b7b481c72833c5dbcab908e879619255d816324b1ce0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:49.187802Z","signature_b64":"v/S31FO+c0INi0rRRwFDZdJAk3/FPerKWFi8MkHQdDzk4xaGccrBp/xtWEOt2+SyvUH7OHz0SnZpoQ7wLsglAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd9f253413f1e5d3b59b7b481c72833c5dbcab908e879619255d816324b1ce0d","last_reissued_at":"2026-05-18T00:01:49.187138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:49.187138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.00321","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NzgYe+bBlbe+S46hyi3L+vT3GbMeGPhyvrreR0/y9BAcRpXd6Gq4swuyJvSVx3nRuoNo0IgrP95W1ULpiMgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:07:05.170093Z"},"content_sha256":"cebb28d3349028bb8ad4158f00a2ca5d194cb0ca5b7f86c4f5d3a2085ed40d66","schema_version":"1.0","event_id":"sha256:cebb28d3349028bb8ad4158f00a2ca5d194cb0ca5b7f86c4f5d3a2085ed40d66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3WPSKNAT6HS5HNM3PNEBY4UDHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a generalized $k$-FL sequence and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kyunghwan Song, WonTae Hwang, Youngwoo Kwon","submitted_at":"2017-01-02T06:24:12Z","abstract_excerpt":"We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant matrices to each generalized $k$-FL sequence, and study the determinantal variety of those matrices as an application."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00321","kind":"arxiv","version":5},"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":"2026-05-18T00:01:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OU76wL9Lcy1qk4M7YsrYaxFEykff4sCdgTwNA36kezUReIIlrK2lN5Po5gEA6i72lpK70tluX9zNhSc1SmGIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:07:05.170452Z"},"content_sha256":"e2eb26e796ffcc01b1b7d76012f61440bf8ff09e89050025d8058a3d8262f657","schema_version":"1.0","event_id":"sha256:e2eb26e796ffcc01b1b7d76012f61440bf8ff09e89050025d8058a3d8262f657"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/bundle.json","state_url":"https://pith.science/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/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":"2026-06-03T14:07:05Z","links":{"resolver":"https://pith.science/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR","bundle":"https://pith.science/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/bundle.json","state":"https://pith.science/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WPSKNAT6HS5HNM3PNEBY4UDHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3WPSKNAT6HS5HNM3PNEBY4UDHR","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":"93d902ffa6ab44ae252f195370a76e98d93781cbcc79088d1e065396167e837a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-02T06:24:12Z","title_canon_sha256":"e436d7c7938fcd4311959130bb927ceba2279df0cacab5f5725f71b65c52e6e4"},"schema_version":"1.0","source":{"id":"1701.00321","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.00321","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"arxiv_version","alias_value":"1701.00321v5","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.00321","created_at":"2026-05-18T00:01:49Z"},{"alias_kind":"pith_short_12","alias_value":"3WPSKNAT6HS5","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3WPSKNAT6HS5HNM3","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3WPSKNAT","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:e2eb26e796ffcc01b1b7d76012f61440bf8ff09e89050025d8058a3d8262f657","target":"graph","created_at":"2026-05-18T00:01:49Z","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":"We introduce a generalized $k$-FL sequence and special kind of pairs of real numbers that are related to it, and give an application on the integral solutions of a certain equation using those pairs. Also, we associate skew circulant and circulant matrices to each generalized $k$-FL sequence, and study the determinantal variety of those matrices as an application.","authors_text":"Kyunghwan Song, WonTae Hwang, Youngwoo Kwon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-02T06:24:12Z","title":"On a generalized $k$-FL sequence and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00321","kind":"arxiv","version":5},"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:cebb28d3349028bb8ad4158f00a2ca5d194cb0ca5b7f86c4f5d3a2085ed40d66","target":"record","created_at":"2026-05-18T00:01:49Z","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":"93d902ffa6ab44ae252f195370a76e98d93781cbcc79088d1e065396167e837a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-02T06:24:12Z","title_canon_sha256":"e436d7c7938fcd4311959130bb927ceba2279df0cacab5f5725f71b65c52e6e4"},"schema_version":"1.0","source":{"id":"1701.00321","kind":"arxiv","version":5}},"canonical_sha256":"dd9f253413f1e5d3b59b7b481c72833c5dbcab908e879619255d816324b1ce0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd9f253413f1e5d3b59b7b481c72833c5dbcab908e879619255d816324b1ce0d","first_computed_at":"2026-05-18T00:01:49.187138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:49.187138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v/S31FO+c0INi0rRRwFDZdJAk3/FPerKWFi8MkHQdDzk4xaGccrBp/xtWEOt2+SyvUH7OHz0SnZpoQ7wLsglAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:49.187802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.00321","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebb28d3349028bb8ad4158f00a2ca5d194cb0ca5b7f86c4f5d3a2085ed40d66","sha256:e2eb26e796ffcc01b1b7d76012f61440bf8ff09e89050025d8058a3d8262f657"],"state_sha256":"6974c67733929b7c1bdec544bdce065557395171f98f5759add6c2097f2935fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4XlN8KxnixEgPIDAdrP3pf5gMgItztQzCF8QB9ExvXnykcONmmNDEo0QpfKFxgYIgZBDtEFgprHUJngwWKGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:07:05.172379Z","bundle_sha256":"01708a142cb058947caa88c0f12d95a23cd4786a6c6dc82d420bdf72a81500e0"}}