{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:QOIU6DS6YL6OGFNYWXTNIT55SJ","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":"c5b9b0436bfcac421518a98cd0d72480bb604c52fca84865c3a1e5783188d5df","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2021-08-06T07:00:34Z","title_canon_sha256":"6ba6eeb4d5ceec6459694569bfa6b44ade1c6d86827b1415fd5ef0e7ec6e87df"},"schema_version":"1.0","source":{"id":"2108.02975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02975","created_at":"2026-07-05T03:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02975v1","created_at":"2026-07-05T03:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02975","created_at":"2026-07-05T03:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"QOIU6DS6YL6O","created_at":"2026-07-05T03:03:44Z"},{"alias_kind":"pith_short_16","alias_value":"QOIU6DS6YL6OGFNY","created_at":"2026-07-05T03:03:44Z"},{"alias_kind":"pith_short_8","alias_value":"QOIU6DS6","created_at":"2026-07-05T03:03:44Z"}],"graph_snapshots":[{"event_id":"sha256:12a05616fd3070f9eb167f4ecd760d56467fdfeb5132aac717097507960c6ec0","target":"graph","created_at":"2026-07-05T03:03:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.02975/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, the biquaternion Z transformation method is proposed to solve a class of biquaternion recurrence relations. Biqueternion Z transform is an natural extension of the complex Z transform. In the design process, special norm presentation is employed to analyze the region of convergence of the biquaternion geometry sequence. In addition, some useful properties have been given. It is shown that the proposed properties is helpful to understand the biquaternion Z transform. Finally, several examples have been given to illustrate the effectiveness of the proposed design method.","authors_text":"Kit Ian Kou, Wenshan Bi, Zhen-Feng Cai","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2021-08-06T07:00:34Z","title":"Biquaternion Z Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02975","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":"sha256:4c4e0a5bd492daa952d0a68feed6ffdb318011ce1f7447fceaa14063ff1b9f0a","target":"record","created_at":"2026-07-05T03:03:44Z","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":"c5b9b0436bfcac421518a98cd0d72480bb604c52fca84865c3a1e5783188d5df","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2021-08-06T07:00:34Z","title_canon_sha256":"6ba6eeb4d5ceec6459694569bfa6b44ade1c6d86827b1415fd5ef0e7ec6e87df"},"schema_version":"1.0","source":{"id":"2108.02975","kind":"arxiv","version":1}},"canonical_sha256":"83914f0e5ec2fce315b8b5e6d44fbd927ee4a6f7872c6067bca1517963139c13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83914f0e5ec2fce315b8b5e6d44fbd927ee4a6f7872c6067bca1517963139c13","first_computed_at":"2026-07-05T03:03:44.452147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:44.452147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uEgBB5vblfBpDDV5jyzru+x8ycte5QFAJTSA0R6rtBjlC6cfwxl+oGznC83dKVwU1iHf2bLVa7z/vAaxYLX9Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:44.452619Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.02975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c4e0a5bd492daa952d0a68feed6ffdb318011ce1f7447fceaa14063ff1b9f0a","sha256:12a05616fd3070f9eb167f4ecd760d56467fdfeb5132aac717097507960c6ec0"],"state_sha256":"804e81dd93d2481c1341fab1231dc80ce9c67729386cd7db54dbc12f12006604"}