{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TYPNG6PWSCVP4FXTK32MREVKTG","short_pith_number":"pith:TYPNG6PW","schema_version":"1.0","canonical_sha256":"9e1ed379f690aafe16f356f4c892aa99adb4611205e702e7d05012affad88688","source":{"kind":"arxiv","id":"1510.02224","version":5},"attestation_state":"computed","paper":{"title":"Linear Quaternion Differential Equations: Basic Theory and Fundamental Results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kit Ian Kou, Yong-hui Xia","submitted_at":"2015-10-08T08:15:35Z","abstract_excerpt":"Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the non-commutativity of the quaternion algebra, the algebraic structure of the solutions to the QDEs is completely different from ODEs. It is actually a left- or right- free module, not a linear vector space.\n  This paper establishes a systematic frame work for the theory of linear QDEs, which can be applied to quantum mechanics, fluid mechanics, Frenet frame in differentia"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.02224","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2015-10-08T08:15:35Z","cross_cats_sorted":[],"title_canon_sha256":"19fa6c786c59668f6d1416c19a7e5ad06306db0a0f129a269c4c749854c7c68f","abstract_canon_sha256":"6f837d604c27401776522211949f0bd8205abe73433ed7b6eae49301b4be324b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:51.941847Z","signature_b64":"F7BnpsLKlco7msj6xDiMjNrI0mdCleAMeOulQITHmTfMf8axmzUhnNuSx/wH5Ls8J0zS+nfO1gsoXSg4Bdh+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e1ed379f690aafe16f356f4c892aa99adb4611205e702e7d05012affad88688","last_reissued_at":"2026-05-18T00:35:51.941430Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:51.941430Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear Quaternion Differential Equations: Basic Theory and Fundamental Results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Kit Ian Kou, Yong-hui Xia","submitted_at":"2015-10-08T08:15:35Z","abstract_excerpt":"Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the non-commutativity of the quaternion algebra, the algebraic structure of the solutions to the QDEs is completely different from ODEs. It is actually a left- or right- free module, not a linear vector space.\n  This paper establishes a systematic frame work for the theory of linear QDEs, which can be applied to quantum mechanics, fluid mechanics, Frenet frame in differentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02224","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1510.02224","created_at":"2026-05-18T00:35:51.941487+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02224v5","created_at":"2026-05-18T00:35:51.941487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02224","created_at":"2026-05-18T00:35:51.941487+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYPNG6PWSCVP","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYPNG6PWSCVP4FXT","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYPNG6PW","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG","json":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG.json","graph_json":"https://pith.science/api/pith-number/TYPNG6PWSCVP4FXTK32MREVKTG/graph.json","events_json":"https://pith.science/api/pith-number/TYPNG6PWSCVP4FXTK32MREVKTG/events.json","paper":"https://pith.science/paper/TYPNG6PW"},"agent_actions":{"view_html":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG","download_json":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG.json","view_paper":"https://pith.science/paper/TYPNG6PW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02224&json=true","fetch_graph":"https://pith.science/api/pith-number/TYPNG6PWSCVP4FXTK32MREVKTG/graph.json","fetch_events":"https://pith.science/api/pith-number/TYPNG6PWSCVP4FXTK32MREVKTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG/action/storage_attestation","attest_author":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG/action/author_attestation","sign_citation":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG/action/citation_signature","submit_replication":"https://pith.science/pith/TYPNG6PWSCVP4FXTK32MREVKTG/action/replication_record"}},"created_at":"2026-05-18T00:35:51.941487+00:00","updated_at":"2026-05-18T00:35:51.941487+00:00"}