{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CRMJMY46NPA46VS6N7HOLQPKEF","short_pith_number":"pith:CRMJMY46","schema_version":"1.0","canonical_sha256":"145896639e6bc1cf565e6fcee5c1ea215590b33779d1704016dd95b610e88bdb","source":{"kind":"arxiv","id":"1707.00685","version":1},"attestation_state":"computed","paper":{"title":"Basis-free Solution to General Linear Quaternionic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Changpeng Shao, Hongbo Li, Lei Huang","submitted_at":"2017-07-02T07:57:09Z","abstract_excerpt":"A linear quaternionic equation in one quaternionic variable q is of the form $a_1 q b_1+a_2 q b_2+ ... +a_m q b_m = c$, where the $a_i, b_j, c$ are given quaternionic coefficients. If introducing basis elements $\\bf i, j, k$ of pure quaternions, then the quaternionic equation becomes four linear equations in four unknowns over the reals, and solving such equations is trivial. On the other hand, finding a quaternionic rational function expression of the solution that involves only the input quaternionic coefficients and their conjugates, called a basis-free solution, is non-trivial.\n  In 1884, "},"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":"1707.00685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-07-02T07:57:09Z","cross_cats_sorted":[],"title_canon_sha256":"a607537b4e9482bc7199b0df666402949091e98e82f2828bec9bdea1086c3c53","abstract_canon_sha256":"6763844bb9b3c909026e98a8860e22445e2ba912dede8637905d846e8347ea9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:57.153293Z","signature_b64":"eGJXOxFu2EjDxsm5wye4hI+UN7NnaxBVA+zpo8/d1Yz6WOmUrx4sXUQsO/nHFLLCcLmvjFK6RbrjvofNdC0pAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"145896639e6bc1cf565e6fcee5c1ea215590b33779d1704016dd95b610e88bdb","last_reissued_at":"2026-05-18T00:40:57.152756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:57.152756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Basis-free Solution to General Linear Quaternionic Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Changpeng Shao, Hongbo Li, Lei Huang","submitted_at":"2017-07-02T07:57:09Z","abstract_excerpt":"A linear quaternionic equation in one quaternionic variable q is of the form $a_1 q b_1+a_2 q b_2+ ... +a_m q b_m = c$, where the $a_i, b_j, c$ are given quaternionic coefficients. If introducing basis elements $\\bf i, j, k$ of pure quaternions, then the quaternionic equation becomes four linear equations in four unknowns over the reals, and solving such equations is trivial. On the other hand, finding a quaternionic rational function expression of the solution that involves only the input quaternionic coefficients and their conjugates, called a basis-free solution, is non-trivial.\n  In 1884, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00685","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.00685","created_at":"2026-05-18T00:40:57.152835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00685v1","created_at":"2026-05-18T00:40:57.152835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00685","created_at":"2026-05-18T00:40:57.152835+00:00"},{"alias_kind":"pith_short_12","alias_value":"CRMJMY46NPA4","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CRMJMY46NPA46VS6","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CRMJMY46","created_at":"2026-05-18T12:31:10.602751+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/CRMJMY46NPA46VS6N7HOLQPKEF","json":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF.json","graph_json":"https://pith.science/api/pith-number/CRMJMY46NPA46VS6N7HOLQPKEF/graph.json","events_json":"https://pith.science/api/pith-number/CRMJMY46NPA46VS6N7HOLQPKEF/events.json","paper":"https://pith.science/paper/CRMJMY46"},"agent_actions":{"view_html":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF","download_json":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF.json","view_paper":"https://pith.science/paper/CRMJMY46","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00685&json=true","fetch_graph":"https://pith.science/api/pith-number/CRMJMY46NPA46VS6N7HOLQPKEF/graph.json","fetch_events":"https://pith.science/api/pith-number/CRMJMY46NPA46VS6N7HOLQPKEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF/action/storage_attestation","attest_author":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF/action/author_attestation","sign_citation":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF/action/citation_signature","submit_replication":"https://pith.science/pith/CRMJMY46NPA46VS6N7HOLQPKEF/action/replication_record"}},"created_at":"2026-05-18T00:40:57.152835+00:00","updated_at":"2026-05-18T00:40:57.152835+00:00"}