{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EXIDMOMDU7POYL5NMNR6GFKTCS","short_pith_number":"pith:EXIDMOMD","schema_version":"1.0","canonical_sha256":"25d0363983a7deec2fad6363e3155314b56eb7eb9808919a5b7e5adf9f0a8c06","source":{"kind":"arxiv","id":"1701.08597","version":1},"attestation_state":"computed","paper":{"title":"A functional calculus and the complex conjugate of a matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olavi Nevanlinna","submitted_at":"2017-01-30T13:54:46Z","abstract_excerpt":"Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation function $\\tau: z \\mapsto \\overline z$. The resulting matrix agrees with the hermitian transpose if and only if the matrix is normal. Two other, as such elementary, approaches to define the complex conjugate of a matrix yield the same result."},"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":"1701.08597","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-30T13:54:46Z","cross_cats_sorted":[],"title_canon_sha256":"2c2546c5fe8fba0e353b3a0be64551e0803e112ae8c702faa7391ed3361e30b3","abstract_canon_sha256":"669623b2be9b5ecfc8a729b80e17eb8c397c8d8ef31cc016a51b648cff518d4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:53.570779Z","signature_b64":"nWeueAKQ0nLAV17tNuobS1kc5AOtgdoeru14neIdxkoZdkx5fVbKI3IbCmb+8HNKQANd7YUV9tTEhCwPUx5tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25d0363983a7deec2fad6363e3155314b56eb7eb9808919a5b7e5adf9f0a8c06","last_reissued_at":"2026-05-18T00:51:53.570088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:53.570088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A functional calculus and the complex conjugate of a matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Olavi Nevanlinna","submitted_at":"2017-01-30T13:54:46Z","abstract_excerpt":"Based on Stokes' theorem we derive a non-holomorphic functional calculus for matrices, assuming sufficient smoothness near eigenvalues, corresponding to the size of related Jordan blocks. It is then applied to the complex conjugation function $\\tau: z \\mapsto \\overline z$. The resulting matrix agrees with the hermitian transpose if and only if the matrix is normal. Two other, as such elementary, approaches to define the complex conjugate of a matrix yield the same result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08597","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":"1701.08597","created_at":"2026-05-18T00:51:53.570195+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.08597v1","created_at":"2026-05-18T00:51:53.570195+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08597","created_at":"2026-05-18T00:51:53.570195+00:00"},{"alias_kind":"pith_short_12","alias_value":"EXIDMOMDU7PO","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EXIDMOMDU7POYL5N","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EXIDMOMD","created_at":"2026-05-18T12:31:12.930513+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/EXIDMOMDU7POYL5NMNR6GFKTCS","json":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS.json","graph_json":"https://pith.science/api/pith-number/EXIDMOMDU7POYL5NMNR6GFKTCS/graph.json","events_json":"https://pith.science/api/pith-number/EXIDMOMDU7POYL5NMNR6GFKTCS/events.json","paper":"https://pith.science/paper/EXIDMOMD"},"agent_actions":{"view_html":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS","download_json":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS.json","view_paper":"https://pith.science/paper/EXIDMOMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.08597&json=true","fetch_graph":"https://pith.science/api/pith-number/EXIDMOMDU7POYL5NMNR6GFKTCS/graph.json","fetch_events":"https://pith.science/api/pith-number/EXIDMOMDU7POYL5NMNR6GFKTCS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS/action/storage_attestation","attest_author":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS/action/author_attestation","sign_citation":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS/action/citation_signature","submit_replication":"https://pith.science/pith/EXIDMOMDU7POYL5NMNR6GFKTCS/action/replication_record"}},"created_at":"2026-05-18T00:51:53.570195+00:00","updated_at":"2026-05-18T00:51:53.570195+00:00"}