{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JEDPA3XXL6KJG2QM5NKWUWCT52","short_pith_number":"pith:JEDPA3XX","schema_version":"1.0","canonical_sha256":"4906f06ef75f94936a0ceb556a5853ee833308c981ff22f2bbb85493524992e7","source":{"kind":"arxiv","id":"1902.02000","version":1},"attestation_state":"computed","paper":{"title":"Schur parameters and Carath\\'eodory class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ming Li, Toshiyuki Sugawa","submitted_at":"2019-02-06T01:47:20Z","abstract_excerpt":"The Schur (resp. Carath\\'eodory) class consists of all the analytic functions $f$ on the unit disk with $|f|\\le 1$ (resp. $\\Re f>0$ and $f(0)=1$). The Schur parameters $\\gamma_0,\\gamma_1,\\dots (|\\gamma_j|\\le 1)$ are known to parametrize the coefficients of functions in the Schur class. By employing a recursive formula for it, we describe the $n$-th coefficient of a Carath\\'eodory function in terms of $n$ independent variables $\\gamma_1,\\dots, \\gamma_n$ with $|\\gamma_j|\\le 1.$ The mapping properties of those correspondences are also studied."},"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":"1902.02000","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-02-06T01:47:20Z","cross_cats_sorted":[],"title_canon_sha256":"582a6666f198350e1a95a389f86074fdd44b7b9110f61626a86066044968cbaf","abstract_canon_sha256":"885924f8fd85ddecc8565554fab4464f5b74183dba6fa4e017cc371f5eb08487"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:38.116758Z","signature_b64":"Z2CwIdml/eZOg3hjiqVX/jF+KTzW7Lvj0eMIFBRiKGtz1WwZa+HoctUzQe14b6Bp82U5abJWmNriGI8WDnF1CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4906f06ef75f94936a0ceb556a5853ee833308c981ff22f2bbb85493524992e7","last_reissued_at":"2026-05-17T23:54:38.116085Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:38.116085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schur parameters and Carath\\'eodory class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ming Li, Toshiyuki Sugawa","submitted_at":"2019-02-06T01:47:20Z","abstract_excerpt":"The Schur (resp. Carath\\'eodory) class consists of all the analytic functions $f$ on the unit disk with $|f|\\le 1$ (resp. $\\Re f>0$ and $f(0)=1$). The Schur parameters $\\gamma_0,\\gamma_1,\\dots (|\\gamma_j|\\le 1)$ are known to parametrize the coefficients of functions in the Schur class. By employing a recursive formula for it, we describe the $n$-th coefficient of a Carath\\'eodory function in terms of $n$ independent variables $\\gamma_1,\\dots, \\gamma_n$ with $|\\gamma_j|\\le 1.$ The mapping properties of those correspondences are also studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02000","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":"1902.02000","created_at":"2026-05-17T23:54:38.116190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1902.02000v1","created_at":"2026-05-17T23:54:38.116190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02000","created_at":"2026-05-17T23:54:38.116190+00:00"},{"alias_kind":"pith_short_12","alias_value":"JEDPA3XXL6KJ","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"JEDPA3XXL6KJG2QM","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"JEDPA3XX","created_at":"2026-05-18T12:33:18.533446+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/JEDPA3XXL6KJG2QM5NKWUWCT52","json":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52.json","graph_json":"https://pith.science/api/pith-number/JEDPA3XXL6KJG2QM5NKWUWCT52/graph.json","events_json":"https://pith.science/api/pith-number/JEDPA3XXL6KJG2QM5NKWUWCT52/events.json","paper":"https://pith.science/paper/JEDPA3XX"},"agent_actions":{"view_html":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52","download_json":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52.json","view_paper":"https://pith.science/paper/JEDPA3XX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1902.02000&json=true","fetch_graph":"https://pith.science/api/pith-number/JEDPA3XXL6KJG2QM5NKWUWCT52/graph.json","fetch_events":"https://pith.science/api/pith-number/JEDPA3XXL6KJG2QM5NKWUWCT52/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52/action/storage_attestation","attest_author":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52/action/author_attestation","sign_citation":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52/action/citation_signature","submit_replication":"https://pith.science/pith/JEDPA3XXL6KJG2QM5NKWUWCT52/action/replication_record"}},"created_at":"2026-05-17T23:54:38.116190+00:00","updated_at":"2026-05-17T23:54:38.116190+00:00"}