{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4OAOIGG4DFX3DQBK5VNSZZC6X6","short_pith_number":"pith:4OAOIGG4","schema_version":"1.0","canonical_sha256":"e380e418dc196fb1c02aed5b2ce45ebf871afbfa6a9985aae4554d365bed8ee9","source":{"kind":"arxiv","id":"1905.08666","version":1},"attestation_state":"computed","paper":{"title":"Univalent functions with quasiconformal extensions: Becker's class and estimates of the third coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ikkei Hotta, Pavel Gumenyuk","submitted_at":"2019-05-21T14:30:37Z","abstract_excerpt":"We investigate univalent functions $f(z)=z+a_2z^2+a_3z^3+\\ldots$ in the unit disk $\\mathbb D$ extendible to $k$-q.c.(=quasiconformal) automorphisms of $\\mathbb C$. In particular, we answer a question on estimation of $|a_3|$ raised by K\\\"uhnau and Niske [Math. Nachr. 78 (1977) 185-192]. This is one of the results we obtain studying univalent functions that admit q.c.-extensions via a construction, based on Loewner's parametric representation method, due to Becker [J. Reine Angew. Math. 255 (1972) 23-43]. Another problem we consider is to find the maximal $k_*\\in(0,1]$ such that every univalent"},"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":"1905.08666","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-05-21T14:30:37Z","cross_cats_sorted":[],"title_canon_sha256":"9c83a8f37d3e9f975761933d828d4046090c846b7b913ceaa617a90d6dfc41f8","abstract_canon_sha256":"0325d70a6c956b1f9ae6a1b4bcf30b2b7079f5df110ad00cd5887f5f1516ef67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:42.454257Z","signature_b64":"EGybC61n9N7hCBze7Z0DpVBCTBySErc8Zi5cPf8Bmt3s7l7ed4bGJweie0NSzLMkT9qghGQWHBRlOvs/VKT8Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e380e418dc196fb1c02aed5b2ce45ebf871afbfa6a9985aae4554d365bed8ee9","last_reissued_at":"2026-05-17T23:45:42.453638Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:42.453638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Univalent functions with quasiconformal extensions: Becker's class and estimates of the third coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ikkei Hotta, Pavel Gumenyuk","submitted_at":"2019-05-21T14:30:37Z","abstract_excerpt":"We investigate univalent functions $f(z)=z+a_2z^2+a_3z^3+\\ldots$ in the unit disk $\\mathbb D$ extendible to $k$-q.c.(=quasiconformal) automorphisms of $\\mathbb C$. In particular, we answer a question on estimation of $|a_3|$ raised by K\\\"uhnau and Niske [Math. Nachr. 78 (1977) 185-192]. This is one of the results we obtain studying univalent functions that admit q.c.-extensions via a construction, based on Loewner's parametric representation method, due to Becker [J. Reine Angew. Math. 255 (1972) 23-43]. Another problem we consider is to find the maximal $k_*\\in(0,1]$ such that every univalent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08666","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":"1905.08666","created_at":"2026-05-17T23:45:42.453747+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.08666v1","created_at":"2026-05-17T23:45:42.453747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.08666","created_at":"2026-05-17T23:45:42.453747+00:00"},{"alias_kind":"pith_short_12","alias_value":"4OAOIGG4DFX3","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"4OAOIGG4DFX3DQBK","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"4OAOIGG4","created_at":"2026-05-18T12:33:10.108867+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/4OAOIGG4DFX3DQBK5VNSZZC6X6","json":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6.json","graph_json":"https://pith.science/api/pith-number/4OAOIGG4DFX3DQBK5VNSZZC6X6/graph.json","events_json":"https://pith.science/api/pith-number/4OAOIGG4DFX3DQBK5VNSZZC6X6/events.json","paper":"https://pith.science/paper/4OAOIGG4"},"agent_actions":{"view_html":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6","download_json":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6.json","view_paper":"https://pith.science/paper/4OAOIGG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.08666&json=true","fetch_graph":"https://pith.science/api/pith-number/4OAOIGG4DFX3DQBK5VNSZZC6X6/graph.json","fetch_events":"https://pith.science/api/pith-number/4OAOIGG4DFX3DQBK5VNSZZC6X6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6/action/storage_attestation","attest_author":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6/action/author_attestation","sign_citation":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6/action/citation_signature","submit_replication":"https://pith.science/pith/4OAOIGG4DFX3DQBK5VNSZZC6X6/action/replication_record"}},"created_at":"2026-05-17T23:45:42.453747+00:00","updated_at":"2026-05-17T23:45:42.453747+00:00"}