{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2OVC3GNCOJ7ZM5UIX7TOTF7OIZ","short_pith_number":"pith:2OVC3GNC","schema_version":"1.0","canonical_sha256":"d3aa2d99a2727f967688bfe6e997ee4661048de89dd3b01dc855230f0c16150f","source":{"kind":"arxiv","id":"1703.02371","version":1},"attestation_state":"computed","paper":{"title":"Coefficients of univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anbareeswaran Sairam Kaliraj, Saminathan Ponnusamy, Victor V. Starkov","submitted_at":"2017-03-07T13:32:58Z","abstract_excerpt":"Let $\\mathcal{S}_H^0$ denote the class of all functions $f(z)=h(z)+\\overline{g(z)}=z+\\sum^\\infty_{n=2} a_nz^n +\\overline{\\sum^\\infty_{n=2} b_nz^n}$ that are sense-preserving, harmonic and univalent in the open unit disk $|z|<1$. The coefficient conjecture for $\\mathcal{S}_H^0$ is still \\emph{open} even for $|a_2|$. The aim of this paper is to show that if $f=h+\\overline{g} \\in \\mathcal{S}^0_H$ then $ |a_n| < 5.24 \\times 10^{-6} n^{17}$ and $|b_n| < 2.32 \\times 10^{-7}n^{17}$ for all $n \\geq 3$. Making use of these coefficient estimates, we also obtain radius of univalence of sections of unival"},"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":"1703.02371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-07T13:32:58Z","cross_cats_sorted":[],"title_canon_sha256":"4a08b03576432b82d89cfeb892d8093121a1663e58dd39378686d89f830b4948","abstract_canon_sha256":"cae549c5b3327abfa8d420c933c750000715cefc3dee720a78b38ad311d98a3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:20.168019Z","signature_b64":"lAbNF0ZeMOtmIVO7CG2eoRR5gsEZkKp1eJZgHpzrwiZJrSwzfoAvK1MtbK7ID4S8q9TqxcHw4AOyR+AJZxSvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3aa2d99a2727f967688bfe6e997ee4661048de89dd3b01dc855230f0c16150f","last_reissued_at":"2026-05-18T00:49:20.167678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:20.167678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coefficients of univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anbareeswaran Sairam Kaliraj, Saminathan Ponnusamy, Victor V. Starkov","submitted_at":"2017-03-07T13:32:58Z","abstract_excerpt":"Let $\\mathcal{S}_H^0$ denote the class of all functions $f(z)=h(z)+\\overline{g(z)}=z+\\sum^\\infty_{n=2} a_nz^n +\\overline{\\sum^\\infty_{n=2} b_nz^n}$ that are sense-preserving, harmonic and univalent in the open unit disk $|z|<1$. The coefficient conjecture for $\\mathcal{S}_H^0$ is still \\emph{open} even for $|a_2|$. The aim of this paper is to show that if $f=h+\\overline{g} \\in \\mathcal{S}^0_H$ then $ |a_n| < 5.24 \\times 10^{-6} n^{17}$ and $|b_n| < 2.32 \\times 10^{-7}n^{17}$ for all $n \\geq 3$. Making use of these coefficient estimates, we also obtain radius of univalence of sections of unival"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02371","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":"1703.02371","created_at":"2026-05-18T00:49:20.167734+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02371v1","created_at":"2026-05-18T00:49:20.167734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02371","created_at":"2026-05-18T00:49:20.167734+00:00"},{"alias_kind":"pith_short_12","alias_value":"2OVC3GNCOJ7Z","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2OVC3GNCOJ7ZM5UI","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2OVC3GNC","created_at":"2026-05-18T12:30:55.937587+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/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ","json":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ.json","graph_json":"https://pith.science/api/pith-number/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/graph.json","events_json":"https://pith.science/api/pith-number/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/events.json","paper":"https://pith.science/paper/2OVC3GNC"},"agent_actions":{"view_html":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ","download_json":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ.json","view_paper":"https://pith.science/paper/2OVC3GNC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02371&json=true","fetch_graph":"https://pith.science/api/pith-number/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/action/storage_attestation","attest_author":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/action/author_attestation","sign_citation":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/action/citation_signature","submit_replication":"https://pith.science/pith/2OVC3GNCOJ7ZM5UIX7TOTF7OIZ/action/replication_record"}},"created_at":"2026-05-18T00:49:20.167734+00:00","updated_at":"2026-05-18T00:49:20.167734+00:00"}