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The results state that if $h(z) =\\sum_{n=0}^{\\infty}a_n z^n$ and $g(z)=\\sum_{n=1}^{\\infty}b_n z^n$, then $$\\sum_{n=1}^{\\infty}(|a_n|+|b_n|)r^n\\leq \\dist (\\varphi(0),\\partial\\varphi(\\ID)) ~\\mbox{ for $r\\leq r^*$} $$ and give estimates for the largest po"},"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":"1905.10334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-05-24T16:49:07Z","cross_cats_sorted":[],"title_canon_sha256":"66b30bac7a4e5d9bd8814cd666a95c0ef3a1c53195f07acb112a5ab31102e2a0","abstract_canon_sha256":"26b15e9441ff3befe125f540f56b7e3579c7c83fb18f50599e84c74e8544a124"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:10.597468Z","signature_b64":"gbxA/Vp5ldhSjcD0tjWZ4vFoJ9IyjZQp/FPUo9HpzJjg0pLNyGBTZv02N5HWTaZ34GufHTa3cwrL/TGLBLgwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fec234bd1abd22c07f302916830bf202aeaff083e8f55261b2d20a62a0bb96b","last_reissued_at":"2026-05-17T23:45:10.596771Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:10.596771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bohr radius for subordination and $K$-quasiconformal harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Saminathan Ponnusamy, Zhihong Liu","submitted_at":"2019-05-24T16:49:07Z","abstract_excerpt":"The present article concerns the Bohr radius for $K$-quasiconformal sense-preserving harmonic mappings $f=h+\\overline{g}$ in the unit disk $\\mathbb{D}$ for which the analytic part $h$ is subordinated to some analytic function $\\varphi$, and the purpose is to look into two cases: when $\\varphi$ is convex, or a general univalent function in $\\ID$. The results state that if $h(z) =\\sum_{n=0}^{\\infty}a_n z^n$ and $g(z)=\\sum_{n=1}^{\\infty}b_n z^n$, then $$\\sum_{n=1}^{\\infty}(|a_n|+|b_n|)r^n\\leq \\dist (\\varphi(0),\\partial\\varphi(\\ID)) ~\\mbox{ for $r\\leq r^*$} $$ and give estimates for the largest po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10334","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":"1905.10334","created_at":"2026-05-17T23:45:10.596892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.10334v1","created_at":"2026-05-17T23:45:10.596892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10334","created_at":"2026-05-17T23:45:10.596892+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7WCGS6RVPJC","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7WCGS6RVPJCYB7T","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7WCGS6R","created_at":"2026-05-18T12:33:27.125529+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/R7WCGS6RVPJCYB7TAKIWQMF7EA","json":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA.json","graph_json":"https://pith.science/api/pith-number/R7WCGS6RVPJCYB7TAKIWQMF7EA/graph.json","events_json":"https://pith.science/api/pith-number/R7WCGS6RVPJCYB7TAKIWQMF7EA/events.json","paper":"https://pith.science/paper/R7WCGS6R"},"agent_actions":{"view_html":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA","download_json":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA.json","view_paper":"https://pith.science/paper/R7WCGS6R","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.10334&json=true","fetch_graph":"https://pith.science/api/pith-number/R7WCGS6RVPJCYB7TAKIWQMF7EA/graph.json","fetch_events":"https://pith.science/api/pith-number/R7WCGS6RVPJCYB7TAKIWQMF7EA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA/action/storage_attestation","attest_author":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA/action/author_attestation","sign_citation":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA/action/citation_signature","submit_replication":"https://pith.science/pith/R7WCGS6RVPJCYB7TAKIWQMF7EA/action/replication_record"}},"created_at":"2026-05-17T23:45:10.596892+00:00","updated_at":"2026-05-17T23:45:10.596892+00:00"}