{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GJWXTAZIIFG5I4QKULY6MIPUNT","short_pith_number":"pith:GJWXTAZI","schema_version":"1.0","canonical_sha256":"326d798328414dd4720aa2f1e621f46cdd54d584a396c727c40015ee58532d32","source":{"kind":"arxiv","id":"1709.08944","version":1},"attestation_state":"computed","paper":{"title":"Improved Bohr's inequality for locally univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Rasila, Saminathan Ponnusamy, Stavros Evdoridis","submitted_at":"2017-09-26T11:20:32Z","abstract_excerpt":"We prove several improved versions of Bohr's inequality for the harmonic mappings of the form $f=h+\\overline{g}$, where $h$ is bounded by 1 and $|g'(z)|\\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. \\cite{KayPon2}, for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided."},"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":"1709.08944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-26T11:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"77d20a00fe8d2508fd812158408bb9419904ea412cccf705c98f71115524df5c","abstract_canon_sha256":"dc0fd281f1a6f82518148de6b0a262e82062aee044d5f3d26f862ddf9c611aa5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:21.516548Z","signature_b64":"AQfRYYrgv9Q8uedPnKrRYKvdfBgAPtlsr/aMRo7G/7I5iD3PIgM0LE+HeHl5PzR3F4C+D7TY/tCTA84qsBwaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"326d798328414dd4720aa2f1e621f46cdd54d584a396c727c40015ee58532d32","last_reissued_at":"2026-05-18T00:34:21.516040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:21.516040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Bohr's inequality for locally univalent harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Rasila, Saminathan Ponnusamy, Stavros Evdoridis","submitted_at":"2017-09-26T11:20:32Z","abstract_excerpt":"We prove several improved versions of Bohr's inequality for the harmonic mappings of the form $f=h+\\overline{g}$, where $h$ is bounded by 1 and $|g'(z)|\\le|h'(z)|$. The improvements are obtained along the lines of an earlier work of Kayumov and Ponnusamy, i.e. \\cite{KayPon2}, for example a term related to the area of the image of the disk $D(0,r)$ under the mapping $f$ is considered. Our results are sharp. In addition, further improvements of the main results for certain special classes of harmonic mappings are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08944","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":"1709.08944","created_at":"2026-05-18T00:34:21.516103+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08944v1","created_at":"2026-05-18T00:34:21.516103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08944","created_at":"2026-05-18T00:34:21.516103+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJWXTAZIIFG5","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJWXTAZIIFG5I4QK","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJWXTAZI","created_at":"2026-05-18T12:31:18.294218+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/GJWXTAZIIFG5I4QKULY6MIPUNT","json":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT.json","graph_json":"https://pith.science/api/pith-number/GJWXTAZIIFG5I4QKULY6MIPUNT/graph.json","events_json":"https://pith.science/api/pith-number/GJWXTAZIIFG5I4QKULY6MIPUNT/events.json","paper":"https://pith.science/paper/GJWXTAZI"},"agent_actions":{"view_html":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT","download_json":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT.json","view_paper":"https://pith.science/paper/GJWXTAZI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08944&json=true","fetch_graph":"https://pith.science/api/pith-number/GJWXTAZIIFG5I4QKULY6MIPUNT/graph.json","fetch_events":"https://pith.science/api/pith-number/GJWXTAZIIFG5I4QKULY6MIPUNT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT/action/storage_attestation","attest_author":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT/action/author_attestation","sign_citation":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT/action/citation_signature","submit_replication":"https://pith.science/pith/GJWXTAZIIFG5I4QKULY6MIPUNT/action/replication_record"}},"created_at":"2026-05-18T00:34:21.516103+00:00","updated_at":"2026-05-18T00:34:21.516103+00:00"}