{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FALZKPOESSARWWFHGRKF35HNF6","short_pith_number":"pith:FALZKPOE","schema_version":"1.0","canonical_sha256":"2817953dc494811b58a734545df4ed2f879d44c2bf7b533d2045194b0b036999","source":{"kind":"arxiv","id":"1808.07393","version":1},"attestation_state":"computed","paper":{"title":"Some properties of univalent log-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":"2018-08-22T14:52:32Z","abstract_excerpt":"We determine the representation theorem, distortion theorem, coefficients estimate and Bohr's radius for log-harmonic starlike mappings of order $\\alpha$, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of $1$-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch's norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained."},"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":"1808.07393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-08-22T14:52:32Z","cross_cats_sorted":[],"title_canon_sha256":"10bfd6dd1aa8f06a367dea26ebe05e2fdc247ee32cec5fea759e578fa59f0913","abstract_canon_sha256":"679512421ba791d03404b3406a9427adc016235d50e363bef662deeaf08fb687"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:28.993523Z","signature_b64":"2Q7cxScPEB7UtS1Tw2aqxyuFc0m9RY24IFxBripRinAmYSuC39SGQsRsLt5g9srxa/3geKtoZdJJy/D3wW6YAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2817953dc494811b58a734545df4ed2f879d44c2bf7b533d2045194b0b036999","last_reissued_at":"2026-05-18T00:07:28.992952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:28.992952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some properties of univalent log-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":"2018-08-22T14:52:32Z","abstract_excerpt":"We determine the representation theorem, distortion theorem, coefficients estimate and Bohr's radius for log-harmonic starlike mappings of order $\\alpha$, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of $1$-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch's norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07393","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":"1808.07393","created_at":"2026-05-18T00:07:28.993013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.07393v1","created_at":"2026-05-18T00:07:28.993013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07393","created_at":"2026-05-18T00:07:28.993013+00:00"},{"alias_kind":"pith_short_12","alias_value":"FALZKPOESSAR","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"FALZKPOESSARWWFH","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"FALZKPOE","created_at":"2026-05-18T12:32:22.470017+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/FALZKPOESSARWWFHGRKF35HNF6","json":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6.json","graph_json":"https://pith.science/api/pith-number/FALZKPOESSARWWFHGRKF35HNF6/graph.json","events_json":"https://pith.science/api/pith-number/FALZKPOESSARWWFHGRKF35HNF6/events.json","paper":"https://pith.science/paper/FALZKPOE"},"agent_actions":{"view_html":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6","download_json":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6.json","view_paper":"https://pith.science/paper/FALZKPOE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.07393&json=true","fetch_graph":"https://pith.science/api/pith-number/FALZKPOESSARWWFHGRKF35HNF6/graph.json","fetch_events":"https://pith.science/api/pith-number/FALZKPOESSARWWFHGRKF35HNF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6/action/storage_attestation","attest_author":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6/action/author_attestation","sign_citation":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6/action/citation_signature","submit_replication":"https://pith.science/pith/FALZKPOESSARWWFHGRKF35HNF6/action/replication_record"}},"created_at":"2026-05-18T00:07:28.993013+00:00","updated_at":"2026-05-18T00:07:28.993013+00:00"}