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Functions in this class can be constructed by the shear construction due to Clunie and Sheil-Small which allows by examining their conformal counterpart. Unlike the conformal case, convolution of two univalent harmonic convex mappings in $\\ID$ is not necessarily even univalent in $\\ID$. In this paper, we fix $f_0\\in{\\mathca"},"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":"1206.4364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-06-20T01:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"18d8f64e7e928caec70a162070bad1bdb86d53af4c0a682b67c3117a8b9c2d94","abstract_canon_sha256":"6379b415081f47b85e7fd1beb84aaa0d439ca3a78d048944f78b347f7006ddb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:06.080844Z","signature_b64":"RggqXSisTGAPXx1onzDZLQobA+VzJSbpvLkIUzwe2/VQunl/KBJT/laA4LOEkY7O9YdEbtkNWVmyyPH0NIRyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d2466c80ec4463b3835af041210a57aab600934dedfb400f32eaf2cbb174a27","last_reissued_at":"2026-05-18T03:53:06.080125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:06.080125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convolutions of slanted half-plane harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Liulan Li, S. Ponnusamy","submitted_at":"2012-06-20T01:00:16Z","abstract_excerpt":"Let ${\\mathcal S^0}(H_{\\gamma})$ denote the class of all univalent, harmonic, sense-preserving and normalized mappings $f$ of the unit disk $\\ID$ onto the slanted half-plane $H_\\gamma :=\\{w:\\,{\\rm Re\\,}(e^{i\\gamma}w) >-1/2\\}$ with an additional condition $f_{\\bar{z}}(0)=0$. Functions in this class can be constructed by the shear construction due to Clunie and Sheil-Small which allows by examining their conformal counterpart. Unlike the conformal case, convolution of two univalent harmonic convex mappings in $\\ID$ is not necessarily even univalent in $\\ID$. In this paper, we fix $f_0\\in{\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4364","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":"1206.4364","created_at":"2026-05-18T03:53:06.080243+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.4364v1","created_at":"2026-05-18T03:53:06.080243+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4364","created_at":"2026-05-18T03:53:06.080243+00:00"},{"alias_kind":"pith_short_12","alias_value":"NUSGNSAOYRDD","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NUSGNSAOYRDDWOBV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NUSGNSAO","created_at":"2026-05-18T12:27:16.716162+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/NUSGNSAOYRDDWOBVV4CBEEFFPK","json":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK.json","graph_json":"https://pith.science/api/pith-number/NUSGNSAOYRDDWOBVV4CBEEFFPK/graph.json","events_json":"https://pith.science/api/pith-number/NUSGNSAOYRDDWOBVV4CBEEFFPK/events.json","paper":"https://pith.science/paper/NUSGNSAO"},"agent_actions":{"view_html":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK","download_json":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK.json","view_paper":"https://pith.science/paper/NUSGNSAO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.4364&json=true","fetch_graph":"https://pith.science/api/pith-number/NUSGNSAOYRDDWOBVV4CBEEFFPK/graph.json","fetch_events":"https://pith.science/api/pith-number/NUSGNSAOYRDDWOBVV4CBEEFFPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK/action/storage_attestation","attest_author":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK/action/author_attestation","sign_citation":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK/action/citation_signature","submit_replication":"https://pith.science/pith/NUSGNSAOYRDDWOBVV4CBEEFFPK/action/replication_record"}},"created_at":"2026-05-18T03:53:06.080243+00:00","updated_at":"2026-05-18T03:53:06.080243+00:00"}