{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QDNVSBUU3RQVHFBXRA54DFF23X","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d5ebd8eba4f645754c1cf65c182d7ea634110a1054bd9376cff5a72bbb4c352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-13T10:30:31Z","title_canon_sha256":"33967d978a80842768774fb5673d6677a1f89597e0ea6c8d77d5fd15de44b277"},"schema_version":"1.0","source":{"id":"1708.03883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03883","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03883v1","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03883","created_at":"2026-05-18T00:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"QDNVSBUU3RQV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QDNVSBUU3RQVHFBX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QDNVSBUU","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:e077f834f95b682d4fd124fabe7155dc454f031e0e3e0ec6dec29eee172c1a2f","target":"graph","created_at":"2026-05-18T00:38:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $f=h+\\overline{g}$ be a normalized harmonic mapping in the unit disk $\\ID$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D_f^{\\epsilon}=zf_{z}-\\epsilon\\overline{z}f_{\\overline{z}}~(|\\epsilon|=1)$ and $F_{\\lambda}(z)=(1-\\lambda)f+\\lambda D_f^{\\epsilon}~(0\\leq\\lambda\\leq 1)$ when the coefficients of $h$ and $g$ satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of $h$ and $g$ satisfy the corresponding necessary conditions of the","authors_text":"Saminathan Ponnusamy, Zhihong Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-13T10:30:31Z","title":"Radius of fully starlikeness and fully convexity of harmonic linear differential operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03883","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:68a41dc141b610935b742c4119c1ac268b0cc53e5fdf91f530e4c29d0c11eff8","target":"record","created_at":"2026-05-18T00:38:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d5ebd8eba4f645754c1cf65c182d7ea634110a1054bd9376cff5a72bbb4c352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-13T10:30:31Z","title_canon_sha256":"33967d978a80842768774fb5673d6677a1f89597e0ea6c8d77d5fd15de44b277"},"schema_version":"1.0","source":{"id":"1708.03883","kind":"arxiv","version":1}},"canonical_sha256":"80db590694dc61539437883bc194baddfef0f45358a5a2ad9ce293437d0b1d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80db590694dc61539437883bc194baddfef0f45358a5a2ad9ce293437d0b1d1d","first_computed_at":"2026-05-18T00:38:07.614789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:07.614789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LsMyTAUHEnsTWyY3uEQU3vdromI6QIxLQT2tyFHWbJOKT+XNEVPL739kPGg3Q3wDureqdl+cIzf/HFufyzdcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:07.615242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68a41dc141b610935b742c4119c1ac268b0cc53e5fdf91f530e4c29d0c11eff8","sha256:e077f834f95b682d4fd124fabe7155dc454f031e0e3e0ec6dec29eee172c1a2f"],"state_sha256":"7cfc1de5056ed4561c70234e12ce782d710c3358ed689ec713851c91844a65fd"}