{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QROJJVD4FPBPOGOBBI6OOPJXRV","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":"565e0972d045f1a2aa4d66f7cd5c96c52d3359719e65cbe5a62c6c22f9cce1b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-28T09:47:51Z","title_canon_sha256":"6c78fb9c61d8c7ab218a779c6d747ca3c45406aa9d123ee720c5bf88a2b638fa"},"schema_version":"1.0","source":{"id":"1703.09478","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09478","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09478v2","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09478","created_at":"2026-05-18T00:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"QROJJVD4FPBP","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QROJJVD4FPBPOGOB","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QROJJVD4","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:4e8a30e2f3d88d9446ca4fa12c5797018efaff62c28d3c9e6ec4c51ad9a08d4c","target":"graph","created_at":"2026-05-18T00:37:42Z","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":"In this paper, we give a negative answer to a problem presented by Bharanedhar and Ponnusamy (Rocky Mountain J. Math. 44: 753--777, 2014) concerning univalency of a class of harmonic mappings. More precisely, we show that for all values of the involved parameter, this class contains a non-univalent function. Moreover, several results on a new subclass of close-to-convex harmonic mappings, which is motivated by work of Ponnusamy and Sairam Kaliraj (Mediterr. J. Math. 12: 647--665, 2015), are obtained.","authors_text":"Antti Rasila, Yong Sun, Zhi-Gang Wang, Zhi-Hong Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-28T09:47:51Z","title":"On a problem of Bharanedhar and Ponnusamy involving planar harmonic mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09478","kind":"arxiv","version":2},"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":"sha256:1dfe86546e41996b27968619cf04af92cc9c640227e420990a2183812f0facaa","target":"record","created_at":"2026-05-18T00:37:42Z","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":"565e0972d045f1a2aa4d66f7cd5c96c52d3359719e65cbe5a62c6c22f9cce1b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-28T09:47:51Z","title_canon_sha256":"6c78fb9c61d8c7ab218a779c6d747ca3c45406aa9d123ee720c5bf88a2b638fa"},"schema_version":"1.0","source":{"id":"1703.09478","kind":"arxiv","version":2}},"canonical_sha256":"845c94d47c2bc2f719c10a3ce73d378d4eb9f6458aedd6d278fee267ddcc6f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"845c94d47c2bc2f719c10a3ce73d378d4eb9f6458aedd6d278fee267ddcc6f65","first_computed_at":"2026-05-18T00:37:42.039875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:42.039875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G+KDS97nF9EuRxQbOZPaVySctPhQ4DQ+uK3gicE/GlLwD7SpXfma84/pnejYPcMN1M002BKrt9zYXGEgZlQNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:42.040597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09478","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dfe86546e41996b27968619cf04af92cc9c640227e420990a2183812f0facaa","sha256:4e8a30e2f3d88d9446ca4fa12c5797018efaff62c28d3c9e6ec4c51ad9a08d4c"],"state_sha256":"a8237b129c90622354cbcbaf51a4216023a851936d22dee8c5569f4c1018c998"}