{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D7UKR54C4RADQY3RTPBFVMUAWM","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":"6fedbbcc2a817f9c8c1ba475486dae5d8781ed91b43e60a7db2e6682e9dd0239","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-23T04:53:32Z","title_canon_sha256":"cf21b83f91f36d74ffe745b2b7ca2c2dc2e616a417c9a8aa1212239ab6f0ac12"},"schema_version":"1.0","source":{"id":"1304.6167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6167","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6167v1","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6167","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"D7UKR54C4RAD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D7UKR54C4RADQY3R","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D7UKR54C","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:35e012f2ff9a2eff5093e2f34052dc0ad991475f076fc8a37c9cc58825f05dd0","target":"graph","created_at":"2026-05-18T03:27:22Z","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":"Dorff, proved in [2] that the convolution of two harmonic right-half plane mappings is convex in the direction of real axis provided that the convolution is locally univalent and sense preserving. Later, it was shown in [3] that the condition of locally univalent and sense preserving can be dropped in some special cases. In this paper, we generalize the main result from [3].","authors_text":"Michael Dorff, Raj Kumar, Sukhjit Singh, Sushma Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-23T04:53:32Z","title":"Convolution properties of some harmonic mappings in the right-half plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6167","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":"sha256:357af80594fd215fbd2a82ec8c499dae08ca901e34e6f5bfd4a53c2b3b3b093c","target":"record","created_at":"2026-05-18T03:27:22Z","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":"6fedbbcc2a817f9c8c1ba475486dae5d8781ed91b43e60a7db2e6682e9dd0239","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-04-23T04:53:32Z","title_canon_sha256":"cf21b83f91f36d74ffe745b2b7ca2c2dc2e616a417c9a8aa1212239ab6f0ac12"},"schema_version":"1.0","source":{"id":"1304.6167","kind":"arxiv","version":1}},"canonical_sha256":"1fe8a8f782e4403863719bc25ab280b33ec57317ee47feefca7a3ea4cb9e6f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fe8a8f782e4403863719bc25ab280b33ec57317ee47feefca7a3ea4cb9e6f65","first_computed_at":"2026-05-18T03:27:22.234770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:22.234770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/8jmRIJKBoCgOyD950Xf3o92oexXD0Y8Iy0QdViK0deXViXnLk51G9yQ18EUZqWsy5xtm1X7IfjLsCjL1IpBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:22.235661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:357af80594fd215fbd2a82ec8c499dae08ca901e34e6f5bfd4a53c2b3b3b093c","sha256:35e012f2ff9a2eff5093e2f34052dc0ad991475f076fc8a37c9cc58825f05dd0"],"state_sha256":"8db10387120d1350b554e8f0184a7508317975473a4d27ecd52583288ba373d2"}