{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WPUHVPGXASOYCOHNLMJEGZDMSB","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":"d040dabb6a51b75e36808e6f38686ed67243fd68347b9327e5954017e546f67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-08T08:36:18Z","title_canon_sha256":"4014a2a117918fe755ac59efece3013f23f28734958617fde13319f31c07a75a"},"schema_version":"1.0","source":{"id":"1605.02293","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02293","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02293v4","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02293","created_at":"2026-05-18T01:00:09Z"},{"alias_kind":"pith_short_12","alias_value":"WPUHVPGXASOY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WPUHVPGXASOYCOHN","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WPUHVPGX","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:4c3c37f03f4f8fa3f0fc8f078530ab9bb4cbcf19b174f08ede2be719ecf7d12f","target":"graph","created_at":"2026-05-18T01:00:09Z","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, a class of $\\log$-polyharmonic mappings $\\mathcal{L}_p\\mathcal{H}$ together with its subclass $\\mathcal{L}_p\\mathcal{H}(G)$ in the unit disk $\\mathbb{D}=\\{z: |z|<1\\}$ is introduced, and several geometrical properties such as the starlikeness, convexity and univalence are investigated. In particular, we consider the Goodman-Saff conjecture and prove that the conjecture is true in $\\mathcal{L}_p\\mathcal{H}(G)$.","authors_text":"Bin Sheng, Jiaolong Chen, Xiaotao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-08T08:36:18Z","title":"Geometric properties of $\\log$-polyharmonic mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02293","kind":"arxiv","version":4},"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":"sha256:3cb0a1229cad8ac494a0c10d254089b59e6fdc0708fea4d90f78883973645377","target":"record","created_at":"2026-05-18T01:00:09Z","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":"d040dabb6a51b75e36808e6f38686ed67243fd68347b9327e5954017e546f67c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-08T08:36:18Z","title_canon_sha256":"4014a2a117918fe755ac59efece3013f23f28734958617fde13319f31c07a75a"},"schema_version":"1.0","source":{"id":"1605.02293","kind":"arxiv","version":4}},"canonical_sha256":"b3e87abcd7049d8138ed5b1243646c907fea819ba896b67123acffbe867bdf36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3e87abcd7049d8138ed5b1243646c907fea819ba896b67123acffbe867bdf36","first_computed_at":"2026-05-18T01:00:09.451614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:09.451614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tiZtbtnVXIXvSlRqiybEtG9zbiKtSOK2SVg46xa3uNwZ1oIPZEM8qeaRXbOPtkyI0hrtucuLd4zhQtO7juuHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:09.452218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02293","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cb0a1229cad8ac494a0c10d254089b59e6fdc0708fea4d90f78883973645377","sha256:4c3c37f03f4f8fa3f0fc8f078530ab9bb4cbcf19b174f08ede2be719ecf7d12f"],"state_sha256":"7780150b6d7ddb9a368a506cb6931e518f1a61948cc532476fde4f807cea8610"}