{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KXIFKEP6ZQVSNIR6V3CXAFIZFF","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":"7c8f6dab5f412bfbe096905d306f497ef1dc4926138abc498fb6986f4c3c3cb1","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-04T16:45:42Z","title_canon_sha256":"1b6260a570929bb27272c33cf16517af6ddfebd4b65e4e7a4935e125efd55c45"},"schema_version":"1.0","source":{"id":"1610.01083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01083","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01083v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01083","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"KXIFKEP6ZQVS","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KXIFKEP6ZQVSNIR6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KXIFKEP6","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:3c732f7c9c0fbbacc9706f9bed9ffd4c757048bdb8ec728b613bbcb667a9b497","target":"graph","created_at":"2026-05-18T01:03:12Z","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":"A 2p-times continuously differentiable complex valued function $f = u + iv$ in a simply connected domain is polyharmonic (or p-harmonic) if it satisfies the polyharmonic equation $\\Delta^pF = 0$ . Every polyharmonic mapping f can be written as $f(z) =\\sum_{k}^{p} |z|^{2(p-1)}G_{p-k+1}(z)$ where each $G_{p-k+1}$ is harmonic. In this paper we investigate the univalence of polyharmonic mappings on linearly connected domains and the relation between univalence of f(z) and that of $G_p(z)$. The notions of stable univalence and logpolyharminc mappings are also considered.","authors_text":"Layan El Hajj","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-04T16:45:42Z","title":"On the univalence of polyharmonic mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01083","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:a8a3916becefd1bcd574574568bb7abce22f88d8319a91e72eaedfde130657d2","target":"record","created_at":"2026-05-18T01:03:12Z","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":"7c8f6dab5f412bfbe096905d306f497ef1dc4926138abc498fb6986f4c3c3cb1","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-10-04T16:45:42Z","title_canon_sha256":"1b6260a570929bb27272c33cf16517af6ddfebd4b65e4e7a4935e125efd55c45"},"schema_version":"1.0","source":{"id":"1610.01083","kind":"arxiv","version":1}},"canonical_sha256":"55d05511fecc2b26a23eaec5701519294220d6822b66406437520b2700594784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55d05511fecc2b26a23eaec5701519294220d6822b66406437520b2700594784","first_computed_at":"2026-05-18T01:03:12.464537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.464537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IK/bIx4XHvxuiF1M+rCDLgBk6Cm9BaB+G3Vr8q4eRHjvdJpo1TGF8nC3U//Dm/DidBSVR0fNxclnNaa2QF9oCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.465067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8a3916becefd1bcd574574568bb7abce22f88d8319a91e72eaedfde130657d2","sha256:3c732f7c9c0fbbacc9706f9bed9ffd4c757048bdb8ec728b613bbcb667a9b497"],"state_sha256":"ab50ec3820e75c64c7f7d1730ac8fa9712c9eb5f6e9dc60bd8f06295b71b52ce"}