{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SM5VM6DOSIKLQE6NPPS5UHKF2Q","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":"7aab5d355f565ae950aa044d11535cb36b85a06689454fff7a26fa15635aa305","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-02T12:55:48Z","title_canon_sha256":"541e412f1677adf6b2b35acf201b15cfd884c6a2f9db58cb0fe1ea2ed0661821"},"schema_version":"1.0","source":{"id":"1502.00457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00457","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00457v2","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00457","created_at":"2026-05-18T02:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"SM5VM6DOSIKL","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SM5VM6DOSIKLQE6N","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SM5VM6DO","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:8e828e13e6f9bddf0558542a247d1f35973772e9a7344efa6eeee7b917dcd84a","target":"graph","created_at":"2026-05-18T02:27:18Z","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":"Using normal family arguments, we show that the degree of the first nonzero homogenous polynomial in the expansion of $n$ dimensional Euclidean harmonic $K$-quasiconformal mapping around an internal point is odd, and that such a map from the unit ball onto a bounded convex domain, with $K< 3^{n-1}$, is co-Lipschitz. Also some generalizations of this result are given, as well as a generalization of Heinz's lemma for harmonic quasiconformal maps in $\\mathbb R^n$ and related results.","authors_text":"Miodrag Mateljevi\\'c, Vladimir Bo\\v{z}in","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-02T12:55:48Z","title":"Bounds for Jacobian of harmonic injective mappings in n-dimensional space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00457","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":"sha256:17f4117a5926c3c5561c019c22e0f88f34972a12954d8936ca1871c651c5405c","target":"record","created_at":"2026-05-18T02:27:18Z","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":"7aab5d355f565ae950aa044d11535cb36b85a06689454fff7a26fa15635aa305","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-02T12:55:48Z","title_canon_sha256":"541e412f1677adf6b2b35acf201b15cfd884c6a2f9db58cb0fe1ea2ed0661821"},"schema_version":"1.0","source":{"id":"1502.00457","kind":"arxiv","version":2}},"canonical_sha256":"933b56786e9214b813cd7be5da1d45d4105627ddb298f518e6cfa708092da476","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"933b56786e9214b813cd7be5da1d45d4105627ddb298f518e6cfa708092da476","first_computed_at":"2026-05-18T02:27:18.033026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:18.033026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ng8UqSDQgqhWSDPlS6tA62DWVTF1WIZAPmECO9ZhdIXq8LQwK2xzRNi8MGPAH5CWPyZJ6nEPk/w690bUT5xaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:18.033708Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17f4117a5926c3c5561c019c22e0f88f34972a12954d8936ca1871c651c5405c","sha256:8e828e13e6f9bddf0558542a247d1f35973772e9a7344efa6eeee7b917dcd84a"],"state_sha256":"34e2e159a3a0d729d1ad482c84674bc3781b8b79a3402cb4641074d031e27d11"}