{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:SM5VM6DOSIKLQE6NPPS5UHKF2Q","short_pith_number":"pith:SM5VM6DO","schema_version":"1.0","canonical_sha256":"933b56786e9214b813cd7be5da1d45d4105627ddb298f518e6cfa708092da476","source":{"kind":"arxiv","id":"1502.00457","version":2},"attestation_state":"computed","paper":{"title":"Bounds for Jacobian of harmonic injective mappings in n-dimensional space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Miodrag Mateljevi\\'c, Vladimir Bo\\v{z}in","submitted_at":"2015-02-02T12:55:48Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.00457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-02T12:55:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"541e412f1677adf6b2b35acf201b15cfd884c6a2f9db58cb0fe1ea2ed0661821","abstract_canon_sha256":"7aab5d355f565ae950aa044d11535cb36b85a06689454fff7a26fa15635aa305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:18.033708Z","signature_b64":"Ng8UqSDQgqhWSDPlS6tA62DWVTF1WIZAPmECO9ZhdIXq8LQwK2xzRNi8MGPAH5CWPyZJ6nEPk/w690bUT5xaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"933b56786e9214b813cd7be5da1d45d4105627ddb298f518e6cfa708092da476","last_reissued_at":"2026-05-18T02:27:18.033026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:18.033026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounds for Jacobian of harmonic injective mappings in n-dimensional space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Miodrag Mateljevi\\'c, Vladimir Bo\\v{z}in","submitted_at":"2015-02-02T12:55:48Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00457","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.00457","created_at":"2026-05-18T02:27:18.033125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.00457v2","created_at":"2026-05-18T02:27:18.033125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00457","created_at":"2026-05-18T02:27:18.033125+00:00"},{"alias_kind":"pith_short_12","alias_value":"SM5VM6DOSIKL","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"SM5VM6DOSIKLQE6N","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"SM5VM6DO","created_at":"2026-05-18T12:29:42.218222+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q","json":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q.json","graph_json":"https://pith.science/api/pith-number/SM5VM6DOSIKLQE6NPPS5UHKF2Q/graph.json","events_json":"https://pith.science/api/pith-number/SM5VM6DOSIKLQE6NPPS5UHKF2Q/events.json","paper":"https://pith.science/paper/SM5VM6DO"},"agent_actions":{"view_html":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q","download_json":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q.json","view_paper":"https://pith.science/paper/SM5VM6DO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.00457&json=true","fetch_graph":"https://pith.science/api/pith-number/SM5VM6DOSIKLQE6NPPS5UHKF2Q/graph.json","fetch_events":"https://pith.science/api/pith-number/SM5VM6DOSIKLQE6NPPS5UHKF2Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q/action/storage_attestation","attest_author":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q/action/author_attestation","sign_citation":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q/action/citation_signature","submit_replication":"https://pith.science/pith/SM5VM6DOSIKLQE6NPPS5UHKF2Q/action/replication_record"}},"created_at":"2026-05-18T02:27:18.033125+00:00","updated_at":"2026-05-18T02:27:18.033125+00:00"}