{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z22P77DGLR24MPW2LGXJ3XFYIW","short_pith_number":"pith:Z22P77DG","schema_version":"1.0","canonical_sha256":"ceb4fffc665c75c63eda59ae9ddcb8459cd0b0003fce5d7712d3920e5e8549d0","source":{"kind":"arxiv","id":"1410.8478","version":1},"attestation_state":"computed","paper":{"title":"Muckenhoupt weights and Lindel\\\"of theorem for harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj","submitted_at":"2014-10-30T18:11:29Z","abstract_excerpt":"We extend the result of Lavrentiev which asserts that the harmonic measure and the arc-length measure are $A_\\infty$ equivalent in a chord-arc Jordan domain. By using this result we extend the classical result of Lindel\\\"of to the class of quasiconformal (q.c.) harmonic mappings by proving the following assertion. Assume that $f$ is a quasiconformal harmonic mapping of the unit disk $\\mathbf{U}$ onto a Jordan domain. Then the function $A(z)=\\arg(\\partial_\\varphi(f(z))/z)$ where $z=re^{i\\varphi}$, is well-defined and smooth in $\\mathbf{U}^*=\\{z: 0<|z|<1\\}$ and has a continuous extension to the "},"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":"1410.8478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-30T18:11:29Z","cross_cats_sorted":[],"title_canon_sha256":"7b20960113c99699d499499af5369e482c7634656f70d231ec060fca3bde2e34","abstract_canon_sha256":"87869dba3ff8d3e16eb4bace6e04e1b4ca67db573cb97f88c87697b734fc595a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:59.835595Z","signature_b64":"m3aa14m30p3VlDRUZqrXrMmiGhNhDkU1WXzWkFknJ4XL9zF5LZLtYBPBQkczwXsO35Zd9oFyqjyp4dfuCZXkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceb4fffc665c75c63eda59ae9ddcb8459cd0b0003fce5d7712d3920e5e8549d0","last_reissued_at":"2026-05-18T02:38:59.835165Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:59.835165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Muckenhoupt weights and Lindel\\\"of theorem for harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj","submitted_at":"2014-10-30T18:11:29Z","abstract_excerpt":"We extend the result of Lavrentiev which asserts that the harmonic measure and the arc-length measure are $A_\\infty$ equivalent in a chord-arc Jordan domain. By using this result we extend the classical result of Lindel\\\"of to the class of quasiconformal (q.c.) harmonic mappings by proving the following assertion. Assume that $f$ is a quasiconformal harmonic mapping of the unit disk $\\mathbf{U}$ onto a Jordan domain. Then the function $A(z)=\\arg(\\partial_\\varphi(f(z))/z)$ where $z=re^{i\\varphi}$, is well-defined and smooth in $\\mathbf{U}^*=\\{z: 0<|z|<1\\}$ and has a continuous extension to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8478","kind":"arxiv","version":1},"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":"1410.8478","created_at":"2026-05-18T02:38:59.835231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.8478v1","created_at":"2026-05-18T02:38:59.835231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8478","created_at":"2026-05-18T02:38:59.835231+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z22P77DGLR24","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z22P77DGLR24MPW2","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z22P77DG","created_at":"2026-05-18T12:28:59.999130+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/Z22P77DGLR24MPW2LGXJ3XFYIW","json":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW.json","graph_json":"https://pith.science/api/pith-number/Z22P77DGLR24MPW2LGXJ3XFYIW/graph.json","events_json":"https://pith.science/api/pith-number/Z22P77DGLR24MPW2LGXJ3XFYIW/events.json","paper":"https://pith.science/paper/Z22P77DG"},"agent_actions":{"view_html":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW","download_json":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW.json","view_paper":"https://pith.science/paper/Z22P77DG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.8478&json=true","fetch_graph":"https://pith.science/api/pith-number/Z22P77DGLR24MPW2LGXJ3XFYIW/graph.json","fetch_events":"https://pith.science/api/pith-number/Z22P77DGLR24MPW2LGXJ3XFYIW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW/action/storage_attestation","attest_author":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW/action/author_attestation","sign_citation":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW/action/citation_signature","submit_replication":"https://pith.science/pith/Z22P77DGLR24MPW2LGXJ3XFYIW/action/replication_record"}},"created_at":"2026-05-18T02:38:59.835231+00:00","updated_at":"2026-05-18T02:38:59.835231+00:00"}