{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SENOYIGZHEXWDQJOBVZPO3JDDM","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":"c052241adf09e4f3233ea55e94a8b12c8188e02e8785ceb4c9f15bf60a9fd125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-07T17:53:58Z","title_canon_sha256":"26dd79dcb17dcbe85152c8850a4500367d47aefdf5ed971f9e1faf1aa01e0d51"},"schema_version":"1.0","source":{"id":"1504.01686","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01686","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01686v2","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01686","created_at":"2026-05-18T02:07:26Z"},{"alias_kind":"pith_short_12","alias_value":"SENOYIGZHEXW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SENOYIGZHEXWDQJO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SENOYIGZ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:6f45ef8cd8fc93795f2fb7bfa208de517c33e6e13267436000fd2a9041c0aef7","target":"graph","created_at":"2026-05-18T02:07:26Z","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":"We first prove the following generalization of Schwarz lemma for harmonic mappings. Let $u$ be a harmonic mapping of the unit ball onto itself. Then we prove the inequality $\\|u(x)-(1-\\|x\\|^2)/(1+\\|x\\|^2)^{n/2} u(0)\\|\\le U(|x| N)$. By using the Schwarz lemma for harmonic mappings we derive Heinz inequality on the boundary of the unit ball by providing a sharp constant $C_n$ in the inequality: $\\|\\partial_r u(r\\eta)\\|_{r=1}\\ge C_n$, $\\|\\eta\\|=1$, for every harmonic mapping of the unit ball into itself satisfying the condition $u(0)=0$, $\\|u(\\eta)\\|=1$.","authors_text":"David Kalaj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-07T17:53:58Z","title":"Heinz inequality for the unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01686","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":"sha256:1453929f7504e1610d5e5066367c4b0d020bc4205bb678fae6676fbd3aacbd3c","target":"record","created_at":"2026-05-18T02:07:26Z","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":"c052241adf09e4f3233ea55e94a8b12c8188e02e8785ceb4c9f15bf60a9fd125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-07T17:53:58Z","title_canon_sha256":"26dd79dcb17dcbe85152c8850a4500367d47aefdf5ed971f9e1faf1aa01e0d51"},"schema_version":"1.0","source":{"id":"1504.01686","kind":"arxiv","version":2}},"canonical_sha256":"911aec20d9392f61c12e0d72f76d231b06f8bac35b8367a6b1462dc74d2cfbbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911aec20d9392f61c12e0d72f76d231b06f8bac35b8367a6b1462dc74d2cfbbd","first_computed_at":"2026-05-18T02:07:26.323264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:26.323264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hbzebd62ubQpyEW+sNdB0D84siEP4PsXdbXQYQgakJgiEhe5xPUs1zO1mR3fuLvEUYtB3EBlPney3FLgDHbbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:26.323784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01686","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1453929f7504e1610d5e5066367c4b0d020bc4205bb678fae6676fbd3aacbd3c","sha256:6f45ef8cd8fc93795f2fb7bfa208de517c33e6e13267436000fd2a9041c0aef7"],"state_sha256":"057872076a27c3b29e9e2a9df87bbfedceaf7a4e597dc3d35a0fc20217bbaccd"}