{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZSYGZ2SZTVMPJMBW7HZFSUOA25","short_pith_number":"pith:ZSYGZ2SZ","schema_version":"1.0","canonical_sha256":"ccb06cea599d58f4b036f9f25951c0d765faf968a763eed6bb3369c6f5b9b5cb","source":{"kind":"arxiv","id":"1010.4905","version":3},"attestation_state":"computed","paper":{"title":"On harmonic functions and the Schwarz lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj, Matti Vuorinen","submitted_at":"2010-10-23T19:36:32Z","abstract_excerpt":"We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings."},"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":"1010.4905","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-10-23T19:36:32Z","cross_cats_sorted":[],"title_canon_sha256":"cb6264c79972f15288b1d78908c96510b987ebfb18a44b7fec3a2ecd6acd84f9","abstract_canon_sha256":"a9714761530b779e5bdf318a217d49eae6b1b5d7ed0ecd9ec896d931c1eca2d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:01.926633Z","signature_b64":"DLXkzO66xM4gjslid2vbbTJrjkGmcAEXx7pRym4VvWjO+UXqxkpdRXuIUHwlzpuul+QolCIwic4HWsPGI5dYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccb06cea599d58f4b036f9f25951c0d765faf968a763eed6bb3369c6f5b9b5cb","last_reissued_at":"2026-05-18T04:02:01.925913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:01.925913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On harmonic functions and the Schwarz lemma","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"David Kalaj, Matti Vuorinen","submitted_at":"2010-10-23T19:36:32Z","abstract_excerpt":"We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4905","kind":"arxiv","version":3},"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":"1010.4905","created_at":"2026-05-18T04:02:01.926026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.4905v3","created_at":"2026-05-18T04:02:01.926026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4905","created_at":"2026-05-18T04:02:01.926026+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSYGZ2SZTVMP","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSYGZ2SZTVMPJMBW","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSYGZ2SZ","created_at":"2026-05-18T12:26:18.847500+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/ZSYGZ2SZTVMPJMBW7HZFSUOA25","json":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25.json","graph_json":"https://pith.science/api/pith-number/ZSYGZ2SZTVMPJMBW7HZFSUOA25/graph.json","events_json":"https://pith.science/api/pith-number/ZSYGZ2SZTVMPJMBW7HZFSUOA25/events.json","paper":"https://pith.science/paper/ZSYGZ2SZ"},"agent_actions":{"view_html":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25","download_json":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25.json","view_paper":"https://pith.science/paper/ZSYGZ2SZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.4905&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSYGZ2SZTVMPJMBW7HZFSUOA25/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSYGZ2SZTVMPJMBW7HZFSUOA25/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25/action/storage_attestation","attest_author":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25/action/author_attestation","sign_citation":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25/action/citation_signature","submit_replication":"https://pith.science/pith/ZSYGZ2SZTVMPJMBW7HZFSUOA25/action/replication_record"}},"created_at":"2026-05-18T04:02:01.926026+00:00","updated_at":"2026-05-18T04:02:01.926026+00:00"}