{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7JIY266BOGUNJFTR5RCALFA64T","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":"a8f15e913fb923822c7f3cfcc8f5ac0d2ef9b078b6ae461db4a6fe2f738a3da2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-17T17:50:02Z","title_canon_sha256":"9febd5bb1628d7c50c2418de2cd1f64ccb2353d90b6664eae5de454d44e1ca2b"},"schema_version":"1.0","source":{"id":"1701.04785","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.04785","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1701.04785v2","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.04785","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"7JIY266BOGUN","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7JIY266BOGUNJFTR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7JIY266B","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:00fabc43f1b858bf59979c2b01fb8858fd7559331886998e91259eb56896cd35","target":"graph","created_at":"2026-05-18T00:52:30Z","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 prove some sharp inequalities for complex harmonic functions on the unit disk. The results extend a M. Riesz conjugate function theorem and some well-known estimates for holomorphic functions. We apply some of results to the isoperimetric inequality for harmonic mappings.","authors_text":"David Kalaj","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-17T17:50:02Z","title":"On Riesz type inequalities for harmonic mappings on the unit disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04785","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:d62cc8463dff64cee7817ff306ba6062cf4ba8d121f23a041dc7dbb043b579d2","target":"record","created_at":"2026-05-18T00:52:30Z","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":"a8f15e913fb923822c7f3cfcc8f5ac0d2ef9b078b6ae461db4a6fe2f738a3da2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-01-17T17:50:02Z","title_canon_sha256":"9febd5bb1628d7c50c2418de2cd1f64ccb2353d90b6664eae5de454d44e1ca2b"},"schema_version":"1.0","source":{"id":"1701.04785","kind":"arxiv","version":2}},"canonical_sha256":"fa518d7bc171a8d49671ec4405941ee4e876dbcdbda4ef0afd8ab8e19cffdffb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa518d7bc171a8d49671ec4405941ee4e876dbcdbda4ef0afd8ab8e19cffdffb","first_computed_at":"2026-05-18T00:52:30.571282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:30.571282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OZOYNygi2V2GceQXPibvgwBlbaBX0PRrpGeJ7y+DRF29pOZKQw5dqc2T4H/fvCrETHdQVKza1pVYWAWxVex7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:30.571777Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.04785","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d62cc8463dff64cee7817ff306ba6062cf4ba8d121f23a041dc7dbb043b579d2","sha256:00fabc43f1b858bf59979c2b01fb8858fd7559331886998e91259eb56896cd35"],"state_sha256":"2613611939d416b00fd3e12771b655c4621a321bcb20dee22fba95d8838824a5"}