{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CAUHLVR4GVRQVQKXQP6GUD4FWB","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":"af000bb5a3502ce2f4201257ef30c67ab97d21bafea2c55e0041840c175154e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-13T04:38:28Z","title_canon_sha256":"5a98e0d06b9f5aa94ea8747e6fbab862a3e3ac1e53f6d7049ad49fc7fa0b1b67"},"schema_version":"1.0","source":{"id":"1203.2711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2711","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2711v1","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2711","created_at":"2026-05-18T04:00:14Z"},{"alias_kind":"pith_short_12","alias_value":"CAUHLVR4GVRQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CAUHLVR4GVRQVQKX","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CAUHLVR4","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:33c87de35081fac8fd7e5f0e71823031745431df01521084b0fcb1a57be9eae8","target":"graph","created_at":"2026-05-18T04:00:14Z","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":"In this paper, we investigate some properties of planar harmonic mappings. First, we generalize the main results in \\cite{CPW3} and \\cite{HT}, and then discuss the relationship between area integral means and harmonic Hardy spaces or harmonic weighted Bergman spaces. At the end, coefficient estimates of mappings in weighted Bergman spaces are obtained.","authors_text":"SH. Chen, S. Ponnusamy, X. Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-13T04:38:28Z","title":"Area integral means, Hardy and weighted Bergman spaces of planar harmonic mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2711","kind":"arxiv","version":1},"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:c2bbf7b0e7be3cb444f8819d5c78bf28266a7c5e455171672463a201ca52de9d","target":"record","created_at":"2026-05-18T04:00:14Z","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":"af000bb5a3502ce2f4201257ef30c67ab97d21bafea2c55e0041840c175154e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-13T04:38:28Z","title_canon_sha256":"5a98e0d06b9f5aa94ea8747e6fbab862a3e3ac1e53f6d7049ad49fc7fa0b1b67"},"schema_version":"1.0","source":{"id":"1203.2711","kind":"arxiv","version":1}},"canonical_sha256":"102875d63c35630ac15783fc6a0f85b0580b5c94382707d88c7cd153187d85c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"102875d63c35630ac15783fc6a0f85b0580b5c94382707d88c7cd153187d85c6","first_computed_at":"2026-05-18T04:00:14.848110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:14.848110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EI8FlStlf2+e+1OfxLWRHgekvgOXOtepZYnjaWYLw9LQ8IvWF1qgPV0vJDamCp3XmV5fHp1RFPTqH19EmfxwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:14.848764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2bbf7b0e7be3cb444f8819d5c78bf28266a7c5e455171672463a201ca52de9d","sha256:33c87de35081fac8fd7e5f0e71823031745431df01521084b0fcb1a57be9eae8"],"state_sha256":"f9819079b9afeb8a51fe46394ff20e4751f4c95a0280f1a6c42b6725db54487b"}