{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P5PWJQ6PFVBUGMXI5BMI7FMEIJ","short_pith_number":"pith:P5PWJQ6P","canonical_record":{"source":{"id":"1302.2018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-08T12:50:24Z","cross_cats_sorted":[],"title_canon_sha256":"36688397e646a8001260a0d9bf46198d275097c369e3d06a5645879859075b5e","abstract_canon_sha256":"65e9b73abcdfb42a2f60e2a03718072100a52d72729dc5e394757c659e8bea77"},"schema_version":"1.0"},"canonical_sha256":"7f5f64c3cf2d434332e8e8588f9584427a403491fa117facaa0e93dc71b889f8","source":{"kind":"arxiv","id":"1302.2018","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2018","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2018v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2018","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"P5PWJQ6PFVBU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P5PWJQ6PFVBUGMXI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P5PWJQ6P","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P5PWJQ6PFVBUGMXI5BMI7FMEIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2018","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-08T12:50:24Z","cross_cats_sorted":[],"title_canon_sha256":"36688397e646a8001260a0d9bf46198d275097c369e3d06a5645879859075b5e","abstract_canon_sha256":"65e9b73abcdfb42a2f60e2a03718072100a52d72729dc5e394757c659e8bea77"},"schema_version":"1.0"},"canonical_sha256":"7f5f64c3cf2d434332e8e8588f9584427a403491fa117facaa0e93dc71b889f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:39.076255Z","signature_b64":"W9mBDQrK6mzh3VGPdrsmORIyePJahII2Y3f1J0Bu5P3QSCfXMg2zKRMp2KLFnpexthAm1LcYTiMyj8tY9QbeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f5f64c3cf2d434332e8e8588f9584427a403491fa117facaa0e93dc71b889f8","last_reissued_at":"2026-05-18T02:49:39.075869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:39.075869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2018","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xt3NECkaneZKkyQ1kogrLHDwaVAt8KZ6Qt5EBv5HgSWQskd24BIExWgEQA4E9BuTFybvt1YAkHehXGiqXFtdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:13:42.259926Z"},"content_sha256":"ae4c043a527eb77eac47cc6677223d6e36d2e146b1f80fe89b007977c86afad1","schema_version":"1.0","event_id":"sha256:ae4c043a527eb77eac47cc6677223d6e36d2e146b1f80fe89b007977c86afad1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P5PWJQ6PFVBUGMXI5BMI7FMEIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On polyharmonic univalent mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Rasila, Jiaolong Chen, Xiantao Wang","submitted_at":"2013-02-08T12:50:24Z","abstract_excerpt":"In this paper, we introduce a class of complex-valued polyharmonic mappings, denoted by $HS_{p}(\\lambda)$, and its subclass $HS_{p}^{0}(\\lambda)$, where $\\lambda\\in [0,1]$ is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in 1950's. We generalize the main results of Avci and Z{\\l}otkiewicz from 1990's to the classes $HS_{p}(\\lambda)$ and $HS_{p}^{0}(\\lambda)$, showing that the mappings in $HS_{p}(\\lambda)$ are univalent and sense preserving. We also prove that the mappings in $HS_{p}^{0}(\\lambda)$ are starlike with respect to the origin, and cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2018","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gSJxXlW2rMJyFQI5IA+jAA5yFZ5GoItrFmO1aGQY2GcJFy18+6pcj/qdRq0d/GuzfMulxKeLUvcaoMDAR+fwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:13:42.260272Z"},"content_sha256":"1597d33782e3cf2480937041a9022be03a75207dcd8cb98230db152e2ead091c","schema_version":"1.0","event_id":"sha256:1597d33782e3cf2480937041a9022be03a75207dcd8cb98230db152e2ead091c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/bundle.json","state_url":"https://pith.science/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T15:13:42Z","links":{"resolver":"https://pith.science/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ","bundle":"https://pith.science/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/bundle.json","state":"https://pith.science/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5PWJQ6PFVBUGMXI5BMI7FMEIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P5PWJQ6PFVBUGMXI5BMI7FMEIJ","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":"65e9b73abcdfb42a2f60e2a03718072100a52d72729dc5e394757c659e8bea77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-08T12:50:24Z","title_canon_sha256":"36688397e646a8001260a0d9bf46198d275097c369e3d06a5645879859075b5e"},"schema_version":"1.0","source":{"id":"1302.2018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2018","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2018v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2018","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"P5PWJQ6PFVBU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P5PWJQ6PFVBUGMXI","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P5PWJQ6P","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1597d33782e3cf2480937041a9022be03a75207dcd8cb98230db152e2ead091c","target":"graph","created_at":"2026-05-18T02:49:39Z","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 introduce a class of complex-valued polyharmonic mappings, denoted by $HS_{p}(\\lambda)$, and its subclass $HS_{p}^{0}(\\lambda)$, where $\\lambda\\in [0,1]$ is a constant. These classes are natural generalizations of a class of mappings studied by Goodman in 1950's. We generalize the main results of Avci and Z{\\l}otkiewicz from 1990's to the classes $HS_{p}(\\lambda)$ and $HS_{p}^{0}(\\lambda)$, showing that the mappings in $HS_{p}(\\lambda)$ are univalent and sense preserving. We also prove that the mappings in $HS_{p}^{0}(\\lambda)$ are starlike with respect to the origin, and cha","authors_text":"Antti Rasila, Jiaolong Chen, Xiantao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-08T12:50:24Z","title":"On polyharmonic univalent mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2018","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:ae4c043a527eb77eac47cc6677223d6e36d2e146b1f80fe89b007977c86afad1","target":"record","created_at":"2026-05-18T02:49:39Z","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":"65e9b73abcdfb42a2f60e2a03718072100a52d72729dc5e394757c659e8bea77","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-08T12:50:24Z","title_canon_sha256":"36688397e646a8001260a0d9bf46198d275097c369e3d06a5645879859075b5e"},"schema_version":"1.0","source":{"id":"1302.2018","kind":"arxiv","version":1}},"canonical_sha256":"7f5f64c3cf2d434332e8e8588f9584427a403491fa117facaa0e93dc71b889f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f5f64c3cf2d434332e8e8588f9584427a403491fa117facaa0e93dc71b889f8","first_computed_at":"2026-05-18T02:49:39.075869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:39.075869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W9mBDQrK6mzh3VGPdrsmORIyePJahII2Y3f1J0Bu5P3QSCfXMg2zKRMp2KLFnpexthAm1LcYTiMyj8tY9QbeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:39.076255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae4c043a527eb77eac47cc6677223d6e36d2e146b1f80fe89b007977c86afad1","sha256:1597d33782e3cf2480937041a9022be03a75207dcd8cb98230db152e2ead091c"],"state_sha256":"b7a5ed7ffa12b6e64ebc6ed9b5f3faff5fb9f791bb73e567d49786290c7ba0e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+I4l+whfZY8Z2zDbz/pTxwxniAiIPSRN0wCMUKaP+s+4H6lJQHdWHMNhH5bJtYnOFZo5FFFMVOtJpXMU6gSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:13:42.262188Z","bundle_sha256":"a6694442fb689aef147e4b54bb01dc363e7d7ef8ac77ac8f91c36f987f7aebab"}}