{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QPWQDBP3OTVVICUEHMSEKJDRMW","short_pith_number":"pith:QPWQDBP3","canonical_record":{"source":{"id":"1804.02945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-09T12:47:29Z","cross_cats_sorted":[],"title_canon_sha256":"57cfc401f89e1e009c30b49da73b6bf906b13d1fdaa0dc56575c3c38863ad54c","abstract_canon_sha256":"c92e3f8da98300e9de53b286366eaf4f41e6bdce533dd3dab51b300ccfd98b8d"},"schema_version":"1.0"},"canonical_sha256":"83ed0185fb74eb540a843b2445247165a4c4ad448781897669c6156baf6c499b","source":{"kind":"arxiv","id":"1804.02945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02945","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02945v1","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02945","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"QPWQDBP3OTVV","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPWQDBP3OTVVICUE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPWQDBP3","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QPWQDBP3OTVVICUEHMSEKJDRMW","target":"record","payload":{"canonical_record":{"source":{"id":"1804.02945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-09T12:47:29Z","cross_cats_sorted":[],"title_canon_sha256":"57cfc401f89e1e009c30b49da73b6bf906b13d1fdaa0dc56575c3c38863ad54c","abstract_canon_sha256":"c92e3f8da98300e9de53b286366eaf4f41e6bdce533dd3dab51b300ccfd98b8d"},"schema_version":"1.0"},"canonical_sha256":"83ed0185fb74eb540a843b2445247165a4c4ad448781897669c6156baf6c499b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:57.878308Z","signature_b64":"khv6NeWKBVn5JMQJld8KaddyjytYBIDuipOfmtjG59ySTZG0ys5Y1CCZDe1dtsEQY+OqUHtAI+/51EDwtQkQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83ed0185fb74eb540a843b2445247165a4c4ad448781897669c6156baf6c499b","last_reissued_at":"2026-05-18T00:18:57.877787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:57.877787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.02945","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":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zfyXcmMUQwqVxbTt2hmk/O7MsgW5Aox55aOWFR60c+wBCrafSCVWDV7ERG9TX9gk1Z0qfYl8gOCzLBRh/XYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:39:42.833247Z"},"content_sha256":"5ab32ff3a664cd8405f3ef316cb20180f3c909ecf788bcd1777a8f621ce4521b","schema_version":"1.0","event_id":"sha256:5ab32ff3a664cd8405f3ef316cb20180f3c909ecf788bcd1777a8f621ce4521b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QPWQDBP3OTVVICUEHMSEKJDRMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal harmonic mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hugo Arbel\\'aez, Rodrigo Hern\\'andez, Willy Sierra","submitted_at":"2018-04-09T12:47:29Z","abstract_excerpt":"The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk $\\mathbb{D}$ to the complex plane. In particular, we obtain necessary conditions for that a function $f$ to be normal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02945","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":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ioVv6qWdO3UlniR1A8WNIhkw21rk1yT542/vuxHMlzD1h8QNSttoTwpmiLtHCIJ7PrqQcLwgY8hB8uohqNG5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:39:42.833596Z"},"content_sha256":"9c6c26299890b1c6d979fddbe2ed10c6f50bf155df6a8511a21c39e13dd357be","schema_version":"1.0","event_id":"sha256:9c6c26299890b1c6d979fddbe2ed10c6f50bf155df6a8511a21c39e13dd357be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/bundle.json","state_url":"https://pith.science/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/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":"2026-06-24T20:39:42Z","links":{"resolver":"https://pith.science/pith/QPWQDBP3OTVVICUEHMSEKJDRMW","bundle":"https://pith.science/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/bundle.json","state":"https://pith.science/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPWQDBP3OTVVICUEHMSEKJDRMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QPWQDBP3OTVVICUEHMSEKJDRMW","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":"c92e3f8da98300e9de53b286366eaf4f41e6bdce533dd3dab51b300ccfd98b8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-09T12:47:29Z","title_canon_sha256":"57cfc401f89e1e009c30b49da73b6bf906b13d1fdaa0dc56575c3c38863ad54c"},"schema_version":"1.0","source":{"id":"1804.02945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.02945","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1804.02945v1","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.02945","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"QPWQDBP3OTVV","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QPWQDBP3OTVVICUE","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QPWQDBP3","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:9c6c26299890b1c6d979fddbe2ed10c6f50bf155df6a8511a21c39e13dd357be","target":"graph","created_at":"2026-05-18T00:18:57Z","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":"The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk $\\mathbb{D}$ to the complex plane. In particular, we obtain necessary conditions for that a function $f$ to be normal.","authors_text":"Hugo Arbel\\'aez, Rodrigo Hern\\'andez, Willy Sierra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-09T12:47:29Z","title":"Normal harmonic mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02945","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":"sha256:5ab32ff3a664cd8405f3ef316cb20180f3c909ecf788bcd1777a8f621ce4521b","target":"record","created_at":"2026-05-18T00:18:57Z","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":"c92e3f8da98300e9de53b286366eaf4f41e6bdce533dd3dab51b300ccfd98b8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-04-09T12:47:29Z","title_canon_sha256":"57cfc401f89e1e009c30b49da73b6bf906b13d1fdaa0dc56575c3c38863ad54c"},"schema_version":"1.0","source":{"id":"1804.02945","kind":"arxiv","version":1}},"canonical_sha256":"83ed0185fb74eb540a843b2445247165a4c4ad448781897669c6156baf6c499b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ed0185fb74eb540a843b2445247165a4c4ad448781897669c6156baf6c499b","first_computed_at":"2026-05-18T00:18:57.877787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:57.877787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khv6NeWKBVn5JMQJld8KaddyjytYBIDuipOfmtjG59ySTZG0ys5Y1CCZDe1dtsEQY+OqUHtAI+/51EDwtQkQDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:57.878308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.02945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ab32ff3a664cd8405f3ef316cb20180f3c909ecf788bcd1777a8f621ce4521b","sha256:9c6c26299890b1c6d979fddbe2ed10c6f50bf155df6a8511a21c39e13dd357be"],"state_sha256":"e4e1650afa4260564786f8cd4c99b89ba106d0eff008bd69f7f3340bd3d5cf62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6M2QHG83M2AWQbUSx6YY3AfNjFVw97mHg9l2IjVbir048DsU2GQUVlVRYMZWbVZDcdNg77ynrR77IfIcPezDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:39:42.835609Z","bundle_sha256":"a341ef23e9cc161337387a1b47441d9e0d89cfcef9ec978f2b699f0d0c21769e"}}