{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R6BQQPXZ3MGPLVHS2FZNGSOC2Z","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":"1f6b886fbdb9053c16c18c5646d145bfd55448f505e1d9bf1cdde096f28ba257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-06T07:57:34Z","title_canon_sha256":"ae2027e83d845f0a08d0beb845d3a5c7646d5f57a38de8b7343ff0c7ab63754a"},"schema_version":"1.0","source":{"id":"1303.1263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1263","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1263v1","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1263","created_at":"2026-05-18T03:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"R6BQQPXZ3MGP","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R6BQQPXZ3MGPLVHS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R6BQQPXZ","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:52b62d76f4ea73e68e7bb26594c45f101e1fd3ebbca130f828569dbf69f5adae","target":"graph","created_at":"2026-05-18T03:12:59Z","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":"For normalized harmonic functions $f(z)=h(z)+\\bar{g(z)}$ in the open unit disk $\\mathbb{U}$, a sufficient condition on $h(z)$ for $f(z)$ to be $p$-valent in $\\mathbb{U}$ is discussed. Moreover, some interesting examples and images of $f(z)$ satisfying the obtained condition are enumerated.","authors_text":"Toshio Hayami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-06T07:57:34Z","title":"A sufficient condition for $p$-valently harmonic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1263","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":"sha256:5bab0c207e57ed1115d36d693c604d05b98e883e0837704c34333a8cb9116910","target":"record","created_at":"2026-05-18T03:12:59Z","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":"1f6b886fbdb9053c16c18c5646d145bfd55448f505e1d9bf1cdde096f28ba257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-06T07:57:34Z","title_canon_sha256":"ae2027e83d845f0a08d0beb845d3a5c7646d5f57a38de8b7343ff0c7ab63754a"},"schema_version":"1.0","source":{"id":"1303.1263","kind":"arxiv","version":1}},"canonical_sha256":"8f83083ef9db0cf5d4f2d172d349c2d64fd11e89a8e17836ec9235624d7b4ebb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f83083ef9db0cf5d4f2d172d349c2d64fd11e89a8e17836ec9235624d7b4ebb","first_computed_at":"2026-05-18T03:12:59.978286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:59.978286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNZ5Hf1V7ft/nQmyjoH1SHeGdC1rRd8xCQn2FXeRFLcy84Q1Vg6YxxdOGw3tTHLA1lXTj3TvcpWJ7bri9TsJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:59.978954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bab0c207e57ed1115d36d693c604d05b98e883e0837704c34333a8cb9116910","sha256:52b62d76f4ea73e68e7bb26594c45f101e1fd3ebbca130f828569dbf69f5adae"],"state_sha256":"b87c021ff64a54a76f9093d6bed02e7f6f35355eccd83be1a2265c2b9e15a39a"}