{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UUVZTM74MNCXG7CQUTTFAETXL2","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":"c2ba425d2f1cd695ee489e483c00247c388599054649348e5fde974e1cab6c4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-14T15:57:16Z","title_canon_sha256":"535aef855436c371c05d6c7d04adfd0a4d2cb367722f23ad7165828bf86572da"},"schema_version":"1.0","source":{"id":"1908.05183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05183","created_at":"2026-07-04T23:56:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05183v1","created_at":"2026-07-04T23:56:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05183","created_at":"2026-07-04T23:56:37Z"},{"alias_kind":"pith_short_12","alias_value":"UUVZTM74MNCX","created_at":"2026-07-04T23:56:37Z"},{"alias_kind":"pith_short_16","alias_value":"UUVZTM74MNCXG7CQ","created_at":"2026-07-04T23:56:37Z"},{"alias_kind":"pith_short_8","alias_value":"UUVZTM74","created_at":"2026-07-04T23:56:37Z"}],"graph_snapshots":[{"event_id":"sha256:003cebcab3197303bdbc6dd9cb583e0ad3be3e89aafe1649e49142c5c0a15580","target":"graph","created_at":"2026-07-04T23:56:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.05183/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using the Bers isomorphism theorem for Teichmuller spaces of punctured Riemann surfaces and some of their other complex geometric features, we prove a general theorem on maximization of homogeneous polynomial (in fact, more general holomorphic) coefficient functionals $J(f) = J(a_{m_1}, a_{m_2},\\dots, a_{m_n}) $ on some classes of univalent functions in the unit disk naturally connected with the canonical class $S$. The given functional $J$ is lifted to the Teichmuller space $\\mathbf T_1$ of the punctured disk $\\mathbb{D}_{*} = \\{0 < |z| < 1\\}$ which is biholomorphically equivalent to the Bers","authors_text":"Samuel L. Krushkal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-14T15:57:16Z","title":"A general coefficient theorem for univalent functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05183","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":"sha256:1838b22e702211238327ccc4501d03b33898df294742c8dc10ffb5b8432c0e22","target":"record","created_at":"2026-07-04T23:56:37Z","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":"c2ba425d2f1cd695ee489e483c00247c388599054649348e5fde974e1cab6c4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-08-14T15:57:16Z","title_canon_sha256":"535aef855436c371c05d6c7d04adfd0a4d2cb367722f23ad7165828bf86572da"},"schema_version":"1.0","source":{"id":"1908.05183","kind":"arxiv","version":1}},"canonical_sha256":"a52b99b3fc6345737c50a4e65012775eaeeb21e88b22098865e83c9a4a653047","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a52b99b3fc6345737c50a4e65012775eaeeb21e88b22098865e83c9a4a653047","first_computed_at":"2026-07-04T23:56:37.074164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:56:37.074164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wI/6f65gxgYThOi8f2jWXJBEcrZl9dpvnE5Hll0J9pMeLNBtjomzcCk+zAvPMA45hWa6YlJsyMei0OeK97uCDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:56:37.074673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1838b22e702211238327ccc4501d03b33898df294742c8dc10ffb5b8432c0e22","sha256:003cebcab3197303bdbc6dd9cb583e0ad3be3e89aafe1649e49142c5c0a15580"],"state_sha256":"70f28bc87a2fd14397d240890f3cacd619f6b717fe59ba440812f40a0e293e05"}