{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:G6L2YT4LJ2DIPF47PCJ4M4PM3C","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":"028d9e77efd2cd3c8972b9fa091f9047c8cb4072b420e5f635b4547c9f07b7f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2020-09-24T20:54:29Z","title_canon_sha256":"973514680db473e781c9ec1bd6ebd5ee54b43c760683287fdffc2c6d897e87e4"},"schema_version":"1.0","source":{"id":"2009.11945","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.11945","created_at":"2026-07-05T11:10:43Z"},{"alias_kind":"arxiv_version","alias_value":"2009.11945v3","created_at":"2026-07-05T11:10:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.11945","created_at":"2026-07-05T11:10:43Z"},{"alias_kind":"pith_short_12","alias_value":"G6L2YT4LJ2DI","created_at":"2026-07-05T11:10:43Z"},{"alias_kind":"pith_short_16","alias_value":"G6L2YT4LJ2DIPF47","created_at":"2026-07-05T11:10:43Z"},{"alias_kind":"pith_short_8","alias_value":"G6L2YT4L","created_at":"2026-07-05T11:10:43Z"}],"graph_snapshots":[{"event_id":"sha256:136859ae9c3f0b96ec68fe3660eb4eadcb37c90b0042fa5874438c94d2eb49d5","target":"graph","created_at":"2026-07-05T11:10:43Z","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/2009.11945/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let function $f$ be normalized, analytic and univalent in the unit disk ${\\mathbb D}=\\{z:|z|<1\\}$ and $f(z)=z+\\sum_{n=2}^{\\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.","authors_text":"Milutin Obradovi\\'c, Nikola Tuneski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2020-09-24T20:54:29Z","title":"Some application of Grunsky coefficients in the theory of univalent functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.11945","kind":"arxiv","version":3},"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":"sha256:48c78df0a6bfbe217c5296bfb3663ebecea0fae5d0e664b7654421658911e48f","target":"record","created_at":"2026-07-05T11:10:43Z","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":"028d9e77efd2cd3c8972b9fa091f9047c8cb4072b420e5f635b4547c9f07b7f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2020-09-24T20:54:29Z","title_canon_sha256":"973514680db473e781c9ec1bd6ebd5ee54b43c760683287fdffc2c6d897e87e4"},"schema_version":"1.0","source":{"id":"2009.11945","kind":"arxiv","version":3}},"canonical_sha256":"3797ac4f8b4e8687979f7893c671ecd8afafda99edb0b0f9617a9ca73a064792","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3797ac4f8b4e8687979f7893c671ecd8afafda99edb0b0f9617a9ca73a064792","first_computed_at":"2026-07-05T11:10:43.225242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:43.225242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8W7jp8ylFnPvYJIE19motjV+F3Z5bThyjGkpVhDuGvzi04hthfkqXUOf81i0rWFC1X0+F4K6Zw06kG2+n+RuBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:43.225823Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.11945","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48c78df0a6bfbe217c5296bfb3663ebecea0fae5d0e664b7654421658911e48f","sha256:136859ae9c3f0b96ec68fe3660eb4eadcb37c90b0042fa5874438c94d2eb49d5"],"state_sha256":"e6b7dc2dbf40aa8620988236ad5d4e5aec780863fbb5e02a9be7b3f78e507418"}