{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EEJ4C4TMDNOE3J6MCSPJO37HNO","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":"604790dd0b4ad26476e4b8b9a157a168a85687144e3bd4b553fa22d5a8114958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-16T12:44:26Z","title_canon_sha256":"147d662a3e7d1055b81f6fa5da06d04cf0e465382f76a7383c17b1b3b5bce633"},"schema_version":"1.0","source":{"id":"1606.05162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.05162","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.05162v1","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.05162","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"EEJ4C4TMDNOE","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EEJ4C4TMDNOE3J6M","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EEJ4C4TM","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:a420f441e21a3da9c9e42986c0ff21e628e5d2c0e5b3dde5d7d68d9cce327ab6","target":"graph","created_at":"2026-05-18T00:44:37Z","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"},"paper":{"abstract_excerpt":"The logarithmic coefficients $\\gamma_n$ of an analytic and univalent function $f$ in the unit disk $\\mathbb{D}=\\{z\\in\\mathbb{C}:|z|<1\\}$ with the normalization $f(0)=0=f'(0)-1$ is defined by $\\log \\frac{f(z)}{z}= 2\\sum_{n=1}^{\\infty} \\gamma_n z^n$. Recently, D.K. Thomas [On the logarithmic coefficients of close to convex functions, {\\it Proc. Amer. Math. Soc.} {\\bf 144} (2016), 1681--1687] proved that $|\\gamma_3|\\le \\frac{7}{12}$ for functions in a subclass of close-to-convex functions (with argument $0$) and claimed that the estimate is sharp by providing a form of a extremal function. In the","authors_text":"A. Vasudevarao, Md Firoz Ali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-16T12:44:26Z","title":"On logarithmic coefficients of some close-to-convex functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.05162","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":"sha256:73bb717baff54fa691036e0899ee77c81ba1a24b9928c68cf0703e99b59a3ce3","target":"record","created_at":"2026-05-18T00:44:37Z","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":"604790dd0b4ad26476e4b8b9a157a168a85687144e3bd4b553fa22d5a8114958","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-16T12:44:26Z","title_canon_sha256":"147d662a3e7d1055b81f6fa5da06d04cf0e465382f76a7383c17b1b3b5bce633"},"schema_version":"1.0","source":{"id":"1606.05162","kind":"arxiv","version":1}},"canonical_sha256":"2113c1726c1b5c4da7cc149e976fe76b935676a80cb62de8b2409e9e1c2738ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2113c1726c1b5c4da7cc149e976fe76b935676a80cb62de8b2409e9e1c2738ff","first_computed_at":"2026-05-18T00:44:37.109566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:37.109566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8nDumo/WzGG6yAZtYyEeo2lorvfaqEX82+cl1Rj5EZBZqhB9vjT6mhMImrKYba9jBAHbWv4mWR5mPj++XwPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:37.110173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.05162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73bb717baff54fa691036e0899ee77c81ba1a24b9928c68cf0703e99b59a3ce3","sha256:a420f441e21a3da9c9e42986c0ff21e628e5d2c0e5b3dde5d7d68d9cce327ab6"],"state_sha256":"fa8634193b2f49887574fd9d806a24d31285480ffa23f374c036b3e9e25655b7"}