{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KW7BXIOOV4JD2EFUK45IDUDG5N","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":"c612057b0fcf4169ecf398bc12afded41faa06aa0f6f281b203c13f3f8e5643a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-12T12:15:33Z","title_canon_sha256":"251eada92d42b1a4acddd60a32769bd21c52c7732105ac61e4f5f1c999e39aac"},"schema_version":"1.0","source":{"id":"1810.05468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.05468","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"arxiv_version","alias_value":"1810.05468v1","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.05468","created_at":"2026-05-18T00:03:30Z"},{"alias_kind":"pith_short_12","alias_value":"KW7BXIOOV4JD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KW7BXIOOV4JD2EFU","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KW7BXIOO","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b7c845564b67983f0a9567e91bc82738faabe05da449e4315c45618d1fe8733d","target":"graph","created_at":"2026-05-18T00:03:30Z","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":"Let function $f$ be analytic in the unit disk ${\\mathbb D}$ and be normalized so that $f(z)=z+a_2z^2+a_3z^3+\\cdots$. In this paper we give sharp bounds of the modulus of its second, third and fourth coefficient, if $f$ satisfies \\[ \\left|\\arg \\left[\\left(\\frac{z}{f(z)}\\right)^{1+\\alpha}f'(z) \\right] \\right|<\\gamma\\frac{\\pi}{2} \\quad\\quad (z\\in {\\mathbb D}),\\] for $0<\\alpha<1$ and $0<\\gamma\\leq1$.","authors_text":"Milutin Obradovic, Nikola Tuneski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-12T12:15:33Z","title":"On the initial coefficients for certain class of functions analytic in the unit disc"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05468","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":"sha256:83d23b72af116fceeab33c0d720323d26045f93172ab32977e12c566a7a26bcd","target":"record","created_at":"2026-05-18T00:03:30Z","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":"c612057b0fcf4169ecf398bc12afded41faa06aa0f6f281b203c13f3f8e5643a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-10-12T12:15:33Z","title_canon_sha256":"251eada92d42b1a4acddd60a32769bd21c52c7732105ac61e4f5f1c999e39aac"},"schema_version":"1.0","source":{"id":"1810.05468","kind":"arxiv","version":1}},"canonical_sha256":"55be1ba1ceaf123d10b4573a81d066eb42ee0f0d9bde70ac76577c7e9aa4e0a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55be1ba1ceaf123d10b4573a81d066eb42ee0f0d9bde70ac76577c7e9aa4e0a3","first_computed_at":"2026-05-18T00:03:30.447875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:30.447875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tx4Ei7E0y/tEQUC72tBD93D8fAhH9OI1j0vAZXN7rpiqaTeO7tWr6NpYHhkwJCTOa72Lnz9HRkASwC9fqy71Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:30.448577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.05468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d23b72af116fceeab33c0d720323d26045f93172ab32977e12c566a7a26bcd","sha256:b7c845564b67983f0a9567e91bc82738faabe05da449e4315c45618d1fe8733d"],"state_sha256":"fd6c83ec548e5aca9d37fa04383975cb62623459a4781d7d823e639ac766350f"}