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We also prove that the radius $\\sqrt{2}/3$ is best possible, i.e. the number $\\sqrt{2}/3$ cannot be replaced by a larger one."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1604.05500","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-04-19T10:10:33Z","cross_cats_sorted":[],"title_canon_sha256":"9f51c8ff5733f01607e28d57668fd4dd406f5b7f2f306dac3a459967f6927b49","abstract_canon_sha256":"599598d30f1bd66c709b5919f0b9a9ca9b68235ac17ae201b1bdb06b3b831bdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:38.614622Z","signature_b64":"5Ody8BBHGiTj+A4cbA84OeJySJIWsSOERCX8anNl+Y+87K6ao3T6z/iELVxzVxZiwqzkL7KQOTDfGI7YP0rYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c68f2454094e9124393ded889cf8340bfffbf368e5ebc548845f9c39582c1acd","last_reissued_at":"2026-05-18T01:16:38.613835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:38.613835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radius of convexity of partial sums of odd functions in the close-to-convex family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sarita Agrawal, Swadesh Kumar Sahoo","submitted_at":"2016-04-19T10:10:33Z","abstract_excerpt":"We consider the class of all analytic and locally univalent functions $f$ of the form $f(z)=z+\\sum_{n=2}^\\infty a_{2n-1} z^{2n-1}$, $|z|<1$, satisfying the condition $$ {\\rm Re}\\,\\left(1+\\frac{zf^{\\prime\\prime}(z)}{f^\\prime (z)}\\right)>-\\frac{1}{2}. $$ We show that every section $s_{2n-1}(z)=z+\\sum_{k=2}^na_{2k-1}z^{2k-1}$, of $f$, is convex in the disk $|z|<\\sqrt{2}/3$. We also prove that the radius $\\sqrt{2}/3$ is best possible, i.e. the number $\\sqrt{2}/3$ cannot be replaced by a larger one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05500","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1604.05500","created_at":"2026-05-18T01:16:38.613955+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.05500v1","created_at":"2026-05-18T01:16:38.613955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05500","created_at":"2026-05-18T01:16:38.613955+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2HSIVAJJ2IS","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2HSIVAJJ2ISIOJ5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2HSIVAJ","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP","json":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP.json","graph_json":"https://pith.science/api/pith-number/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/graph.json","events_json":"https://pith.science/api/pith-number/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/events.json","paper":"https://pith.science/paper/Y2HSIVAJ"},"agent_actions":{"view_html":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP","download_json":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP.json","view_paper":"https://pith.science/paper/Y2HSIVAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.05500&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/action/storage_attestation","attest_author":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/action/author_attestation","sign_citation":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/action/citation_signature","submit_replication":"https://pith.science/pith/Y2HSIVAJJ2ISIOJ55WEJZ6BUBP/action/replication_record"}},"created_at":"2026-05-18T01:16:38.613955+00:00","updated_at":"2026-05-18T01:16:38.613955+00:00"}