{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XJEWEVRA73TO2NOHXK4IX5LG23","short_pith_number":"pith:XJEWEVRA","schema_version":"1.0","canonical_sha256":"ba49625620fee6ed35c7bab88bf566d6f3ecf40b02131d86b11d005acb893bc5","source":{"kind":"arxiv","id":"1008.4860","version":1},"attestation_state":"computed","paper":{"title":"Coefficient Inequalities for Concave and Meromorphically Starlike Univalent Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Saminathan Ponnusamy","submitted_at":"2010-08-28T12:46:52Z","abstract_excerpt":"Let $\\ID$ denote the open unit disk and $f:\\,\\ID\\TO\\BAR\\IC$ be meromorphic and univalent in $\\ID$ with the simple pole at $p\\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion $$f(z)=\\sum_{n=-1}^{\\infty}a_n(z-p)^n,\\quad |z-p|<1-p, $$ such that $f$ maps $\\ID$ onto a domain whose complement with respect to $\\BAR{\\IC}$ is a convex set (starlike set with respect to a point $w_0\\in \\IC, w_0\\neq 0$ resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)$ $(\\Sigma^s(p, w_0)$ res"},"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":"1008.4860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-08-28T12:46:52Z","cross_cats_sorted":[],"title_canon_sha256":"8bd1c12f5e2f4e32c80aea3c26e0eb6d96cdb65cf6317d71c61f9be241dd8467","abstract_canon_sha256":"07e0e962a196bd1418214db9946e6132f8809f69f6c3705fb8a0063619ca7322"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:43.540165Z","signature_b64":"ZgxW6xmeMtC+ukrpg+9ftUWlyAiMKXuDqooLOiAzH4sCKqsjyS3vJfnVzVpznMvywq8igrOVqQFGywr3XMkWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba49625620fee6ed35c7bab88bf566d6f3ecf40b02131d86b11d005acb893bc5","last_reissued_at":"2026-05-18T04:41:43.539731Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:43.539731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coefficient Inequalities for Concave and Meromorphically Starlike Univalent Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bappaditya Bhowmik, Saminathan Ponnusamy","submitted_at":"2010-08-28T12:46:52Z","abstract_excerpt":"Let $\\ID$ denote the open unit disk and $f:\\,\\ID\\TO\\BAR\\IC$ be meromorphic and univalent in $\\ID$ with the simple pole at $p\\in (0,1)$ and satisfying the standard normalization $f(0)=f'(0)-1=0$. Also, let $f$ have the expansion $$f(z)=\\sum_{n=-1}^{\\infty}a_n(z-p)^n,\\quad |z-p|<1-p, $$ such that $f$ maps $\\ID$ onto a domain whose complement with respect to $\\BAR{\\IC}$ is a convex set (starlike set with respect to a point $w_0\\in \\IC, w_0\\neq 0$ resp.). We call these functions as concave (meromorphically starlike resp.) univalent functions and denote this class by $Co(p)$ $(\\Sigma^s(p, w_0)$ res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4860","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":"1008.4860","created_at":"2026-05-18T04:41:43.539795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4860v1","created_at":"2026-05-18T04:41:43.539795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4860","created_at":"2026-05-18T04:41:43.539795+00:00"},{"alias_kind":"pith_short_12","alias_value":"XJEWEVRA73TO","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XJEWEVRA73TO2NOH","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XJEWEVRA","created_at":"2026-05-18T12:26:17.028572+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/XJEWEVRA73TO2NOHXK4IX5LG23","json":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23.json","graph_json":"https://pith.science/api/pith-number/XJEWEVRA73TO2NOHXK4IX5LG23/graph.json","events_json":"https://pith.science/api/pith-number/XJEWEVRA73TO2NOHXK4IX5LG23/events.json","paper":"https://pith.science/paper/XJEWEVRA"},"agent_actions":{"view_html":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23","download_json":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23.json","view_paper":"https://pith.science/paper/XJEWEVRA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4860&json=true","fetch_graph":"https://pith.science/api/pith-number/XJEWEVRA73TO2NOHXK4IX5LG23/graph.json","fetch_events":"https://pith.science/api/pith-number/XJEWEVRA73TO2NOHXK4IX5LG23/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23/action/storage_attestation","attest_author":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23/action/author_attestation","sign_citation":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23/action/citation_signature","submit_replication":"https://pith.science/pith/XJEWEVRA73TO2NOHXK4IX5LG23/action/replication_record"}},"created_at":"2026-05-18T04:41:43.539795+00:00","updated_at":"2026-05-18T04:41:43.539795+00:00"}