{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:5N2ICZATM2F2NV5O4SNOPZ3ZBL","short_pith_number":"pith:5N2ICZAT","schema_version":"1.0","canonical_sha256":"eb74816413668ba6d7aee49ae7e7790ae1ce7fc5c22be9540cbda92edeb7e068","source":{"kind":"arxiv","id":"1603.07116","version":1},"attestation_state":"computed","paper":{"title":"Generalized Zalcman conjecture for convex functions of order $\\alpha$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jinjing Qiao, Liulan Li, Saminathan Ponnusamy","submitted_at":"2016-03-23T10:16:29Z","abstract_excerpt":"Let $\\mathcal S$ denote the class of all functions of the form $f(z)=z+a_2z^2+a_3z^3+\\cdots$ which are analytic and univalent in the open unit disk $\\ID$ and, for $\\lambda >0$, let $\\Phi_\\lambda (n,f)=\\lambda a_n^2-a_{2n-1}$ denote the generalized Zalcman coefficient functional. Zalcman conjectured that if $f\\in \\mathcal S$, then $|\\Phi_1 (n,f)|\\leq (n-1)^2$ for $n\\ge 3$. The functional of the form $\\Phi_\\lambda (n,f)$ is indeed related to Fekete-Szeg\\H{o} functional of the $n$-th root transform of the corresponding function in $\\mathcal S$. This conjecture has been verified for a certain spec"},"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":"1603.07116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-23T10:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"45e57b88916455d0bca32da41cba8c844d3d9f61ae60726c0e290e099c5827e7","abstract_canon_sha256":"b62b8efc98b18dc1a8784670e94a192a2ae0b5af2e526e471b36b4c9662c6827"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:24.405541Z","signature_b64":"V+EPQ+WADKMUQAaxBlXqpRkl+Bqnvg8plplpjYAFo80/aIV47rElVAQjcFG2LjniSDYpk72B1nHftJ1rlOg6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb74816413668ba6d7aee49ae7e7790ae1ce7fc5c22be9540cbda92edeb7e068","last_reissued_at":"2026-05-18T01:18:24.404859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:24.404859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Zalcman conjecture for convex functions of order $\\alpha$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Jinjing Qiao, Liulan Li, Saminathan Ponnusamy","submitted_at":"2016-03-23T10:16:29Z","abstract_excerpt":"Let $\\mathcal S$ denote the class of all functions of the form $f(z)=z+a_2z^2+a_3z^3+\\cdots$ which are analytic and univalent in the open unit disk $\\ID$ and, for $\\lambda >0$, let $\\Phi_\\lambda (n,f)=\\lambda a_n^2-a_{2n-1}$ denote the generalized Zalcman coefficient functional. Zalcman conjectured that if $f\\in \\mathcal S$, then $|\\Phi_1 (n,f)|\\leq (n-1)^2$ for $n\\ge 3$. The functional of the form $\\Phi_\\lambda (n,f)$ is indeed related to Fekete-Szeg\\H{o} functional of the $n$-th root transform of the corresponding function in $\\mathcal S$. This conjecture has been verified for a certain spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07116","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":"1603.07116","created_at":"2026-05-18T01:18:24.404968+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.07116v1","created_at":"2026-05-18T01:18:24.404968+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07116","created_at":"2026-05-18T01:18:24.404968+00:00"},{"alias_kind":"pith_short_12","alias_value":"5N2ICZATM2F2","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"5N2ICZATM2F2NV5O","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"5N2ICZAT","created_at":"2026-05-18T12:30:01.593930+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/5N2ICZATM2F2NV5O4SNOPZ3ZBL","json":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL.json","graph_json":"https://pith.science/api/pith-number/5N2ICZATM2F2NV5O4SNOPZ3ZBL/graph.json","events_json":"https://pith.science/api/pith-number/5N2ICZATM2F2NV5O4SNOPZ3ZBL/events.json","paper":"https://pith.science/paper/5N2ICZAT"},"agent_actions":{"view_html":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL","download_json":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL.json","view_paper":"https://pith.science/paper/5N2ICZAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.07116&json=true","fetch_graph":"https://pith.science/api/pith-number/5N2ICZATM2F2NV5O4SNOPZ3ZBL/graph.json","fetch_events":"https://pith.science/api/pith-number/5N2ICZATM2F2NV5O4SNOPZ3ZBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL/action/storage_attestation","attest_author":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL/action/author_attestation","sign_citation":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL/action/citation_signature","submit_replication":"https://pith.science/pith/5N2ICZATM2F2NV5O4SNOPZ3ZBL/action/replication_record"}},"created_at":"2026-05-18T01:18:24.404968+00:00","updated_at":"2026-05-18T01:18:24.404968+00:00"}