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Ruscheweyh posed the following conjecture: For $\\rho\\in(0,1]$ and $0<\\mu\\leq\\mu^{\\ast}(\\rho)$, the partial sum $s_n^{\\mu}(z)=\\displaystyle\\sum_{k=0}^n \\frac{(\\mu)_k}{k!}z^k$, $0<\\mu\\leq1$, $|z|<1$, satisfies %\n\\begin{align*} (1-z)^{\\rho}s_n^{\\mu}(z) \\prec \\left(\\frac{1+z}{1-z}\\right)^{\\rho}, \\qquad n\\in \\mathbb{N}, \\end{align*} where $\\mu^{\\ast}(\\rho)$ is the unique solution of \\begin{align*} \\int_0^{(\\rho+1)\\pi} \\sin(t-\\rho\\pi)t^{\\mu-1}dt=0. \\end{align*} This conjecture is already settled for $\\rho=\\frac{1}{2}$, $\\frac{1}{4}$, $\\frac{3}{4}$ and $\\rho=1$. In this work, we v"},"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":"1806.06999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-06-19T01:26:46Z","cross_cats_sorted":[],"title_canon_sha256":"6befcdbed3cc7d0979374c6b4afb79601ca635699ac6d8fbaf7b4ae427eacd37","abstract_canon_sha256":"7b637b7bfe537f1c93f0be0bdd944287046229498b3041aafb31d24d3b7d9776"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.803237Z","signature_b64":"I1rKoR17koPgO/Rsh9REb7FdUy6QcXleqdr1VqeoBMmYJy5jY/Q48aCJ7MMLFZc0WkCsRV0aQvD2X4HxzxBUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"824921ec9408f7737211a2366b1156763088923123d48cb6cd9ff8d73fa0219b","last_reissued_at":"2026-05-18T00:12:57.802581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.802581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a conjecture for trigonometric sums by S. 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