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Moreover, one gets that the $n$-th derivative of $\\xi (w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute lower bound for the $n$-th derivative $(-1)^n \\xi^{(n)}(1) \\geq {(2n+1)!! \\over 2^{2n}}$. Moreover, for the curvature we find $\\xi ''(1) \\geq {1 \\over 5} [4 \\rho^2 + 3(\\rho^2)^2]$ where $\\rho^2 = - \\xi '(1)$. We show that the quadratic term ${3 \\over 5} (\\rho^2)^2$ has a transparent phys"},"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":"hep-ph/0412144","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-ph","submitted_at":"2004-12-10T16:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"e090fa426b84614f38331f4c9234ef2ae0068a2bd1a408749795b194350bfc86","abstract_canon_sha256":"1ce1047183a11a16376f97760e2cc8b0bd439d5b539cd4c630c0c9f5b0571869"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:28.533007Z","signature_b64":"de3pwHPn0KJXCYJpfYRlmaXWe5j73l8oKJbpJG3DbD7MgEUqnpfgZ7JF7qFwuRrJPYzGGASaXo2YHWiaTvTrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56be6dbaa3c529ecc17f4b124d88e6bb1e4171b985e94e4e0798dfe351e5f667","last_reissued_at":"2026-05-18T00:37:28.532436Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:28.532436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sum rules in the heavy quark limit of QCD and Isgur-Wise functions","license":"","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"A. 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