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This gives a negative answer to a question of Lata{\\l}a concerning the va"},"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":"2607.00538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-07-01T07:28:32Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"37a78ecaba981d69d5587619399bce8a844911f46c2b3cb5f3ec4da03d495788","abstract_canon_sha256":"2a860d7875473f4442fe72aa7b9890b16a98e4118013521f02693a4c73611087"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:17:47.001335Z","signature_b64":"V/GGhJ3PW47opxtrSSyau4cEA+CGRUGn8YxUdmX4eepvFgPv0QOUOUBmMgDZPz58l5LvtKbrl97q67VVZWjRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82094ce2623593b605dfc44844cc3ee9a7549a8df08776c199005e58728419bc","last_reissued_at":"2026-07-02T01:17:47.000920Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:17:47.000920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Failure of Convex-Hull Bounds under Log-Convex Tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Hanchao Wang, Xuanang Hu","submitted_at":"2026-07-01T07:28:32Z","abstract_excerpt":"Fix $0<r<1$, and let $X_1,X_2,\\dots$ be independent symmetric Weibull$(r)$ random variables, that is, \\[ \\textsf{P}(|X_i|>t)=e^{-t^r},\\qquad t\\ge 0. \\] We prove that there is no constant $C_r$, depending only on $r$, with the following universal property: for every finite set $T\\subset \\R^N$ there exists a sequence $(y_k)_{k\\ge 1}\\subset \\R^N$ such that \\[ T-T\\subset conv\\{y_k:k\\ge 1\\}, \\qquad \\|X_{y_k}\\|_{L_{\\log(k+2)}}\\le C_r\\,\\bx(T) \\quad (k\\ge 1), \\] where $X_t=\\sum_i t_i X_i$ and $\\bx(T)=\\textsf{E}\\sup_{t\\in T}X_t$. 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