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For each p,"},"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":"1203.0685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2012-03-03T21:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"4eb1a36fe0f009c649f6cee06404a8878a03f6e7ee5b627b36d9b43b78e1cb59","abstract_canon_sha256":"d07471dc966fb468292739333c451692de8faf358387aa767e0e8f8a88c0edc6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:50.881565Z","signature_b64":"YCo0LR2tzlYxUTCnTh/DCE5VnaN/T1a6NDxS2n0S4MfCd5zB6jiR85Oy6VTkqfVzQYu6016eKTbRhOlTEDj4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cebb69f2943758d4b3234dac5bfa0d4b5f92ac7d1a2ab3b484376952af980741","last_reissued_at":"2026-05-18T04:00:50.880975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:50.880975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a discrete Hill's statistical process based on sum-product statistics and its finite-dimensional asymptotic theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Gane Samb Lo","submitted_at":"2012-03-03T21:27:52Z","abstract_excerpt":"The following class of sum-product statistics\n  T_n(p)=\\frac{1}{k}\\sum_{h=1}^p \\sum_{(s_1...s_h)\\in P(p,h)} \\sum_{i_1=l+1}^{i_0} ... \\sum_{i_h=l+1}^{i_{h-1}}  i_h \\prod_{i=i_1}^{i_h} \\frac{(Y_{n-i+1,n}-Y_{n-i,n})^{s_i}}{s_i!}\n (where $l,$ $k=i_{0}$ and n are positive integers, $0<l<k<n,$ $P(p,h)$ is the set of all ordered parititions of $\\ p>0$ into $\\ h$ positive integers and $Y_{1,n}\\leq ...\\leq Y_{n,n}$ are the order statistics based on a sequence of independent random variables $Y_{1},$ $Y_{2},...$with underlying distribution $\\mathbb{P}(Y\\leq y)=G(Y)=F(e^{y})$), is introduced. 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