{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IDY3D53NFSWERWW5R36KVQK5M2","short_pith_number":"pith:IDY3D53N","schema_version":"1.0","canonical_sha256":"40f1b1f76d2cac48dadd8efcaac15d6687b4df2b65768178e8ad5be723921446","source":{"kind":"arxiv","id":"1611.07207","version":3},"attestation_state":"computed","paper":{"title":"On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2016-11-22T09:13:38Z","abstract_excerpt":"Let $\\{B_k\\}_{k=1}^\\infty, \\{X_k\\}_{k=1}^\\infty$ all be independent random variables. Assume that $\\{B_k\\}_{k=1}^\\infty$ are $\\{0,1\\}$-valued Bernoulli random variables satisfying $B_k\\stackrel{\\text{dist}}{=}\\text{Ber}(p_k)$, with $\\sum_{k=1}^\\infty p_k=\\infty$, and assume that $\\{X_k\\}_{k=1}^\\infty$ satisfy:\n  $X_k>0,\\ \\ \\ \\mu_k\\equiv EX_k<\\infty, \\ \\ \\ \\lim_{k\\to\\infty}\\frac{X_k}{\\mu_k}\\stackrel{\\text{dist}}{=}1$. Let $M_n=\\sum_{k=1}^np_k\\mu_k$, assume that $M_n\\to\\infty$ and define the normalized sum of independent random variables $W_n=\\frac1{M_n}\\sum_{k=1}^nB_kX_k$. We give a general con"},"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":"1611.07207","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-11-22T09:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"e9f7babf9c3d6b9d46d2778216a1856fddcaae347d972ca684fa1668c132f654","abstract_canon_sha256":"899c08186ff21f7fec28bd45804170b5710efa84a4cd81b4911af07d8afbe3c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:24.015021Z","signature_b64":"i7/M7db62A0ZaYa/MNBYe4GYbE80D9i3FqYa6WWdKQnvDYPrOUlwoFGfmRdrycDneoWmkXdihmev9CxBrahkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f1b1f76d2cac48dadd8efcaac15d6687b4df2b65768178e8ad5be723921446","last_reissued_at":"2026-05-18T00:53:24.014597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:24.014597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the strange domain of attraction to generalized Dickman distributions for sums of independent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2016-11-22T09:13:38Z","abstract_excerpt":"Let $\\{B_k\\}_{k=1}^\\infty, \\{X_k\\}_{k=1}^\\infty$ all be independent random variables. Assume that $\\{B_k\\}_{k=1}^\\infty$ are $\\{0,1\\}$-valued Bernoulli random variables satisfying $B_k\\stackrel{\\text{dist}}{=}\\text{Ber}(p_k)$, with $\\sum_{k=1}^\\infty p_k=\\infty$, and assume that $\\{X_k\\}_{k=1}^\\infty$ satisfy:\n  $X_k>0,\\ \\ \\ \\mu_k\\equiv EX_k<\\infty, \\ \\ \\ \\lim_{k\\to\\infty}\\frac{X_k}{\\mu_k}\\stackrel{\\text{dist}}{=}1$. Let $M_n=\\sum_{k=1}^np_k\\mu_k$, assume that $M_n\\to\\infty$ and define the normalized sum of independent random variables $W_n=\\frac1{M_n}\\sum_{k=1}^nB_kX_k$. We give a general con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07207","kind":"arxiv","version":3},"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":"1611.07207","created_at":"2026-05-18T00:53:24.014664+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07207v3","created_at":"2026-05-18T00:53:24.014664+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07207","created_at":"2026-05-18T00:53:24.014664+00:00"},{"alias_kind":"pith_short_12","alias_value":"IDY3D53NFSWE","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IDY3D53NFSWERWW5","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IDY3D53N","created_at":"2026-05-18T12:30:22.444734+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/IDY3D53NFSWERWW5R36KVQK5M2","json":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2.json","graph_json":"https://pith.science/api/pith-number/IDY3D53NFSWERWW5R36KVQK5M2/graph.json","events_json":"https://pith.science/api/pith-number/IDY3D53NFSWERWW5R36KVQK5M2/events.json","paper":"https://pith.science/paper/IDY3D53N"},"agent_actions":{"view_html":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2","download_json":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2.json","view_paper":"https://pith.science/paper/IDY3D53N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07207&json=true","fetch_graph":"https://pith.science/api/pith-number/IDY3D53NFSWERWW5R36KVQK5M2/graph.json","fetch_events":"https://pith.science/api/pith-number/IDY3D53NFSWERWW5R36KVQK5M2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2/action/storage_attestation","attest_author":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2/action/author_attestation","sign_citation":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2/action/citation_signature","submit_replication":"https://pith.science/pith/IDY3D53NFSWERWW5R36KVQK5M2/action/replication_record"}},"created_at":"2026-05-18T00:53:24.014664+00:00","updated_at":"2026-05-18T00:53:24.014664+00:00"}