{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LPELL7ED3BU5JEBBMWGAMYBP3F","short_pith_number":"pith:LPELL7ED","schema_version":"1.0","canonical_sha256":"5bc8b5fc83d869d49021658c06602fd941cd592f27f2da488dc989dd91f7c146","source":{"kind":"arxiv","id":"1511.06640","version":2},"attestation_state":"computed","paper":{"title":"Bivariate Binomial Moments and Bonferroni-type Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Seneta, Qin Ding","submitted_at":"2015-11-20T15:32:08Z","abstract_excerpt":"We obtain bivariate forms of Gumbel's, Fr\\'echet's and Chung's linear inequalities for $P(S\\ge u, T\\ge v)$ in terms of the bivariate binomial moments $\\{S_{i,j}\\}$, $1\\le i\\le k, 1\\le j\\le l$ of the joint distribution of $(S,T)$. At $u=v=1$, the Gumbel and Fr\\'echet bounds improve monotonically with non-decreasing $(k,l)$. The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points."},"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":"1511.06640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-20T15:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"ddfcdc2a6c6d79135686120a3111125b269603c9db4e9b532f0ea6ec32718a7a","abstract_canon_sha256":"8fed598a320bc5e3d57ff0e434a359fb33d351d1189cd7d4d66cf6a5268e4359"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:46.221679Z","signature_b64":"GL7eLfGWoYFtAZSi6bj9faBrpsuy7QfLcEzAO/35iwIsFxi6j6CRsOLcQJan0O/lkMenl0afT7LXXvhsSohbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bc8b5fc83d869d49021658c06602fd941cd592f27f2da488dc989dd91f7c146","last_reissued_at":"2026-05-18T01:22:46.221132Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:46.221132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bivariate Binomial Moments and Bonferroni-type Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Seneta, Qin Ding","submitted_at":"2015-11-20T15:32:08Z","abstract_excerpt":"We obtain bivariate forms of Gumbel's, Fr\\'echet's and Chung's linear inequalities for $P(S\\ge u, T\\ge v)$ in terms of the bivariate binomial moments $\\{S_{i,j}\\}$, $1\\le i\\le k, 1\\le j\\le l$ of the joint distribution of $(S,T)$. At $u=v=1$, the Gumbel and Fr\\'echet bounds improve monotonically with non-decreasing $(k,l)$. The method of proof uses combinatorial identities, and reveals a multiplicative structure before taking expectation over sample points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06640","kind":"arxiv","version":2},"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":"1511.06640","created_at":"2026-05-18T01:22:46.221221+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.06640v2","created_at":"2026-05-18T01:22:46.221221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.06640","created_at":"2026-05-18T01:22:46.221221+00:00"},{"alias_kind":"pith_short_12","alias_value":"LPELL7ED3BU5","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LPELL7ED3BU5JEBB","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LPELL7ED","created_at":"2026-05-18T12:29:29.992203+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/LPELL7ED3BU5JEBBMWGAMYBP3F","json":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F.json","graph_json":"https://pith.science/api/pith-number/LPELL7ED3BU5JEBBMWGAMYBP3F/graph.json","events_json":"https://pith.science/api/pith-number/LPELL7ED3BU5JEBBMWGAMYBP3F/events.json","paper":"https://pith.science/paper/LPELL7ED"},"agent_actions":{"view_html":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F","download_json":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F.json","view_paper":"https://pith.science/paper/LPELL7ED","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.06640&json=true","fetch_graph":"https://pith.science/api/pith-number/LPELL7ED3BU5JEBBMWGAMYBP3F/graph.json","fetch_events":"https://pith.science/api/pith-number/LPELL7ED3BU5JEBBMWGAMYBP3F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F/action/storage_attestation","attest_author":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F/action/author_attestation","sign_citation":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F/action/citation_signature","submit_replication":"https://pith.science/pith/LPELL7ED3BU5JEBBMWGAMYBP3F/action/replication_record"}},"created_at":"2026-05-18T01:22:46.221221+00:00","updated_at":"2026-05-18T01:22:46.221221+00:00"}