{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:TEBUX6GWCBPK2GJP6ER6RF4KMW","short_pith_number":"pith:TEBUX6GW","schema_version":"1.0","canonical_sha256":"99034bf8d6105ead192ff123e8978a658325050efeca669cdc4294f48f40884a","source":{"kind":"arxiv","id":"2002.04357","version":2},"attestation_state":"computed","paper":{"title":"Concentration inequality using unconfirmed knowledge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.PR","authors_text":"Go Kato","submitted_at":"2020-02-11T13:02:32Z","abstract_excerpt":"We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the sum of conditional expectations and that of the observed values takes a small value with high probability when the expected values are evaluated under the condition that the past values are known. Our inequality outperforms other well-known inequalities, e.g. the Azuma-Hoeffding inequality, especially in terms of the convergence speed when the random variabl"},"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":"2002.04357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-02-11T13:02:32Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"44392ae42192de3f7de17a9056c589fe301b13842b3d363938042f44d42a6071","abstract_canon_sha256":"eadfc826443109ded083349c37a31317c42cb504e5eaa1e6e5894490d83d93bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:42:34.267626Z","signature_b64":"Jn/Q7wilTAcg2sW98AO0bX5+NRqpLqjes7C/9SwSaQZ1DQF5Zc1jSRbZx0wSxkwgZRJAN/BhkQjYxpHyerkxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99034bf8d6105ead192ff123e8978a658325050efeca669cdc4294f48f40884a","last_reissued_at":"2026-07-05T00:42:34.267134Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:42:34.267134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration inequality using unconfirmed knowledge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.PR","authors_text":"Go Kato","submitted_at":"2020-02-11T13:02:32Z","abstract_excerpt":"We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the sum of conditional expectations and that of the observed values takes a small value with high probability when the expected values are evaluated under the condition that the past values are known. Our inequality outperforms other well-known inequalities, e.g. the Azuma-Hoeffding inequality, especially in terms of the convergence speed when the random variabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.04357","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.04357/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2002.04357","created_at":"2026-07-05T00:42:34.267209+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.04357v2","created_at":"2026-07-05T00:42:34.267209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.04357","created_at":"2026-07-05T00:42:34.267209+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEBUX6GWCBPK","created_at":"2026-07-05T00:42:34.267209+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEBUX6GWCBPK2GJP","created_at":"2026-07-05T00:42:34.267209+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEBUX6GW","created_at":"2026-07-05T00:42:34.267209+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2501.12709","citing_title":"Experimentally validated quantum-secure federated learning over a multi-user quantum network","ref_index":73,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12984","citing_title":"Numerical security analysis for practical quantum key distribution","ref_index":59,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW","json":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW.json","graph_json":"https://pith.science/api/pith-number/TEBUX6GWCBPK2GJP6ER6RF4KMW/graph.json","events_json":"https://pith.science/api/pith-number/TEBUX6GWCBPK2GJP6ER6RF4KMW/events.json","paper":"https://pith.science/paper/TEBUX6GW"},"agent_actions":{"view_html":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW","download_json":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW.json","view_paper":"https://pith.science/paper/TEBUX6GW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.04357&json=true","fetch_graph":"https://pith.science/api/pith-number/TEBUX6GWCBPK2GJP6ER6RF4KMW/graph.json","fetch_events":"https://pith.science/api/pith-number/TEBUX6GWCBPK2GJP6ER6RF4KMW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW/action/storage_attestation","attest_author":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW/action/author_attestation","sign_citation":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW/action/citation_signature","submit_replication":"https://pith.science/pith/TEBUX6GWCBPK2GJP6ER6RF4KMW/action/replication_record"}},"created_at":"2026-07-05T00:42:34.267209+00:00","updated_at":"2026-07-05T00:42:34.267209+00:00"}