{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:CS2LE3HI7KTJ64HXRQLCXH26SB","short_pith_number":"pith:CS2LE3HI","schema_version":"1.0","canonical_sha256":"14b4b26ce8faa69f70f78c162b9f5e906b414c9ccc2f20b42710f872aa4c40ed","source":{"kind":"arxiv","id":"1507.07576","version":1},"attestation_state":"computed","paper":{"title":"Grand Lebesgue norm estimation for binary random variables, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Ostrovsky, Leonid Sirota","submitted_at":"2015-07-27T20:19:38Z","abstract_excerpt":"We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable.\n  This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates."},"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":"1507.07576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-27T20:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"b321fcf610dbbb5fff000bc0af8731e094840c63e688c3ff6ac08e363a0d397d","abstract_canon_sha256":"7983cfc5e0a8725965d16cac300235aec82f7c925607fefe66c0d0ec9135edff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:12.408308Z","signature_b64":"ADA5Zj2J1o7dPMpnVdpEKicpzHsueAUBIWKbya47jCdeHatakLmwc8HHr6amY4ATAxBXDwCJHLrkG2t79aQODQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14b4b26ce8faa69f70f78c162b9f5e906b414c9ccc2f20b42710f872aa4c40ed","last_reissued_at":"2026-05-18T01:36:12.407771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:12.407771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Grand Lebesgue norm estimation for binary random variables, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Ostrovsky, Leonid Sirota","submitted_at":"2015-07-27T20:19:38Z","abstract_excerpt":"We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable.\n  This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07576","kind":"arxiv","version":1},"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":"1507.07576","created_at":"2026-05-18T01:36:12.407849+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.07576v1","created_at":"2026-05-18T01:36:12.407849+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07576","created_at":"2026-05-18T01:36:12.407849+00:00"},{"alias_kind":"pith_short_12","alias_value":"CS2LE3HI7KTJ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"CS2LE3HI7KTJ64HX","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"CS2LE3HI","created_at":"2026-05-18T12:29:17.054201+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/CS2LE3HI7KTJ64HXRQLCXH26SB","json":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB.json","graph_json":"https://pith.science/api/pith-number/CS2LE3HI7KTJ64HXRQLCXH26SB/graph.json","events_json":"https://pith.science/api/pith-number/CS2LE3HI7KTJ64HXRQLCXH26SB/events.json","paper":"https://pith.science/paper/CS2LE3HI"},"agent_actions":{"view_html":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB","download_json":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB.json","view_paper":"https://pith.science/paper/CS2LE3HI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.07576&json=true","fetch_graph":"https://pith.science/api/pith-number/CS2LE3HI7KTJ64HXRQLCXH26SB/graph.json","fetch_events":"https://pith.science/api/pith-number/CS2LE3HI7KTJ64HXRQLCXH26SB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB/action/storage_attestation","attest_author":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB/action/author_attestation","sign_citation":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB/action/citation_signature","submit_replication":"https://pith.science/pith/CS2LE3HI7KTJ64HXRQLCXH26SB/action/replication_record"}},"created_at":"2026-05-18T01:36:12.407849+00:00","updated_at":"2026-05-18T01:36:12.407849+00:00"}