{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EHYVRKGXAY2STNZCB46BG5JIE6","short_pith_number":"pith:EHYVRKGX","canonical_record":{"source":{"id":"1809.04719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-13T00:27:12Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"58f6b8c514eb5629fbfd7d9745a20883c4a312b5593e2b2efe2e5f940908f844","abstract_canon_sha256":"2fa6bafe2fa843fb638e0f17b4ea1ad0721514e50bb747b413320eb25f90253c"},"schema_version":"1.0"},"canonical_sha256":"21f158a8d7063529b7220f3c137528279b1a242f02a171b1e6365b4f83c3b2a1","source":{"kind":"arxiv","id":"1809.04719","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04719","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04719v1","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04719","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"EHYVRKGXAY2S","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EHYVRKGXAY2STNZC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EHYVRKGX","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EHYVRKGXAY2STNZCB46BG5JIE6","target":"record","payload":{"canonical_record":{"source":{"id":"1809.04719","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-13T00:27:12Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"58f6b8c514eb5629fbfd7d9745a20883c4a312b5593e2b2efe2e5f940908f844","abstract_canon_sha256":"2fa6bafe2fa843fb638e0f17b4ea1ad0721514e50bb747b413320eb25f90253c"},"schema_version":"1.0"},"canonical_sha256":"21f158a8d7063529b7220f3c137528279b1a242f02a171b1e6365b4f83c3b2a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:49.844786Z","signature_b64":"mxldWlt7wAyUJ0Uo2ZmHOPnoXBTVUStViWtCp4UKR7cZ2UE23yEr8YJPcoBFshKj5r6np8o8ZOJtASrfzbOtBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21f158a8d7063529b7220f3c137528279b1a242f02a171b1e6365b4f83c3b2a1","last_reissued_at":"2026-05-18T00:05:49.844234Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:49.844234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.04719","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zYnswvfKzUfr3qJ7msp6YRqdRGYC1GFLT8bvGMAZNnazTezfmteNtRLhy5a+z3/48RzFczuDlkJAwOa5bwm4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:27:14.627939Z"},"content_sha256":"c39804a5c633ab473f34b63724e11f1ce629c8450dde3489c8c6fefe2c9cc128","schema_version":"1.0","event_id":"sha256:c39804a5c633ab473f34b63724e11f1ce629c8450dde3489c8c6fefe2c9cc128"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EHYVRKGXAY2STNZCB46BG5JIE6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Eugeny Ostrovsky, Leonid Sirota, Maria Rosaria Formica, Yurii Vasilovich Kozachenko","submitted_at":"2018-09-13T00:27:12Z","abstract_excerpt":"We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04719","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8M5nxBTUSnEiHnY0P2HNxlT29PgYx5nE788Ie6gOq+t/6UyJjm5hdps1UmXjsyEgScikR4l2MpWmH2fjKnwmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:27:14.628295Z"},"content_sha256":"f2217097b75d7e8866dba87c3ae4f46353244debd52d05c17aa7dd48fcde5c0d","schema_version":"1.0","event_id":"sha256:f2217097b75d7e8866dba87c3ae4f46353244debd52d05c17aa7dd48fcde5c0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHYVRKGXAY2STNZCB46BG5JIE6/bundle.json","state_url":"https://pith.science/pith/EHYVRKGXAY2STNZCB46BG5JIE6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHYVRKGXAY2STNZCB46BG5JIE6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T11:27:14Z","links":{"resolver":"https://pith.science/pith/EHYVRKGXAY2STNZCB46BG5JIE6","bundle":"https://pith.science/pith/EHYVRKGXAY2STNZCB46BG5JIE6/bundle.json","state":"https://pith.science/pith/EHYVRKGXAY2STNZCB46BG5JIE6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHYVRKGXAY2STNZCB46BG5JIE6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EHYVRKGXAY2STNZCB46BG5JIE6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2fa6bafe2fa843fb638e0f17b4ea1ad0721514e50bb747b413320eb25f90253c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-13T00:27:12Z","title_canon_sha256":"58f6b8c514eb5629fbfd7d9745a20883c4a312b5593e2b2efe2e5f940908f844"},"schema_version":"1.0","source":{"id":"1809.04719","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.04719","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"arxiv_version","alias_value":"1809.04719v1","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.04719","created_at":"2026-05-18T00:05:49Z"},{"alias_kind":"pith_short_12","alias_value":"EHYVRKGXAY2S","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EHYVRKGXAY2STNZC","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EHYVRKGX","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:f2217097b75d7e8866dba87c3ae4f46353244debd52d05c17aa7dd48fcde5c0d","target":"graph","created_at":"2026-05-18T00:05:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We derive exponential bounds for tail of distribution for natural, i.e. under ordinary logarithm, normalized sums of arrays of random variables, not necessarily independent.","authors_text":"Eugeny Ostrovsky, Leonid Sirota, Maria Rosaria Formica, Yurii Vasilovich Kozachenko","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-13T00:27:12Z","title":"Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.04719","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c39804a5c633ab473f34b63724e11f1ce629c8450dde3489c8c6fefe2c9cc128","target":"record","created_at":"2026-05-18T00:05:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2fa6bafe2fa843fb638e0f17b4ea1ad0721514e50bb747b413320eb25f90253c","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-09-13T00:27:12Z","title_canon_sha256":"58f6b8c514eb5629fbfd7d9745a20883c4a312b5593e2b2efe2e5f940908f844"},"schema_version":"1.0","source":{"id":"1809.04719","kind":"arxiv","version":1}},"canonical_sha256":"21f158a8d7063529b7220f3c137528279b1a242f02a171b1e6365b4f83c3b2a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21f158a8d7063529b7220f3c137528279b1a242f02a171b1e6365b4f83c3b2a1","first_computed_at":"2026-05-18T00:05:49.844234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:49.844234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mxldWlt7wAyUJ0Uo2ZmHOPnoXBTVUStViWtCp4UKR7cZ2UE23yEr8YJPcoBFshKj5r6np8o8ZOJtASrfzbOtBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:49.844786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.04719","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c39804a5c633ab473f34b63724e11f1ce629c8450dde3489c8c6fefe2c9cc128","sha256:f2217097b75d7e8866dba87c3ae4f46353244debd52d05c17aa7dd48fcde5c0d"],"state_sha256":"1377e16e24971a22507714470d4db100b50ff06e4f6e959ef57c50d462af2ba2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1HgnzSjRzrceft3n2JZc/BWNrvgqm8+qrL9BRtBKe4RsKNe330WAuem+Dftk2aOil8UZCYJm8HjOjG5b5PQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:27:14.631339Z","bundle_sha256":"3bc8f21b2593f0901a29f5da9fb1ba836e0a9820f065abdcf6afcfec7ff3dbc3"}}