{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:R4OLDBE5WAEM7LHZWWBOAHLYE3","short_pith_number":"pith:R4OLDBE5","canonical_record":{"source":{"id":"1902.02852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-07T21:30:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"72a50f684819606dc4d73c9caf4775d8cca84189694aad16ce1867591471f9bc","abstract_canon_sha256":"707f062024c88da203d9c3532aaea3af9ba2d535d43e68d4bc8f95a71bed4a27"},"schema_version":"1.0"},"canonical_sha256":"8f1cb1849db008cfacf9b582e01d7826e3a7b30817e1a0b6af9b8772200ebcd9","source":{"kind":"arxiv","id":"1902.02852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02852","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02852v1","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02852","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"R4OLDBE5WAEM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"R4OLDBE5WAEM7LHZ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"R4OLDBE5","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:R4OLDBE5WAEM7LHZWWBOAHLYE3","target":"record","payload":{"canonical_record":{"source":{"id":"1902.02852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-07T21:30:27Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"72a50f684819606dc4d73c9caf4775d8cca84189694aad16ce1867591471f9bc","abstract_canon_sha256":"707f062024c88da203d9c3532aaea3af9ba2d535d43e68d4bc8f95a71bed4a27"},"schema_version":"1.0"},"canonical_sha256":"8f1cb1849db008cfacf9b582e01d7826e3a7b30817e1a0b6af9b8772200ebcd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:29.028154Z","signature_b64":"oya7kxIOqlST94ThYQTQXKD8sUTC4WtEZ73G65ft3yZKd0R2t5/KQunAGAXDheD8RSRxg3X+eBjM+iJ8tosvAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f1cb1849db008cfacf9b582e01d7826e3a7b30817e1a0b6af9b8772200ebcd9","last_reissued_at":"2026-05-17T23:54:29.027679Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:29.027679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.02852","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":"2026-05-17T23:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qPGlR0Rvcspdt1ijbWt9k79UxO+UmECB3ZqzMCmc8FO16y6sBmdxbo4XVGEpLMiJuF1Aww8yMwMH7+ZyaDkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:34:20.452568Z"},"content_sha256":"f91e3c7fb1390c393bc8e2bca1a6467c4e923b5166e906e22bb0b5630c025044","schema_version":"1.0","event_id":"sha256:f91e3c7fb1390c393bc8e2bca1a6467c4e923b5166e906e22bb0b5630c025044"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:R4OLDBE5WAEM7LHZWWBOAHLYE3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Asymptotically Tight Tail Bounds for Sums of Geometric and Exponential Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Yaonan Jin, Yingkai Li, Yining Wang, Yuan Zhou","submitted_at":"2019-02-07T21:30:27Z","abstract_excerpt":"In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically tight."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02852","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":"2026-05-17T23:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DXlv3KRc7HqWzYN2hnj5zRfajh51CVviLRQBDaEKMJCADM1l2GYAQtRae/bU+wtH4kJGx/gD9g08+zyYyUClDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:34:20.453191Z"},"content_sha256":"2c6688d05d9b30314c7ff57d2494c8acf7c0f211f584e381fba99b84a574e456","schema_version":"1.0","event_id":"sha256:2c6688d05d9b30314c7ff57d2494c8acf7c0f211f584e381fba99b84a574e456"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/bundle.json","state_url":"https://pith.science/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/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":"2026-05-28T07:34:20Z","links":{"resolver":"https://pith.science/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3","bundle":"https://pith.science/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/bundle.json","state":"https://pith.science/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4OLDBE5WAEM7LHZWWBOAHLYE3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:R4OLDBE5WAEM7LHZWWBOAHLYE3","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":"707f062024c88da203d9c3532aaea3af9ba2d535d43e68d4bc8f95a71bed4a27","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-07T21:30:27Z","title_canon_sha256":"72a50f684819606dc4d73c9caf4775d8cca84189694aad16ce1867591471f9bc"},"schema_version":"1.0","source":{"id":"1902.02852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.02852","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1902.02852v1","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.02852","created_at":"2026-05-17T23:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"R4OLDBE5WAEM","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"R4OLDBE5WAEM7LHZ","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"R4OLDBE5","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:2c6688d05d9b30314c7ff57d2494c8acf7c0f211f584e381fba99b84a574e456","target":"graph","created_at":"2026-05-17T23:54:29Z","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":"In this note we prove bounds on the upper and lower probability tails of sums of independent geometric or exponentially distributed random variables. We also prove negative results showing that our established tail bounds are asymptotically tight.","authors_text":"Yaonan Jin, Yingkai Li, Yining Wang, Yuan Zhou","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-07T21:30:27Z","title":"On Asymptotically Tight Tail Bounds for Sums of Geometric and Exponential Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.02852","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:f91e3c7fb1390c393bc8e2bca1a6467c4e923b5166e906e22bb0b5630c025044","target":"record","created_at":"2026-05-17T23:54:29Z","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":"707f062024c88da203d9c3532aaea3af9ba2d535d43e68d4bc8f95a71bed4a27","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-02-07T21:30:27Z","title_canon_sha256":"72a50f684819606dc4d73c9caf4775d8cca84189694aad16ce1867591471f9bc"},"schema_version":"1.0","source":{"id":"1902.02852","kind":"arxiv","version":1}},"canonical_sha256":"8f1cb1849db008cfacf9b582e01d7826e3a7b30817e1a0b6af9b8772200ebcd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f1cb1849db008cfacf9b582e01d7826e3a7b30817e1a0b6af9b8772200ebcd9","first_computed_at":"2026-05-17T23:54:29.027679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:29.027679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oya7kxIOqlST94ThYQTQXKD8sUTC4WtEZ73G65ft3yZKd0R2t5/KQunAGAXDheD8RSRxg3X+eBjM+iJ8tosvAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:29.028154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.02852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f91e3c7fb1390c393bc8e2bca1a6467c4e923b5166e906e22bb0b5630c025044","sha256:2c6688d05d9b30314c7ff57d2494c8acf7c0f211f584e381fba99b84a574e456"],"state_sha256":"91cbd8372f5d8fba3d7d097c8202784aad42d9245d83c3f23e3a35463d51d880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4b0n0S6apOW/3H4ybBuFNW9M3Vzu2dktEvm7Fv7SXTNqoQqmUfEoXsp7TJHbKvDQIqMLY1p9p9COJmFnRDkxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:34:20.456574Z","bundle_sha256":"037747275365ca10b2090e989e396928249f38e9566c3ee2980fd8394a139743"}}