{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Y3SMSSTJOV23ZGGT4MOHX4JP47","short_pith_number":"pith:Y3SMSSTJ","canonical_record":{"source":{"id":"1206.2592","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T17:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"84e6051728d92dfa906119e0f0656682db948fb876fedb84d75712e9d69de1fd","abstract_canon_sha256":"d0b70d0b9aa0c00126bc9258d1dcbf3f4c5a391c06ed6ae5f600da7bcffd6dd7"},"schema_version":"1.0"},"canonical_sha256":"c6e4c94a697575bc98d3e31c7bf12fe7e46a39af5ba90bdb8a88348ef43138c6","source":{"kind":"arxiv","id":"1206.2592","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2592","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2592v6","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2592","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"Y3SMSSTJOV23","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3SMSSTJOV23ZGGT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3SMSSTJ","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Y3SMSSTJOV23ZGGT4MOHX4JP47","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2592","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T17:07:13Z","cross_cats_sorted":[],"title_canon_sha256":"84e6051728d92dfa906119e0f0656682db948fb876fedb84d75712e9d69de1fd","abstract_canon_sha256":"d0b70d0b9aa0c00126bc9258d1dcbf3f4c5a391c06ed6ae5f600da7bcffd6dd7"},"schema_version":"1.0"},"canonical_sha256":"c6e4c94a697575bc98d3e31c7bf12fe7e46a39af5ba90bdb8a88348ef43138c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:05.996432Z","signature_b64":"myzVhHH98ENrmgO97sgLaIyphS1g7PTl36OMEkWqMDMV+L0GKMONuiBYKjuiEXJcwcfxGZwfozb+w406X9FQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6e4c94a697575bc98d3e31c7bf12fe7e46a39af5ba90bdb8a88348ef43138c6","last_reissued_at":"2026-05-18T01:37:05.995696Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:05.995696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2592","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vMEcDg80CnKi3eZQBrS46lgbGq4PS5leflFRb2rIbJHvt5KAr2n+Gm5F90aUkSZm1HA5R9TnzohhMOG59MY7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:21:54.405025Z"},"content_sha256":"854abca02d4acbef47d9632f015d0173b6a874c328441bd9b1968b1ea5ffc53d","schema_version":"1.0","event_id":"sha256:854abca02d4acbef47d9632f015d0173b6a874c328441bd9b1968b1ea5ffc53d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Y3SMSSTJOV23ZGGT4MOHX4JP47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp large deviation results for sums of independent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ion Grama, Quansheng Liu, Xiequan Fan","submitted_at":"2012-06-12T17:07:13Z","abstract_excerpt":"We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand (1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram\\'{e}r (1938), Bahadur-Rao (1960) and Sakhanenko (1991). We also show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2592","kind":"arxiv","version":6},"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":"2026-05-18T01:37:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jI/cpUrfYaaRcwY1ZNAfHsfVnAroMDP3Si/OxvTdUFOUnsRRaKX29SiZYcobMl9O7HfJKhlPKCLW0YQCaeg5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:21:54.405387Z"},"content_sha256":"b1ef7751a6d6acdab17951716275241ef5444cfb39e5edb570c8ba1c9157243e","schema_version":"1.0","event_id":"sha256:b1ef7751a6d6acdab17951716275241ef5444cfb39e5edb570c8ba1c9157243e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/bundle.json","state_url":"https://pith.science/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/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":"2026-05-31T04:21:54Z","links":{"resolver":"https://pith.science/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47","bundle":"https://pith.science/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/bundle.json","state":"https://pith.science/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y3SMSSTJOV23ZGGT4MOHX4JP47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y3SMSSTJOV23ZGGT4MOHX4JP47","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":"d0b70d0b9aa0c00126bc9258d1dcbf3f4c5a391c06ed6ae5f600da7bcffd6dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T17:07:13Z","title_canon_sha256":"84e6051728d92dfa906119e0f0656682db948fb876fedb84d75712e9d69de1fd"},"schema_version":"1.0","source":{"id":"1206.2592","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2592","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2592v6","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2592","created_at":"2026-05-18T01:37:05Z"},{"alias_kind":"pith_short_12","alias_value":"Y3SMSSTJOV23","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3SMSSTJOV23ZGGT","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3SMSSTJ","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:b1ef7751a6d6acdab17951716275241ef5444cfb39e5edb570c8ba1c9157243e","target":"graph","created_at":"2026-05-18T01:37:05Z","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 show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds improve the inequalities of Bennett and Hoeffding by adding missing factors in the spirit of Talagrand (1995). We also complete Talagrand's inequality by giving a lower bound of the same form, leading to an equality. As a consequence, we obtain large deviation expansions similar to those of Cram\\'{e}r (1938), Bahadur-Rao (1960) and Sakhanenko (1991). We also show ","authors_text":"Ion Grama, Quansheng Liu, Xiequan Fan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T17:07:13Z","title":"Sharp large deviation results for sums of independent random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2592","kind":"arxiv","version":6},"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":"sha256:854abca02d4acbef47d9632f015d0173b6a874c328441bd9b1968b1ea5ffc53d","target":"record","created_at":"2026-05-18T01:37:05Z","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":"d0b70d0b9aa0c00126bc9258d1dcbf3f4c5a391c06ed6ae5f600da7bcffd6dd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-12T17:07:13Z","title_canon_sha256":"84e6051728d92dfa906119e0f0656682db948fb876fedb84d75712e9d69de1fd"},"schema_version":"1.0","source":{"id":"1206.2592","kind":"arxiv","version":6}},"canonical_sha256":"c6e4c94a697575bc98d3e31c7bf12fe7e46a39af5ba90bdb8a88348ef43138c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6e4c94a697575bc98d3e31c7bf12fe7e46a39af5ba90bdb8a88348ef43138c6","first_computed_at":"2026-05-18T01:37:05.995696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:05.995696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"myzVhHH98ENrmgO97sgLaIyphS1g7PTl36OMEkWqMDMV+L0GKMONuiBYKjuiEXJcwcfxGZwfozb+w406X9FQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:05.996432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2592","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:854abca02d4acbef47d9632f015d0173b6a874c328441bd9b1968b1ea5ffc53d","sha256:b1ef7751a6d6acdab17951716275241ef5444cfb39e5edb570c8ba1c9157243e"],"state_sha256":"30eed71940efce5ebe2807a3285204952f1577432afd2799beb0d3844c35e2c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1a1ndQB37E2c47CX65ZtcNWK6ZQHCLuvri8MRSecML52X3Yjj+mZX1arlZhPDtUR0EmkPKyIiAYsI0ti0Bz3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:21:54.407562Z","bundle_sha256":"beffdd035395467ef24aedfc0c9f1bcb91472925d3b8b035069284bfe3d98606"}}