{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GA67FUNPNY7CPO2VSOMYC7AMT4","short_pith_number":"pith:GA67FUNP","canonical_record":{"source":{"id":"1503.02284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-08T15:07:05Z","cross_cats_sorted":[],"title_canon_sha256":"1b76a322868df6879d55da537c984c46d8c866626d551607f1279fb660e29973","abstract_canon_sha256":"caaeb5f06fcfebb43d236c2e48d2c7d22587c2c287db0d8ad7bdd56ea8061a42"},"schema_version":"1.0"},"canonical_sha256":"303df2d1af6e3e27bb559399817c0c9f034be106d3ad737cad961e469c967784","source":{"kind":"arxiv","id":"1503.02284","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02284","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02284v2","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02284","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"pith_short_12","alias_value":"GA67FUNPNY7C","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GA67FUNPNY7CPO2V","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GA67FUNP","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GA67FUNPNY7CPO2VSOMYC7AMT4","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-08T15:07:05Z","cross_cats_sorted":[],"title_canon_sha256":"1b76a322868df6879d55da537c984c46d8c866626d551607f1279fb660e29973","abstract_canon_sha256":"caaeb5f06fcfebb43d236c2e48d2c7d22587c2c287db0d8ad7bdd56ea8061a42"},"schema_version":"1.0"},"canonical_sha256":"303df2d1af6e3e27bb559399817c0c9f034be106d3ad737cad961e469c967784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:24.350795Z","signature_b64":"npqWl6k1TzmE/kATQwrCIk4pA9pAww/qqb1bmaZrVJOG6QQk2v1ajpqTCeovTQmxowhuWCvSACjZfrc1MqPqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"303df2d1af6e3e27bb559399817c0c9f034be106d3ad737cad961e469c967784","last_reissued_at":"2026-05-18T01:34:24.350138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:24.350138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02284","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M0O7mLkc8c0srR9Fnj00VJP73MJn4v4n8sb14isnBVj1X+F9anv+kcNbgr/g5q7k4qJd/r8ZR3u2xq3vm1VRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:10:18.212426Z"},"content_sha256":"98567a8905246330ebf83863cf6a7a4833048e4f5fd87999dea4a8c67c4a53f9","schema_version":"1.0","event_id":"sha256:98567a8905246330ebf83863cf6a7a4833048e4f5fd87999dea4a8c67c4a53f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GA67FUNPNY7CPO2VSOMYC7AMT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Bernstein-Hoeffding method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christos Pelekis, Jan Ramon, Yuyi Wang","submitted_at":"2015-03-08T15:07:05Z","abstract_excerpt":"We show that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding, for sums of independent and bounded random variables whose mean is assumed to be known. As a result we can generalise and improve upon this inequality. We show that Hoeffding's bound is optimal in a broader sense. Our approach allows to obtain \"missing\" factors in Hoeffding's inequality whose existence is motivated by the central limit theorem. The later re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02284","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":""},"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":"2026-05-18T01:34:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4n5aVPvv8UZewlsJVHFrBiTkh7tBBiNFBN/D/wKk4AK2GPDnSvUJcNC9FZLUY7iZjvDKEx6UNegnUNqFcLtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:10:18.213151Z"},"content_sha256":"ae5b4177ec7432bcc09b21d7754b2f7f962f1fd354913820fcf84ca47bc9f443","schema_version":"1.0","event_id":"sha256:ae5b4177ec7432bcc09b21d7754b2f7f962f1fd354913820fcf84ca47bc9f443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/bundle.json","state_url":"https://pith.science/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/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":"2026-06-10T05:10:18Z","links":{"resolver":"https://pith.science/pith/GA67FUNPNY7CPO2VSOMYC7AMT4","bundle":"https://pith.science/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/bundle.json","state":"https://pith.science/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GA67FUNPNY7CPO2VSOMYC7AMT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GA67FUNPNY7CPO2VSOMYC7AMT4","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":"caaeb5f06fcfebb43d236c2e48d2c7d22587c2c287db0d8ad7bdd56ea8061a42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-08T15:07:05Z","title_canon_sha256":"1b76a322868df6879d55da537c984c46d8c866626d551607f1279fb660e29973"},"schema_version":"1.0","source":{"id":"1503.02284","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02284","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02284v2","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02284","created_at":"2026-05-18T01:34:24Z"},{"alias_kind":"pith_short_12","alias_value":"GA67FUNPNY7C","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GA67FUNPNY7CPO2V","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GA67FUNP","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:ae5b4177ec7432bcc09b21d7754b2f7f962f1fd354913820fcf84ca47bc9f443","target":"graph","created_at":"2026-05-18T01:34:24Z","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 that the Bernstein-Hoeffding method can be employed to a larger class of generalized moments. This class includes the exponential moments whose properties play a key role in the proof of a well-known inequality of Wassily Hoeffding, for sums of independent and bounded random variables whose mean is assumed to be known. As a result we can generalise and improve upon this inequality. We show that Hoeffding's bound is optimal in a broader sense. Our approach allows to obtain \"missing\" factors in Hoeffding's inequality whose existence is motivated by the central limit theorem. The later re","authors_text":"Christos Pelekis, Jan Ramon, Yuyi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-08T15:07:05Z","title":"On the Bernstein-Hoeffding method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02284","kind":"arxiv","version":2},"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":"sha256:98567a8905246330ebf83863cf6a7a4833048e4f5fd87999dea4a8c67c4a53f9","target":"record","created_at":"2026-05-18T01:34:24Z","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":"caaeb5f06fcfebb43d236c2e48d2c7d22587c2c287db0d8ad7bdd56ea8061a42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-03-08T15:07:05Z","title_canon_sha256":"1b76a322868df6879d55da537c984c46d8c866626d551607f1279fb660e29973"},"schema_version":"1.0","source":{"id":"1503.02284","kind":"arxiv","version":2}},"canonical_sha256":"303df2d1af6e3e27bb559399817c0c9f034be106d3ad737cad961e469c967784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"303df2d1af6e3e27bb559399817c0c9f034be106d3ad737cad961e469c967784","first_computed_at":"2026-05-18T01:34:24.350138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:24.350138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"npqWl6k1TzmE/kATQwrCIk4pA9pAww/qqb1bmaZrVJOG6QQk2v1ajpqTCeovTQmxowhuWCvSACjZfrc1MqPqDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:24.350795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02284","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98567a8905246330ebf83863cf6a7a4833048e4f5fd87999dea4a8c67c4a53f9","sha256:ae5b4177ec7432bcc09b21d7754b2f7f962f1fd354913820fcf84ca47bc9f443"],"state_sha256":"95b81b5018a6fc017bc83cbb30edb425a030e46e4bbd04d3965fba14487196ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4CxmWBs+ULeFWN0CosNK/8JzfprHsYh1OFusXRSv8/HLrWWBbPIfCTEUL/U+j3JsC2XxZ28o9LUGAABtwKOCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:10:18.217570Z","bundle_sha256":"c908d28dfd84e46caa91d482a5ea5f31694696774414a5d4686f83987b0aad87"}}