{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NWTTQWLJ6UYVAK5WENHWU4POSM","short_pith_number":"pith:NWTTQWLJ","canonical_record":{"source":{"id":"1207.0436","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T16:20:44Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"c12d2947df45d8ca44409ad49a7f806978e12289ad970d8566d973dd1960ad8c","abstract_canon_sha256":"42d1ca9245b372d2509bc5ec177d33289baabbf386b74972c4dc74300f0e7f65"},"schema_version":"1.0"},"canonical_sha256":"6da7385969f531502bb6234f6a71ee933a22ac97ff950231e702db9114a35276","source":{"kind":"arxiv","id":"1207.0436","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0436","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0436v3","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0436","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWTTQWLJ6UYV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWTTQWLJ6UYVAK5W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWTTQWLJ","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NWTTQWLJ6UYVAK5WENHWU4POSM","target":"record","payload":{"canonical_record":{"source":{"id":"1207.0436","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T16:20:44Z","cross_cats_sorted":["math.IT","math.PR"],"title_canon_sha256":"c12d2947df45d8ca44409ad49a7f806978e12289ad970d8566d973dd1960ad8c","abstract_canon_sha256":"42d1ca9245b372d2509bc5ec177d33289baabbf386b74972c4dc74300f0e7f65"},"schema_version":"1.0"},"canonical_sha256":"6da7385969f531502bb6234f6a71ee933a22ac97ff950231e702db9114a35276","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:42.987693Z","signature_b64":"vArCNKUGtayV8I5ySHsyuyYNPGqZvND93O1MrY1tvjQL5ZFUiAZtxa4ANud9v92KRiGOkbMWH7taBJNmp3VfBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6da7385969f531502bb6234f6a71ee933a22ac97ff950231e702db9114a35276","last_reissued_at":"2026-05-18T00:58:42.987274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:42.987274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.0436","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6W76V4byRSUra9Nbz95QV7IWg04eMELDz0jenr4BXBbgCq69hqtkGXfsHd0DdWcFMrznMRSv/pPJfTgdNMUdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:07:56.904632Z"},"content_sha256":"117e0e1421254c32f26d6408d7c9ecbd5fa94663ae3580813d8ad0d05af45312","schema_version":"1.0","event_id":"sha256:117e0e1421254c32f26d6408d7c9ecbd5fa94663ae3580813d8ad0d05af45312"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NWTTQWLJ6UYVAK5WENHWU4POSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Entropy of Sums of Bernoulli Random Variables via the Chen-Stein Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Igal Sason","submitted_at":"2012-07-02T16:20:44Z","abstract_excerpt":"This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random variable with the same mean are derived. The derivation of these bounds combines elements of information theory with the Chen-Stein method for Poisson approximation. The resulting bounds are easy to compute, and their applicability is exemplified. This conference paper presents in part the first half of the paper entitled \"An information-theoretic perspectiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0436","kind":"arxiv","version":3},"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":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+Vz8+yEDipy1y4xAlMExLFUZiQIChDQWRHEYxHoo/fSuV8QQgbnWyyQdOhc1Yq+FpTUJ4qs+dcHq5IgSixPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:07:56.904974Z"},"content_sha256":"3af4af464c185e3c43710216ece209836e06a07ea19bb9ca91f0aaddbe4e54f5","schema_version":"1.0","event_id":"sha256:3af4af464c185e3c43710216ece209836e06a07ea19bb9ca91f0aaddbe4e54f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/bundle.json","state_url":"https://pith.science/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/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":"2026-06-11T09:07:56Z","links":{"resolver":"https://pith.science/pith/NWTTQWLJ6UYVAK5WENHWU4POSM","bundle":"https://pith.science/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/bundle.json","state":"https://pith.science/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWTTQWLJ6UYVAK5WENHWU4POSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NWTTQWLJ6UYVAK5WENHWU4POSM","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":"42d1ca9245b372d2509bc5ec177d33289baabbf386b74972c4dc74300f0e7f65","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T16:20:44Z","title_canon_sha256":"c12d2947df45d8ca44409ad49a7f806978e12289ad970d8566d973dd1960ad8c"},"schema_version":"1.0","source":{"id":"1207.0436","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0436","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0436v3","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0436","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"NWTTQWLJ6UYV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NWTTQWLJ6UYVAK5W","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NWTTQWLJ","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:3af4af464c185e3c43710216ece209836e06a07ea19bb9ca91f0aaddbe4e54f5","target":"graph","created_at":"2026-05-18T00:58:42Z","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":"This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random variable with the same mean are derived. The derivation of these bounds combines elements of information theory with the Chen-Stein method for Poisson approximation. The resulting bounds are easy to compute, and their applicability is exemplified. This conference paper presents in part the first half of the paper entitled \"An information-theoretic perspectiv","authors_text":"Igal Sason","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T16:20:44Z","title":"On the Entropy of Sums of Bernoulli Random Variables via the Chen-Stein Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0436","kind":"arxiv","version":3},"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":"sha256:117e0e1421254c32f26d6408d7c9ecbd5fa94663ae3580813d8ad0d05af45312","target":"record","created_at":"2026-05-18T00:58:42Z","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":"42d1ca9245b372d2509bc5ec177d33289baabbf386b74972c4dc74300f0e7f65","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-02T16:20:44Z","title_canon_sha256":"c12d2947df45d8ca44409ad49a7f806978e12289ad970d8566d973dd1960ad8c"},"schema_version":"1.0","source":{"id":"1207.0436","kind":"arxiv","version":3}},"canonical_sha256":"6da7385969f531502bb6234f6a71ee933a22ac97ff950231e702db9114a35276","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6da7385969f531502bb6234f6a71ee933a22ac97ff950231e702db9114a35276","first_computed_at":"2026-05-18T00:58:42.987274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:42.987274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vArCNKUGtayV8I5ySHsyuyYNPGqZvND93O1MrY1tvjQL5ZFUiAZtxa4ANud9v92KRiGOkbMWH7taBJNmp3VfBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:42.987693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0436","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:117e0e1421254c32f26d6408d7c9ecbd5fa94663ae3580813d8ad0d05af45312","sha256:3af4af464c185e3c43710216ece209836e06a07ea19bb9ca91f0aaddbe4e54f5"],"state_sha256":"9ad426b93f65e28d3f3d93b22952fb9df17fafab49953dcb76a11d8f1da7cc17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5tjyIzQkwITWm9WD+111OFyL1O81NwkKBC/UfRWefq5kFQ4mGSHwpP64BkrJLOOdnJPW4YIfojBy6Z5NO6d6CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:07:56.906953Z","bundle_sha256":"6e230cb7c33ba75928d80aa32467139715a296a7564f19273055d52005e6585e"}}