{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7PAT2LHTQNR2QNHO5GJODH47KG","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":"163225e4faca34e5dcb41ea3eb6240b2ee41066079f663e255c8f2bfbeb0f5fa","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-04-09T02:43:46Z","title_canon_sha256":"53316bf8e08957cb350148eadbd793a7ba0d611d2a961d6e33ba52560fc17450"},"schema_version":"1.0","source":{"id":"0804.1399","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.1399","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"arxiv_version","alias_value":"0804.1399v3","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.1399","created_at":"2026-05-18T03:39:14Z"},{"alias_kind":"pith_short_12","alias_value":"7PAT2LHTQNR2","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7PAT2LHTQNR2QNHO","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7PAT2LHT","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:f7223981a893a0f9b75e68825391b064e9946f054fbd40c9c9c676b916a4b971","target":"graph","created_at":"2026-05-18T03:39:14Z","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 paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed criterion of absolute and relative errors. By employing the Chernoff-Hoeffding bound and the concept of sampling, the minimization of a probabilistic function is transformed into an optimization problem amenable for gradient descendent algorithms.","authors_text":"Xinjia Chen","cross_cats":["math.PR","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-04-09T02:43:46Z","title":"On Estimation and Optimization of Mean Values of Bounded Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1399","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:b165acbfed4d0dfd217be571cb9f38b3a1ec7a88027f4f9ffe096bfa0c4a41f9","target":"record","created_at":"2026-05-18T03:39:14Z","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":"163225e4faca34e5dcb41ea3eb6240b2ee41066079f663e255c8f2bfbeb0f5fa","cross_cats_sorted":["math.PR","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2008-04-09T02:43:46Z","title_canon_sha256":"53316bf8e08957cb350148eadbd793a7ba0d611d2a961d6e33ba52560fc17450"},"schema_version":"1.0","source":{"id":"0804.1399","kind":"arxiv","version":3}},"canonical_sha256":"fbc13d2cf38363a834eee992e19f9f51b0d20d75fa05b6d5c2ee694a8cc6163c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbc13d2cf38363a834eee992e19f9f51b0d20d75fa05b6d5c2ee694a8cc6163c","first_computed_at":"2026-05-18T03:39:14.927865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:14.927865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rQWVUMbrLNT4DkEh98ckD1+kG7G4/4Cim9bC7svarZGtGHTXNYJRTOWejgylHaTbdzkN6qOJkp7zfwo6FQznAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:14.928369Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.1399","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b165acbfed4d0dfd217be571cb9f38b3a1ec7a88027f4f9ffe096bfa0c4a41f9","sha256:f7223981a893a0f9b75e68825391b064e9946f054fbd40c9c9c676b916a4b971"],"state_sha256":"f923ff9f122f83dd176008bb749bced3b643b093e41cd203aea688bc9d677e06"}