{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5JHYY4KM4EXJNNTD6DJLBSLFKM","short_pith_number":"pith:5JHYY4KM","canonical_record":{"source":{"id":"1309.6488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-25T12:55:01Z","cross_cats_sorted":["math.HO","stat.TH"],"title_canon_sha256":"bda2528af2aea4eff6d644de8a60a5ac1633d08c9f2bf92925339d90ec6fe7b4","abstract_canon_sha256":"564d91c44978578e94281ed1c36db3679ed9ff3a33b70eb945a37c399d545847"},"schema_version":"1.0"},"canonical_sha256":"ea4f8c714ce12e96b663f0d2b0c96553100cab2b8d8d3fda44cab9f9a9f9a417","source":{"kind":"arxiv","id":"1309.6488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6488","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6488v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6488","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"5JHYY4KM4EXJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5JHYY4KM4EXJNNTD","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5JHYY4KM","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5JHYY4KM4EXJNNTD6DJLBSLFKM","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-25T12:55:01Z","cross_cats_sorted":["math.HO","stat.TH"],"title_canon_sha256":"bda2528af2aea4eff6d644de8a60a5ac1633d08c9f2bf92925339d90ec6fe7b4","abstract_canon_sha256":"564d91c44978578e94281ed1c36db3679ed9ff3a33b70eb945a37c399d545847"},"schema_version":"1.0"},"canonical_sha256":"ea4f8c714ce12e96b663f0d2b0c96553100cab2b8d8d3fda44cab9f9a9f9a417","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:20.887241Z","signature_b64":"7WRjCHNYZjSHmgt7+J9ZZXfSvw/LIS6qY1BwBPU3iZV8M6zlPe/FFd4t+D2CT8sHpFwFJ0l9P7QyJXJTfvJbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea4f8c714ce12e96b663f0d2b0c96553100cab2b8d8d3fda44cab9f9a9f9a417","last_reissued_at":"2026-05-18T03:12:20.886368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:20.886368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6488","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZ+tjposmTEBJ215dYHuDAHm/GuwGyiE6kRh415W7lC7AWKYUfJlMJFYYpwPtJeXIKY7Gq44woNdkor745CBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:27:31.268148Z"},"content_sha256":"d740e61ce85ad8565caa71afddfefbda7b922c788748e1e800dc44d5b68d0edc","schema_version":"1.0","event_id":"sha256:d740e61ce85ad8565caa71afddfefbda7b922c788748e1e800dc44d5b68d0edc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5JHYY4KM4EXJNNTD6DJLBSLFKM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tricentenary history of the Law of Large Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO","stat.TH"],"primary_cat":"math.ST","authors_text":"Eugene Seneta","submitted_at":"2013-09-25T12:55:01Z","abstract_excerpt":"The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob Bernoulli's Theorem: 1. As limit theorem (sample size $n\\to\\infty$), and: 2. Determining sufficiently large sample size for specified precision, for known and also unknown p (the inversion problem), are studied, in frequentist and Bayesian settings. The Bienaym\\'{e}-Chebyshev Inequality is shown to be a meeting point of the French and Russian directions in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6488","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2apywu78lrSlwBQsmFtVxmUemJHIU3bTESvg4qR/kTIas7BPMcXMr8r1FBtKzDXOhUoclffMBbjGPgP58zyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:27:31.268544Z"},"content_sha256":"f2d6c712b4e447fedbbf56c2944d09b32fc27ab9dd699a24ec54ec57db28f38f","schema_version":"1.0","event_id":"sha256:f2d6c712b4e447fedbbf56c2944d09b32fc27ab9dd699a24ec54ec57db28f38f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/bundle.json","state_url":"https://pith.science/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/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":"2026-05-22T14:27:31Z","links":{"resolver":"https://pith.science/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM","bundle":"https://pith.science/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/bundle.json","state":"https://pith.science/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JHYY4KM4EXJNNTD6DJLBSLFKM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5JHYY4KM4EXJNNTD6DJLBSLFKM","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":"564d91c44978578e94281ed1c36db3679ed9ff3a33b70eb945a37c399d545847","cross_cats_sorted":["math.HO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-25T12:55:01Z","title_canon_sha256":"bda2528af2aea4eff6d644de8a60a5ac1633d08c9f2bf92925339d90ec6fe7b4"},"schema_version":"1.0","source":{"id":"1309.6488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6488","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6488v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6488","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"5JHYY4KM4EXJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5JHYY4KM4EXJNNTD","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5JHYY4KM","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:f2d6c712b4e447fedbbf56c2944d09b32fc27ab9dd699a24ec54ec57db28f38f","target":"graph","created_at":"2026-05-18T03:12:20Z","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":"The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob Bernoulli's Theorem: 1. As limit theorem (sample size $n\\to\\infty$), and: 2. Determining sufficiently large sample size for specified precision, for known and also unknown p (the inversion problem), are studied, in frequentist and Bayesian settings. The Bienaym\\'{e}-Chebyshev Inequality is shown to be a meeting point of the French and Russian directions in the ","authors_text":"Eugene Seneta","cross_cats":["math.HO","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-25T12:55:01Z","title":"A Tricentenary history of the Law of Large Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6488","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:d740e61ce85ad8565caa71afddfefbda7b922c788748e1e800dc44d5b68d0edc","target":"record","created_at":"2026-05-18T03:12:20Z","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":"564d91c44978578e94281ed1c36db3679ed9ff3a33b70eb945a37c399d545847","cross_cats_sorted":["math.HO","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-09-25T12:55:01Z","title_canon_sha256":"bda2528af2aea4eff6d644de8a60a5ac1633d08c9f2bf92925339d90ec6fe7b4"},"schema_version":"1.0","source":{"id":"1309.6488","kind":"arxiv","version":1}},"canonical_sha256":"ea4f8c714ce12e96b663f0d2b0c96553100cab2b8d8d3fda44cab9f9a9f9a417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea4f8c714ce12e96b663f0d2b0c96553100cab2b8d8d3fda44cab9f9a9f9a417","first_computed_at":"2026-05-18T03:12:20.886368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:20.886368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7WRjCHNYZjSHmgt7+J9ZZXfSvw/LIS6qY1BwBPU3iZV8M6zlPe/FFd4t+D2CT8sHpFwFJ0l9P7QyJXJTfvJbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:20.887241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d740e61ce85ad8565caa71afddfefbda7b922c788748e1e800dc44d5b68d0edc","sha256:f2d6c712b4e447fedbbf56c2944d09b32fc27ab9dd699a24ec54ec57db28f38f"],"state_sha256":"8b24ffd57b50fca08cad90174da96ecf5a2e89c19b1e8b9f352871d24cc30351"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeQp481rQtna3pe1cuHL2nNG6/7p+WCtIW7QNubEVPFetGUte6Ce9gtR04AC93KGxs+qt/5ABArx6/unXq3HAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:27:31.270974Z","bundle_sha256":"678101e12974bd414af7daeae0b697adb0c5d08a2ea62fa2989430bff8fffb7c"}}