{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:N5DES6SBTPZ5ZRUCJUAFURNACB","short_pith_number":"pith:N5DES6SB","canonical_record":{"source":{"id":"1612.07950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T12:14:08Z","cross_cats_sorted":[],"title_canon_sha256":"e2430987f2a9a4bca07f6f9b1a8081d5152190a8d567e9348865e47116f94171","abstract_canon_sha256":"8a23ea752590c031771611b85db7dffc36a7cdc520fa3948d6e3a4fdd20d6120"},"schema_version":"1.0"},"canonical_sha256":"6f46497a419bf3dcc6824d005a45a0107a22b42a51f77a39ddd3c3afe091d39c","source":{"kind":"arxiv","id":"1612.07950","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07950","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07950v1","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07950","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"N5DES6SBTPZ5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5DES6SBTPZ5ZRUC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5DES6SB","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:N5DES6SBTPZ5ZRUCJUAFURNACB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T12:14:08Z","cross_cats_sorted":[],"title_canon_sha256":"e2430987f2a9a4bca07f6f9b1a8081d5152190a8d567e9348865e47116f94171","abstract_canon_sha256":"8a23ea752590c031771611b85db7dffc36a7cdc520fa3948d6e3a4fdd20d6120"},"schema_version":"1.0"},"canonical_sha256":"6f46497a419bf3dcc6824d005a45a0107a22b42a51f77a39ddd3c3afe091d39c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:05.235075Z","signature_b64":"K1KRLGDKu4PfJqBBLH/BXYKtxkj02xvZjUgUn9FJTxcSvpBx8ZeKHKXrcl7juMJYuZKSyFkb9+GsLprp/PfqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f46497a419bf3dcc6824d005a45a0107a22b42a51f77a39ddd3c3afe091d39c","last_reissued_at":"2026-05-18T00:54:05.234511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:05.234511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07950","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":"2026-05-18T00:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5B9GJTwwFqgbGVxcxY3ycejMWbEE6CXOWs/mE/LUWechf2WlfoQyHWpdnsNYHU/0Wb8He1ogqCk1oILfGXVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:27:41.646727Z"},"content_sha256":"9da8c4ca1e59d05cb0ec50a288d52a398cf83bee1f3fad5335722cd8ed1e6124","schema_version":"1.0","event_id":"sha256:9da8c4ca1e59d05cb0ec50a288d52a398cf83bee1f3fad5335722cd8ed1e6124"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:N5DES6SBTPZ5ZRUCJUAFURNACB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate central limit theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ben Berckmoes, Geert Molenberghs","submitted_at":"2016-12-23T12:14:08Z","abstract_excerpt":"We refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg's condition. This allows us to continue to provide information in non-standard settings in which the classical central limit theorem fails to hold. Stein's method p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07950","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":"2026-05-18T00:54:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ubts19T7s5qs96MGthk39ONDq6YMv7AA2sAXbgDQi26RbCFuvFotT51Dicc/PtiV+gI4s0ZIYso6y/pY82W9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:27:41.647428Z"},"content_sha256":"fd95d3552c03e9391b18c4e8a8c4968de4d2a9bb7498b6523e45bf89abbda5fa","schema_version":"1.0","event_id":"sha256:fd95d3552c03e9391b18c4e8a8c4968de4d2a9bb7498b6523e45bf89abbda5fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/bundle.json","state_url":"https://pith.science/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/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":"2026-05-31T00:27:41Z","links":{"resolver":"https://pith.science/pith/N5DES6SBTPZ5ZRUCJUAFURNACB","bundle":"https://pith.science/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/bundle.json","state":"https://pith.science/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5DES6SBTPZ5ZRUCJUAFURNACB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N5DES6SBTPZ5ZRUCJUAFURNACB","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":"8a23ea752590c031771611b85db7dffc36a7cdc520fa3948d6e3a4fdd20d6120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T12:14:08Z","title_canon_sha256":"e2430987f2a9a4bca07f6f9b1a8081d5152190a8d567e9348865e47116f94171"},"schema_version":"1.0","source":{"id":"1612.07950","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07950","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07950v1","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07950","created_at":"2026-05-18T00:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"N5DES6SBTPZ5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5DES6SBTPZ5ZRUC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5DES6SB","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:fd95d3552c03e9391b18c4e8a8c4968de4d2a9bb7498b6523e45bf89abbda5fa","target":"graph","created_at":"2026-05-18T00:54:05Z","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 refine the classical Lindeberg-Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parametrized Prokhorov distances in terms of a Lindeberg index. We thus obtain more general approximate central limit theorems, which roughly state that the row-wise sums of a triangular array are approximately asymptotically normal if the array approximately satisfies Lindeberg's condition. This allows us to continue to provide information in non-standard settings in which the classical central limit theorem fails to hold. Stein's method p","authors_text":"Ben Berckmoes, Geert Molenberghs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T12:14:08Z","title":"Approximate central limit theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07950","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":"sha256:9da8c4ca1e59d05cb0ec50a288d52a398cf83bee1f3fad5335722cd8ed1e6124","target":"record","created_at":"2026-05-18T00:54:05Z","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":"8a23ea752590c031771611b85db7dffc36a7cdc520fa3948d6e3a4fdd20d6120","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T12:14:08Z","title_canon_sha256":"e2430987f2a9a4bca07f6f9b1a8081d5152190a8d567e9348865e47116f94171"},"schema_version":"1.0","source":{"id":"1612.07950","kind":"arxiv","version":1}},"canonical_sha256":"6f46497a419bf3dcc6824d005a45a0107a22b42a51f77a39ddd3c3afe091d39c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f46497a419bf3dcc6824d005a45a0107a22b42a51f77a39ddd3c3afe091d39c","first_computed_at":"2026-05-18T00:54:05.234511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:05.234511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K1KRLGDKu4PfJqBBLH/BXYKtxkj02xvZjUgUn9FJTxcSvpBx8ZeKHKXrcl7juMJYuZKSyFkb9+GsLprp/PfqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:05.235075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07950","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9da8c4ca1e59d05cb0ec50a288d52a398cf83bee1f3fad5335722cd8ed1e6124","sha256:fd95d3552c03e9391b18c4e8a8c4968de4d2a9bb7498b6523e45bf89abbda5fa"],"state_sha256":"3880d6e1ef02e2559aa9ff40b56fb168c8cc9bef2c11ac429ffe08cf6489a72c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYVQ6U+BC8VveLkRZu5swVvsjUAglomvBla26YlbN4RirvZ+Qqn+Z7UY2uMRN16QZoNA+mANgmrK2pGhu/+4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:27:41.651423Z","bundle_sha256":"1f360ec8782d36437e593ce3a4ae5d37149642ddf232580768d93338ebc74fda"}}