{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HSWZJUNKDE2WQNSBMNF6WFFH6Z","short_pith_number":"pith:HSWZJUNK","canonical_record":{"source":{"id":"1608.01805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T08:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"11b8a8c5288420047b193dc1e19d456c9649bb0160cf0f4853683709e588b528","abstract_canon_sha256":"1e49991882fef3473c74b57af0e6fbd688d99a83fca0aa2ccace661efb090e29"},"schema_version":"1.0"},"canonical_sha256":"3cad94d1aa1935683641634beb14a7f6582d88c1c35689c7aa644a3cb3e88a1b","source":{"kind":"arxiv","id":"1608.01805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01805","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01805v1","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01805","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"HSWZJUNKDE2W","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HSWZJUNKDE2WQNSB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HSWZJUNK","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HSWZJUNKDE2WQNSBMNF6WFFH6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T08:44:47Z","cross_cats_sorted":[],"title_canon_sha256":"11b8a8c5288420047b193dc1e19d456c9649bb0160cf0f4853683709e588b528","abstract_canon_sha256":"1e49991882fef3473c74b57af0e6fbd688d99a83fca0aa2ccace661efb090e29"},"schema_version":"1.0"},"canonical_sha256":"3cad94d1aa1935683641634beb14a7f6582d88c1c35689c7aa644a3cb3e88a1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:44.544394Z","signature_b64":"h3pb6S646nUx3W+wsW3+bBffepfZTTg9t/ZkuDH0yqG36HTDQATcfTw2SaHZbnlpG1HD8z7vKDE7wGOiiaUOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cad94d1aa1935683641634beb14a7f6582d88c1c35689c7aa644a3cb3e88a1b","last_reissued_at":"2026-05-18T01:09:44.543800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:44.543800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01805","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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tkB+7MnNvqqFyYnBzs27xfYZZ7ox84ILkP/emXn8STKxE5yG4ta5L3BoRHURSLOtncjTm5NYURlW94iDM7FeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:31:55.255412Z"},"content_sha256":"3c558ddab8e0c3c1a4e0fe45029eb7a71cfa226fabddf1429ec5281472646f0a","schema_version":"1.0","event_id":"sha256:3c558ddab8e0c3c1a4e0fe45029eb7a71cfa226fabddf1429ec5281472646f0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HSWZJUNKDE2WQNSBMNF6WFFH6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"R\\'enyi divergence and the central limit theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. G\\\"otze, G. P. Chistyakov, S. G. Bobkov","submitted_at":"2016-08-05T08:44:47Z","abstract_excerpt":"We explore properties of the $\\chi^2$ and more general R\\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01805","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":"2026-05-18T01:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjK+lxJPj9OSL4z3ucdnnUhqfrYxUlTDM+3F0wRJzoelteGp+rTE8WC7J5CKNz2biNBOKTbWqRsgPHVLo7LGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:31:55.256133Z"},"content_sha256":"a1453fda077930a5e5ad2c5c144334c0a6aaf487d9a255522e8e9c60a3115b28","schema_version":"1.0","event_id":"sha256:a1453fda077930a5e5ad2c5c144334c0a6aaf487d9a255522e8e9c60a3115b28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/bundle.json","state_url":"https://pith.science/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/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":"2026-05-31T13:31:55Z","links":{"resolver":"https://pith.science/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z","bundle":"https://pith.science/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/bundle.json","state":"https://pith.science/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSWZJUNKDE2WQNSBMNF6WFFH6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HSWZJUNKDE2WQNSBMNF6WFFH6Z","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":"1e49991882fef3473c74b57af0e6fbd688d99a83fca0aa2ccace661efb090e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T08:44:47Z","title_canon_sha256":"11b8a8c5288420047b193dc1e19d456c9649bb0160cf0f4853683709e588b528"},"schema_version":"1.0","source":{"id":"1608.01805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01805","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01805v1","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01805","created_at":"2026-05-18T01:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"HSWZJUNKDE2W","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HSWZJUNKDE2WQNSB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HSWZJUNK","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:a1453fda077930a5e5ad2c5c144334c0a6aaf487d9a255522e8e9c60a3115b28","target":"graph","created_at":"2026-05-18T01:09:44Z","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 explore properties of the $\\chi^2$ and more general R\\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distances. Moreover, we derive exact rates of convergence in these distances with respect to an increasing number of summands.","authors_text":"F. G\\\"otze, G. P. Chistyakov, S. G. Bobkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T08:44:47Z","title":"R\\'enyi divergence and the central limit theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01805","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":"sha256:3c558ddab8e0c3c1a4e0fe45029eb7a71cfa226fabddf1429ec5281472646f0a","target":"record","created_at":"2026-05-18T01:09:44Z","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":"1e49991882fef3473c74b57af0e6fbd688d99a83fca0aa2ccace661efb090e29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-05T08:44:47Z","title_canon_sha256":"11b8a8c5288420047b193dc1e19d456c9649bb0160cf0f4853683709e588b528"},"schema_version":"1.0","source":{"id":"1608.01805","kind":"arxiv","version":1}},"canonical_sha256":"3cad94d1aa1935683641634beb14a7f6582d88c1c35689c7aa644a3cb3e88a1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cad94d1aa1935683641634beb14a7f6582d88c1c35689c7aa644a3cb3e88a1b","first_computed_at":"2026-05-18T01:09:44.543800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:44.543800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h3pb6S646nUx3W+wsW3+bBffepfZTTg9t/ZkuDH0yqG36HTDQATcfTw2SaHZbnlpG1HD8z7vKDE7wGOiiaUOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:44.544394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c558ddab8e0c3c1a4e0fe45029eb7a71cfa226fabddf1429ec5281472646f0a","sha256:a1453fda077930a5e5ad2c5c144334c0a6aaf487d9a255522e8e9c60a3115b28"],"state_sha256":"ec8c88383a19e74ceb3ab21398c146587586057ab8f80acf4f664923ae97a3e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJ9MM92RuY3p0yf5UAJjB7HHFlm1nEFlTW23voS/mtYCheAG3FaDevSv9lpStFQ+9YtnzdQ1pCYpi1gI0mnrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:31:55.262064Z","bundle_sha256":"572451950774f73a12b4f733748cee11eff1793844bfb9eb8ed2b3d8801c2e38"}}