{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4Y42FBYQ773UQXFZCBJX3TXQES","short_pith_number":"pith:4Y42FBYQ","canonical_record":{"source":{"id":"1806.05339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-14T02:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"5d529d2e2796b4351cc53eac823a07077ab6d8e5079793025864bb674eee84b9","abstract_canon_sha256":"e04e944421ab8e8d82aec4e51b9d66b351e0284aec656b6a293fb394ba5a324a"},"schema_version":"1.0"},"canonical_sha256":"e639a28710fff7485cb910537dcef02480fb5eb13ccc12cc7768f544c18aaf3b","source":{"kind":"arxiv","id":"1806.05339","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05339","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05339v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05339","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"4Y42FBYQ773U","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4Y42FBYQ773UQXFZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4Y42FBYQ","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4Y42FBYQ773UQXFZCBJX3TXQES","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-14T02:45:44Z","cross_cats_sorted":[],"title_canon_sha256":"5d529d2e2796b4351cc53eac823a07077ab6d8e5079793025864bb674eee84b9","abstract_canon_sha256":"e04e944421ab8e8d82aec4e51b9d66b351e0284aec656b6a293fb394ba5a324a"},"schema_version":"1.0"},"canonical_sha256":"e639a28710fff7485cb910537dcef02480fb5eb13ccc12cc7768f544c18aaf3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:16.298937Z","signature_b64":"R5jq4S00TDCf7d6d+vyvHkncgrPQU2zrCSa4UuAO7QO9nLiCbB6V9GzjOxJRUjFlRHjTepjUDO3tFE16Qb9UDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e639a28710fff7485cb910537dcef02480fb5eb13ccc12cc7768f544c18aaf3b","last_reissued_at":"2026-05-18T00:13:16.298270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:16.298270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05339","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":"2026-05-18T00:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZ6VCs9xO9yWPkfuTi7nih479wzKcBEx37vCNEHe46EMKq1AST2ZDRFpz6JunFYsOQZVTrL8qPeEKREVootkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:35:55.956674Z"},"content_sha256":"aa16f197036d0c57553788a6d10d440284d69d1b0029d54d2806e748c0852ef1","schema_version":"1.0","event_id":"sha256:aa16f197036d0c57553788a6d10d440284d69d1b0029d54d2806e748c0852ef1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4Y42FBYQ773UQXFZCBJX3TXQES","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal approximation for sums of discrete $U$-statistics - application to Kolmogorov bounds in random subgraph counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Grzegorz Serafin, Nicolas Privault","submitted_at":"2018-06-14T02:45:44Z","abstract_excerpt":"We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraphs counts in the Erd{\\H o}s-R\\'enyi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering and improving recent results derived for triangles as well as results using the Wasserstein distance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05339","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":"2026-05-18T00:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDfSgfG6rrGjjXxXbCagqL0z3lbGjs5SoqGC/8Cq8BkPKQVN8t/Z3g5/1zckh58NsT1OUmzc/4G6VYoIAM0UCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:35:55.957163Z"},"content_sha256":"ceabb4b7ba1ce262ce463af06393c09450862573426974044daa477b05205eb4","schema_version":"1.0","event_id":"sha256:ceabb4b7ba1ce262ce463af06393c09450862573426974044daa477b05205eb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Y42FBYQ773UQXFZCBJX3TXQES/bundle.json","state_url":"https://pith.science/pith/4Y42FBYQ773UQXFZCBJX3TXQES/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Y42FBYQ773UQXFZCBJX3TXQES/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":"2026-06-25T21:35:55Z","links":{"resolver":"https://pith.science/pith/4Y42FBYQ773UQXFZCBJX3TXQES","bundle":"https://pith.science/pith/4Y42FBYQ773UQXFZCBJX3TXQES/bundle.json","state":"https://pith.science/pith/4Y42FBYQ773UQXFZCBJX3TXQES/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Y42FBYQ773UQXFZCBJX3TXQES/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4Y42FBYQ773UQXFZCBJX3TXQES","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":"e04e944421ab8e8d82aec4e51b9d66b351e0284aec656b6a293fb394ba5a324a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-14T02:45:44Z","title_canon_sha256":"5d529d2e2796b4351cc53eac823a07077ab6d8e5079793025864bb674eee84b9"},"schema_version":"1.0","source":{"id":"1806.05339","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05339","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05339v1","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05339","created_at":"2026-05-18T00:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"4Y42FBYQ773U","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4Y42FBYQ773UQXFZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4Y42FBYQ","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:ceabb4b7ba1ce262ce463af06393c09450862573426974044daa477b05205eb4","target":"graph","created_at":"2026-05-18T00:13:16Z","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 derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and $U$-statistics made of independent Bernoulli random variables. Such bounds are applied to normal approximation for the renormalized subgraphs counts in the Erd{\\H o}s-R\\'enyi random graph. This approach completely solves a long-standing conjecture in the general setting of arbitrary graph counting, while recovering and improving recent results derived for triangles as well as results using the Wasserstein distance.","authors_text":"Grzegorz Serafin, Nicolas Privault","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-14T02:45:44Z","title":"Normal approximation for sums of discrete $U$-statistics - application to Kolmogorov bounds in random subgraph counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05339","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:aa16f197036d0c57553788a6d10d440284d69d1b0029d54d2806e748c0852ef1","target":"record","created_at":"2026-05-18T00:13:16Z","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":"e04e944421ab8e8d82aec4e51b9d66b351e0284aec656b6a293fb394ba5a324a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-14T02:45:44Z","title_canon_sha256":"5d529d2e2796b4351cc53eac823a07077ab6d8e5079793025864bb674eee84b9"},"schema_version":"1.0","source":{"id":"1806.05339","kind":"arxiv","version":1}},"canonical_sha256":"e639a28710fff7485cb910537dcef02480fb5eb13ccc12cc7768f544c18aaf3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e639a28710fff7485cb910537dcef02480fb5eb13ccc12cc7768f544c18aaf3b","first_computed_at":"2026-05-18T00:13:16.298270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:16.298270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R5jq4S00TDCf7d6d+vyvHkncgrPQU2zrCSa4UuAO7QO9nLiCbB6V9GzjOxJRUjFlRHjTepjUDO3tFE16Qb9UDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:16.298937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05339","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa16f197036d0c57553788a6d10d440284d69d1b0029d54d2806e748c0852ef1","sha256:ceabb4b7ba1ce262ce463af06393c09450862573426974044daa477b05205eb4"],"state_sha256":"ba945f4d5f51dabdb1010930d9178f549b71a2cb936415c72220a864ad2e806e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rf52eriwQsAWdR1HVfczvWJ9WEo25YnZGyiEWKWR4mJj9Jmuelx+ymPtNr9gpe1S/9SD0vGvQzR/d57Unr9CDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:35:55.959720Z","bundle_sha256":"9407ada9be5de927a9695102880324c7209e0cc968d03bc35b29ff3b3240157e"}}