{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:SSIDJ2PKMR7QGZCQ2EA3PGUZ2R","short_pith_number":"pith:SSIDJ2PK","canonical_record":{"source":{"id":"2406.12437","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-18T09:38:51Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"6e674d148afdf1a9a5dc80fe325638e114405a266cd269f0038ea6ca51eba53e","abstract_canon_sha256":"6a3dc00e06dac2426737289f4af4d66bb2b9aaab54aa037cf6459245c5e94746"},"schema_version":"1.0"},"canonical_sha256":"949034e9ea647f036450d101b79a99d46091e8fe49f11c217eebb86eab979b54","source":{"kind":"arxiv","id":"2406.12437","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12437","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12437v1","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12437","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"SSIDJ2PKMR7Q","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"SSIDJ2PKMR7QGZCQ","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"SSIDJ2PK","created_at":"2026-07-05T08:33:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:SSIDJ2PKMR7QGZCQ2EA3PGUZ2R","target":"record","payload":{"canonical_record":{"source":{"id":"2406.12437","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-18T09:38:51Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"6e674d148afdf1a9a5dc80fe325638e114405a266cd269f0038ea6ca51eba53e","abstract_canon_sha256":"6a3dc00e06dac2426737289f4af4d66bb2b9aaab54aa037cf6459245c5e94746"},"schema_version":"1.0"},"canonical_sha256":"949034e9ea647f036450d101b79a99d46091e8fe49f11c217eebb86eab979b54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:46.256677Z","signature_b64":"nxKvMjX4E5QVA6CU6/1oa+VV3Y1AK6CKrxzIGD8pEQK61EL3Hb39PTcbijukpJa2W06md17ksGm58feVsvmaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"949034e9ea647f036450d101b79a99d46091e8fe49f11c217eebb86eab979b54","last_reissued_at":"2026-07-05T08:33:46.256237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:46.256237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.12437","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":"2026-07-05T08:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"67o4HRXTNpUmmH2HQ8BQTdpqZWlEGt6tVTpVLfvFqyXpnsbZlFPno18KvsOh1+yuJ0cxeE6t7WHNYkJm/dsjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:17:52.393783Z"},"content_sha256":"7a46b5ba67b3f3841ffecbaf5d5b27468e3eadc3839021ddc94158d38253fd04","schema_version":"1.0","event_id":"sha256:7a46b5ba67b3f3841ffecbaf5d5b27468e3eadc3839021ddc94158d38253fd04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:SSIDJ2PKMR7QGZCQ2EA3PGUZ2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Kevin Han Huang, Peter Orbanz","submitted_at":"2024-06-18T09:38:51Z","abstract_excerpt":"We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\\mathbb{R}^{d(n)}$, whose $\\nu$-th moments exist for ${\\nu > 2}$, and provide tight bounds on the error of approximating both statistics by a quadratic form of Gaussians. In the case ${\\nu=3}$, the error of approximation is $\\Theta(n^{-1/12})$. The proof adapts a result of Huang, Austern and Orbanz [12] to U- and V-statistics. The lower bound for U-statistics is a simple example of the concept of variance domination used in [12]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12437","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.12437/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyvlQjQODDYIo36bjdnO6DoYazXCEDYQgwcBd9s56joSt9OHsW/fgv+6Dsy2y+sUdg4lhhW0EesKxrkF9/CECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T13:17:52.394840Z"},"content_sha256":"d2cabdecc1db3b8f32cc9e548bcd11cf96f5eacbc6c802ee0839ab8b537dcb46","schema_version":"1.0","event_id":"sha256:d2cabdecc1db3b8f32cc9e548bcd11cf96f5eacbc6c802ee0839ab8b537dcb46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/bundle.json","state_url":"https://pith.science/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/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":"2026-08-13T13:17:52Z","links":{"resolver":"https://pith.science/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R","bundle":"https://pith.science/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/bundle.json","state":"https://pith.science/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSIDJ2PKMR7QGZCQ2EA3PGUZ2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SSIDJ2PKMR7QGZCQ2EA3PGUZ2R","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":"6a3dc00e06dac2426737289f4af4d66bb2b9aaab54aa037cf6459245c5e94746","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-18T09:38:51Z","title_canon_sha256":"6e674d148afdf1a9a5dc80fe325638e114405a266cd269f0038ea6ca51eba53e"},"schema_version":"1.0","source":{"id":"2406.12437","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.12437","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"2406.12437v1","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.12437","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"SSIDJ2PKMR7Q","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"SSIDJ2PKMR7QGZCQ","created_at":"2026-07-05T08:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"SSIDJ2PK","created_at":"2026-07-05T08:33:46Z"}],"graph_snapshots":[{"event_id":"sha256:d2cabdecc1db3b8f32cc9e548bcd11cf96f5eacbc6c802ee0839ab8b537dcb46","target":"graph","created_at":"2026-07-05T08:33:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2406.12437/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct examples of degree-two U- and V-statistics of $n$ i.i.d.~heavy-tailed random vectors in $\\mathbb{R}^{d(n)}$, whose $\\nu$-th moments exist for ${\\nu > 2}$, and provide tight bounds on the error of approximating both statistics by a quadratic form of Gaussians. In the case ${\\nu=3}$, the error of approximation is $\\Theta(n^{-1/12})$. The proof adapts a result of Huang, Austern and Orbanz [12] to U- and V-statistics. The lower bound for U-statistics is a simple example of the concept of variance domination used in [12].","authors_text":"Kevin Han Huang, Peter Orbanz","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-18T09:38:51Z","title":"Slow rates of approximation of U-statistics and V-statistics by quadratic forms of Gaussians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.12437","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":"sha256:7a46b5ba67b3f3841ffecbaf5d5b27468e3eadc3839021ddc94158d38253fd04","target":"record","created_at":"2026-07-05T08:33:46Z","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":"6a3dc00e06dac2426737289f4af4d66bb2b9aaab54aa037cf6459245c5e94746","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2024-06-18T09:38:51Z","title_canon_sha256":"6e674d148afdf1a9a5dc80fe325638e114405a266cd269f0038ea6ca51eba53e"},"schema_version":"1.0","source":{"id":"2406.12437","kind":"arxiv","version":1}},"canonical_sha256":"949034e9ea647f036450d101b79a99d46091e8fe49f11c217eebb86eab979b54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"949034e9ea647f036450d101b79a99d46091e8fe49f11c217eebb86eab979b54","first_computed_at":"2026-07-05T08:33:46.256237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:46.256237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxKvMjX4E5QVA6CU6/1oa+VV3Y1AK6CKrxzIGD8pEQK61EL3Hb39PTcbijukpJa2W06md17ksGm58feVsvmaDw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:46.256677Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.12437","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a46b5ba67b3f3841ffecbaf5d5b27468e3eadc3839021ddc94158d38253fd04","sha256:d2cabdecc1db3b8f32cc9e548bcd11cf96f5eacbc6c802ee0839ab8b537dcb46"],"state_sha256":"db547f7d8149c139cb6ab895dfcdf3b063ec17516526a3af2e873a49f973f5b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L7qxHGsit3BqVisroOMZIOtK8I2tRTcu+TTynkurEo0YPXjG++o3ON/WWdf1dN0O/Ij3JtAxj4743EaxtcXmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T13:17:52.402045Z","bundle_sha256":"88f283d42d75274f5e28aaa917614f8c67b56c4d6882a3578c6ee51d4fbce26e"}}