{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:KTAWBXOSYULDIZZ3YA42CUQSSM","short_pith_number":"pith:KTAWBXOS","canonical_record":{"source":{"id":"2207.03136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-07T07:50:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ac32dbd5ff5ab6d3ef0ba9fa723eaf941fd25db64df6c428595c38c324756154","abstract_canon_sha256":"994c55a5346d283df593158f31d760a575e608dff6758b60b8397335e32041e6"},"schema_version":"1.0"},"canonical_sha256":"54c160ddd2c51634673bc039a15212932dc8bcdb36f87ba59569f9a3f93de84c","source":{"kind":"arxiv","id":"2207.03136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.03136","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"2207.03136v1","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.03136","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"KTAWBXOSYULD","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_16","alias_value":"KTAWBXOSYULDIZZ3","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_8","alias_value":"KTAWBXOS","created_at":"2026-07-05T04:38:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:KTAWBXOSYULDIZZ3YA42CUQSSM","target":"record","payload":{"canonical_record":{"source":{"id":"2207.03136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-07T07:50:39Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ac32dbd5ff5ab6d3ef0ba9fa723eaf941fd25db64df6c428595c38c324756154","abstract_canon_sha256":"994c55a5346d283df593158f31d760a575e608dff6758b60b8397335e32041e6"},"schema_version":"1.0"},"canonical_sha256":"54c160ddd2c51634673bc039a15212932dc8bcdb36f87ba59569f9a3f93de84c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:19.307818Z","signature_b64":"HkqFrNVf4ZYlC9a5/gKQ9dRk02aWjXd2KVW/k4KDRFnWnB+iubHDsKvwobQDl46xxsFehNB7jx62uWZa4kp3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54c160ddd2c51634673bc039a15212932dc8bcdb36f87ba59569f9a3f93de84c","last_reissued_at":"2026-07-05T04:38:19.307437Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:19.307437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.03136","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":"2026-07-05T04:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibBSb+y2aC/OEYgaycSCGI6YJ/faHVCSgZHp0hqIp6lhJ8TioXVVZugtDyQeRNsO2geGEYmU3yDvRor4KeepAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:48:53.045342Z"},"content_sha256":"d929f9357bb21644da78eff1d7861a6a263713746de6770b6be79b27c363f13c","schema_version":"1.0","event_id":"sha256:d929f9357bb21644da78eff1d7861a6a263713746de6770b6be79b27c363f13c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:KTAWBXOSYULDIZZ3YA42CUQSSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exponential finite sample bounds for incomplete U-statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Andreas Maurer","submitted_at":"2022-07-07T07:50:39Z","abstract_excerpt":"Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's inequality. Applied to complete U-statistics the resulting inequality improves over the bounds of both Hoeffding and Arcones. For randomly determined subsamples it is shown, that, as soon as the their number reaches the square of the sample-size, the same order bound is obtained as for the complete statistic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.03136","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/2207.03136/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":"2026-07-05T04:38:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CObS91lRQj6UNQNU3nuYXpNPCkiAAfXhlyDnd2Lasm0wejxRcYX4EKtkDbsIXE4EPcg7W4sShRNKiNh2i58VAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T22:48:53.045849Z"},"content_sha256":"70eee318b7c0968bcf0ce2824afb6ba56bc0ea570000052ddcf6935094e5f5fc","schema_version":"1.0","event_id":"sha256:70eee318b7c0968bcf0ce2824afb6ba56bc0ea570000052ddcf6935094e5f5fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/bundle.json","state_url":"https://pith.science/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/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":"2026-08-05T22:48:53Z","links":{"resolver":"https://pith.science/pith/KTAWBXOSYULDIZZ3YA42CUQSSM","bundle":"https://pith.science/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/bundle.json","state":"https://pith.science/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTAWBXOSYULDIZZ3YA42CUQSSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KTAWBXOSYULDIZZ3YA42CUQSSM","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":"994c55a5346d283df593158f31d760a575e608dff6758b60b8397335e32041e6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-07T07:50:39Z","title_canon_sha256":"ac32dbd5ff5ab6d3ef0ba9fa723eaf941fd25db64df6c428595c38c324756154"},"schema_version":"1.0","source":{"id":"2207.03136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.03136","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"arxiv_version","alias_value":"2207.03136v1","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.03136","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_12","alias_value":"KTAWBXOSYULD","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_16","alias_value":"KTAWBXOSYULDIZZ3","created_at":"2026-07-05T04:38:19Z"},{"alias_kind":"pith_short_8","alias_value":"KTAWBXOS","created_at":"2026-07-05T04:38:19Z"}],"graph_snapshots":[{"event_id":"sha256:70eee318b7c0968bcf0ce2824afb6ba56bc0ea570000052ddcf6935094e5f5fc","target":"graph","created_at":"2026-07-05T04:38:19Z","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/2207.03136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Incomplete U-statistics have been proposed to accelerate computation. They use only a subset of the subsamples required for kernel evaluations by complete U-statistics. This paper gives a finite sample bound in the style of Bernstein's inequality. Applied to complete U-statistics the resulting inequality improves over the bounds of both Hoeffding and Arcones. For randomly determined subsamples it is shown, that, as soon as the their number reaches the square of the sample-size, the same order bound is obtained as for the complete statistic.","authors_text":"Andreas Maurer","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-07T07:50:39Z","title":"Exponential finite sample bounds for incomplete U-statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.03136","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:d929f9357bb21644da78eff1d7861a6a263713746de6770b6be79b27c363f13c","target":"record","created_at":"2026-07-05T04:38:19Z","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":"994c55a5346d283df593158f31d760a575e608dff6758b60b8397335e32041e6","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2022-07-07T07:50:39Z","title_canon_sha256":"ac32dbd5ff5ab6d3ef0ba9fa723eaf941fd25db64df6c428595c38c324756154"},"schema_version":"1.0","source":{"id":"2207.03136","kind":"arxiv","version":1}},"canonical_sha256":"54c160ddd2c51634673bc039a15212932dc8bcdb36f87ba59569f9a3f93de84c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54c160ddd2c51634673bc039a15212932dc8bcdb36f87ba59569f9a3f93de84c","first_computed_at":"2026-07-05T04:38:19.307437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:19.307437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HkqFrNVf4ZYlC9a5/gKQ9dRk02aWjXd2KVW/k4KDRFnWnB+iubHDsKvwobQDl46xxsFehNB7jx62uWZa4kp3BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:19.307818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.03136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d929f9357bb21644da78eff1d7861a6a263713746de6770b6be79b27c363f13c","sha256:70eee318b7c0968bcf0ce2824afb6ba56bc0ea570000052ddcf6935094e5f5fc"],"state_sha256":"be162f462a19da9969230e7472b423fa1e73b9b57d7e15bce62936f6928af7f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6EXHIgAnScJHaY9cq1SEAEh6o65Glsg8mAdcDk7wMWUC31ILQi+tXTJUqGOr4dtERxE1Q/z4NK3C5gB4XLmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T22:48:53.049637Z","bundle_sha256":"217cf64fcd24b097c59c86a154183badd4fe182c0832efe3546d83a8b7d2cfb2"}}