{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:76LFUYITINZU24ZR54ZJX3XDL2","short_pith_number":"pith:76LFUYIT","canonical_record":{"source":{"id":"1803.03934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-11T10:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"e32f8ad69ef108a684728a543d1147b1d1a048020d4dd36c044e611d0279db66","abstract_canon_sha256":"1f6ae57f472a74cbb70b2dc6e4bf77b069d27c26dc1615a401e4f09aca53a81e"},"schema_version":"1.0"},"canonical_sha256":"ff965a611343734d7331ef329beee35e832d5071de2e9a4e29d6f1c2b2c0c7ee","source":{"kind":"arxiv","id":"1803.03934","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03934","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03934v1","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03934","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"76LFUYITINZU","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"76LFUYITINZU24ZR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"76LFUYIT","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:76LFUYITINZU24ZR54ZJX3XDL2","target":"record","payload":{"canonical_record":{"source":{"id":"1803.03934","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-11T10:28:45Z","cross_cats_sorted":[],"title_canon_sha256":"e32f8ad69ef108a684728a543d1147b1d1a048020d4dd36c044e611d0279db66","abstract_canon_sha256":"1f6ae57f472a74cbb70b2dc6e4bf77b069d27c26dc1615a401e4f09aca53a81e"},"schema_version":"1.0"},"canonical_sha256":"ff965a611343734d7331ef329beee35e832d5071de2e9a4e29d6f1c2b2c0c7ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:33.415908Z","signature_b64":"BJhQe/0Xm9GzdaiL5e2CZH/AXxy8JLVS8MIRfQBa4cchfDwT40U0HWx8/rntdaSsH1mr7rxUBz5D34H1hGSXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff965a611343734d7331ef329beee35e832d5071de2e9a4e29d6f1c2b2c0c7ee","last_reissued_at":"2026-05-18T00:21:33.415294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:33.415294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.03934","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":"2026-05-18T00:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niXJsBpz43vayDgMT3Og0RhEh3FN7qA64K0n4HzAPQciJ2+Te4rPeXQPWgq+Ft+Far29HTGlV4wtJC22ole4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:41:40.420178Z"},"content_sha256":"48a237a9b4d5a377d07d6a7f90c572cad94e3dc2bd6a0e4697f8726d6fc8727a","schema_version":"1.0","event_id":"sha256:48a237a9b4d5a377d07d6a7f90c572cad94e3dc2bd6a0e4697f8726d6fc8727a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:76LFUYITINZU24ZR54ZJX3XDL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical bounds for functions with weak interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Andreas Maurer, Massimiliano Pontil","submitted_at":"2018-03-11T10:28:45Z","abstract_excerpt":"We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error functionals of L2-regularized algorithms and Gibbs algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03934","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":"2026-05-18T00:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrykRqq+ygMC8V+gWh4fLYxgTfR0ctbFviIbnXNuQOfqBFYP2eCvumLiMd3NjdSUKZK6Z84tQQ6Orh3w0tDaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:41:40.420543Z"},"content_sha256":"9d194e191853c44cc2f2d8c1d5ff75edc6da2b2c312a63e444d76e54931ecb83","schema_version":"1.0","event_id":"sha256:9d194e191853c44cc2f2d8c1d5ff75edc6da2b2c312a63e444d76e54931ecb83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/76LFUYITINZU24ZR54ZJX3XDL2/bundle.json","state_url":"https://pith.science/pith/76LFUYITINZU24ZR54ZJX3XDL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/76LFUYITINZU24ZR54ZJX3XDL2/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":"2026-06-20T08:41:40Z","links":{"resolver":"https://pith.science/pith/76LFUYITINZU24ZR54ZJX3XDL2","bundle":"https://pith.science/pith/76LFUYITINZU24ZR54ZJX3XDL2/bundle.json","state":"https://pith.science/pith/76LFUYITINZU24ZR54ZJX3XDL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/76LFUYITINZU24ZR54ZJX3XDL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:76LFUYITINZU24ZR54ZJX3XDL2","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":"1f6ae57f472a74cbb70b2dc6e4bf77b069d27c26dc1615a401e4f09aca53a81e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-11T10:28:45Z","title_canon_sha256":"e32f8ad69ef108a684728a543d1147b1d1a048020d4dd36c044e611d0279db66"},"schema_version":"1.0","source":{"id":"1803.03934","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03934","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03934v1","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03934","created_at":"2026-05-18T00:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"76LFUYITINZU","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"76LFUYITINZU24ZR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"76LFUYIT","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:9d194e191853c44cc2f2d8c1d5ff75edc6da2b2c312a63e444d76e54931ecb83","target":"graph","created_at":"2026-05-18T00:21:33Z","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 provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error functionals of L2-regularized algorithms and Gibbs algorithms.","authors_text":"Andreas Maurer, Massimiliano Pontil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-11T10:28:45Z","title":"Empirical bounds for functions with weak interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03934","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":"sha256:48a237a9b4d5a377d07d6a7f90c572cad94e3dc2bd6a0e4697f8726d6fc8727a","target":"record","created_at":"2026-05-18T00:21:33Z","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":"1f6ae57f472a74cbb70b2dc6e4bf77b069d27c26dc1615a401e4f09aca53a81e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-11T10:28:45Z","title_canon_sha256":"e32f8ad69ef108a684728a543d1147b1d1a048020d4dd36c044e611d0279db66"},"schema_version":"1.0","source":{"id":"1803.03934","kind":"arxiv","version":1}},"canonical_sha256":"ff965a611343734d7331ef329beee35e832d5071de2e9a4e29d6f1c2b2c0c7ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff965a611343734d7331ef329beee35e832d5071de2e9a4e29d6f1c2b2c0c7ee","first_computed_at":"2026-05-18T00:21:33.415294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:33.415294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BJhQe/0Xm9GzdaiL5e2CZH/AXxy8JLVS8MIRfQBa4cchfDwT40U0HWx8/rntdaSsH1mr7rxUBz5D34H1hGSXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:33.415908Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03934","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48a237a9b4d5a377d07d6a7f90c572cad94e3dc2bd6a0e4697f8726d6fc8727a","sha256:9d194e191853c44cc2f2d8c1d5ff75edc6da2b2c312a63e444d76e54931ecb83"],"state_sha256":"98e04d353887a51e18830e207eea89719e2652c55a5f5a8c1a9400f5dc88c732"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9pln00/Ki+OEYS4+1x+8v2adHK5NCezTqM9ACMRtPHvUKi+I9naGk7rnPO5laJbiZq+8oMsfvGzULnR9QiDHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:41:40.422422Z","bundle_sha256":"7126e62f0c0b0485bfc87ef05e1766275a60575c38bbbd1ae447b987d7a55f1d"}}