{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FTPQMBZXQVMLQ7C2ILCR3IVWXC","short_pith_number":"pith:FTPQMBZX","canonical_record":{"source":{"id":"1701.06191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T17:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"48b40acf94190fd270faabce62bc4c316f61d1d7599de697474f9bde6181c14d","abstract_canon_sha256":"01abe12f59493a769b3ebb604f24b6bb762b0b32bfd399b019aeaee66c18d0cc"},"schema_version":"1.0"},"canonical_sha256":"2cdf0607378558b87c5a42c51da2b6b8ba36040f1a308054e7c0a5126b694fbf","source":{"kind":"arxiv","id":"1701.06191","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06191","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06191v2","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06191","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"FTPQMBZXQVML","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FTPQMBZXQVMLQ7C2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FTPQMBZX","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FTPQMBZXQVMLQ7C2ILCR3IVWXC","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T17:21:56Z","cross_cats_sorted":[],"title_canon_sha256":"48b40acf94190fd270faabce62bc4c316f61d1d7599de697474f9bde6181c14d","abstract_canon_sha256":"01abe12f59493a769b3ebb604f24b6bb762b0b32bfd399b019aeaee66c18d0cc"},"schema_version":"1.0"},"canonical_sha256":"2cdf0607378558b87c5a42c51da2b6b8ba36040f1a308054e7c0a5126b694fbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:42.156364Z","signature_b64":"MLuLpg1oyURBl8qq9WRFesZ1dDdKRGzyL2KL+5Qd5SZu3xLXgz9ShQ3WGlqkVsX1ikCNBNzhmuk1wLjfTviTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cdf0607378558b87c5a42c51da2b6b8ba36040f1a308054e7c0a5126b694fbf","last_reissued_at":"2026-05-18T00:44:42.155889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:42.155889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06191","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIC7VvbJWBULPHtN/OzMojaJFEhL08VXLVTkIbLj85g2CCWJlxlR2E3JcqdFukfdEo3WyKMolVoLIY4uSSSOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:36.061053Z"},"content_sha256":"9abb78ee2510316c620cc2eec93c89c13e29403ebdd0974c23a1fe026cd7d506","schema_version":"1.0","event_id":"sha256:9abb78ee2510316c620cc2eec93c89c13e29403ebdd0974c23a1fe026cd7d506"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FTPQMBZXQVMLQ7C2ILCR3IVWXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bernstein-type inequality for functions of bounded interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Maurer","submitted_at":"2017-01-22T17:21:56Z","abstract_excerpt":"We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06191","kind":"arxiv","version":2},"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":"2026-05-18T00:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f533KuPGVeoGo6upZ3jwh9gLJg8KvmFX8MUNzq8kr7VYD0QMcl7jF0xuUBkaMuzdK8adzT1r3hb57zYXM+v9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:36.061410Z"},"content_sha256":"d830d3d7f6d17e6fef2e63ad65bf25e17ffdfb6e95e6e57d2fef856dec3286bc","schema_version":"1.0","event_id":"sha256:d830d3d7f6d17e6fef2e63ad65bf25e17ffdfb6e95e6e57d2fef856dec3286bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/bundle.json","state_url":"https://pith.science/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/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":"2026-06-20T04:05:36Z","links":{"resolver":"https://pith.science/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC","bundle":"https://pith.science/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/bundle.json","state":"https://pith.science/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FTPQMBZXQVMLQ7C2ILCR3IVWXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FTPQMBZXQVMLQ7C2ILCR3IVWXC","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":"01abe12f59493a769b3ebb604f24b6bb762b0b32bfd399b019aeaee66c18d0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T17:21:56Z","title_canon_sha256":"48b40acf94190fd270faabce62bc4c316f61d1d7599de697474f9bde6181c14d"},"schema_version":"1.0","source":{"id":"1701.06191","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06191","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06191v2","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06191","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"FTPQMBZXQVML","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FTPQMBZXQVMLQ7C2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FTPQMBZX","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:d830d3d7f6d17e6fef2e63ad65bf25e17ffdfb6e95e6e57d2fef856dec3286bc","target":"graph","created_at":"2026-05-18T00:44:42Z","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 give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the other arguments. Applications sharpen existing bounds for U-statistics and the generalization error of regularized least squares.","authors_text":"Andreas Maurer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T17:21:56Z","title":"A Bernstein-type inequality for functions of bounded interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06191","kind":"arxiv","version":2},"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":"sha256:9abb78ee2510316c620cc2eec93c89c13e29403ebdd0974c23a1fe026cd7d506","target":"record","created_at":"2026-05-18T00:44:42Z","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":"01abe12f59493a769b3ebb604f24b6bb762b0b32bfd399b019aeaee66c18d0cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-22T17:21:56Z","title_canon_sha256":"48b40acf94190fd270faabce62bc4c316f61d1d7599de697474f9bde6181c14d"},"schema_version":"1.0","source":{"id":"1701.06191","kind":"arxiv","version":2}},"canonical_sha256":"2cdf0607378558b87c5a42c51da2b6b8ba36040f1a308054e7c0a5126b694fbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cdf0607378558b87c5a42c51da2b6b8ba36040f1a308054e7c0a5126b694fbf","first_computed_at":"2026-05-18T00:44:42.155889Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:42.155889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MLuLpg1oyURBl8qq9WRFesZ1dDdKRGzyL2KL+5Qd5SZu3xLXgz9ShQ3WGlqkVsX1ikCNBNzhmuk1wLjfTviTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:42.156364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06191","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9abb78ee2510316c620cc2eec93c89c13e29403ebdd0974c23a1fe026cd7d506","sha256:d830d3d7f6d17e6fef2e63ad65bf25e17ffdfb6e95e6e57d2fef856dec3286bc"],"state_sha256":"6bed665950f579cdc8ba7816be6891f48cc3b8b21723f6b33b69b12fcd5bc2bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sz7ZlCOHcjy16x8BbWwmgJgx8Z5j0IyWjQ43vzG3XpYs1Fw8ckWefa11CXrCWEKROLi8tAAH/I147EX2dPXWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:05:36.063330Z","bundle_sha256":"54c4fdc57f256a6881ecbc0c708d24819fc3c2092e33b0b7b5d56883932ca2fc"}}