{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:I74R2AG7XBIA6VFON7MWI225WX","short_pith_number":"pith:I74R2AG7","canonical_record":{"source":{"id":"2404.06457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-04-09T16:56:48Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"6415797fc3280624544dbd7235e2a85d5347fc22db88e8f2a5238f880fc5578e","abstract_canon_sha256":"462583eab21ef75595f267280e895ea249bab4b62b76841410ceb8539c416363"},"schema_version":"1.0"},"canonical_sha256":"47f91d00dfb8500f54ae6fd9646b5db5d493f35263f09b1f40ae1ff277eb9cce","source":{"kind":"arxiv","id":"2404.06457","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06457","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06457v3","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06457","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_12","alias_value":"I74R2AG7XBIA","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_16","alias_value":"I74R2AG7XBIA6VFO","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_8","alias_value":"I74R2AG7","created_at":"2026-07-05T11:50:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:I74R2AG7XBIA6VFON7MWI225WX","target":"record","payload":{"canonical_record":{"source":{"id":"2404.06457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-04-09T16:56:48Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"6415797fc3280624544dbd7235e2a85d5347fc22db88e8f2a5238f880fc5578e","abstract_canon_sha256":"462583eab21ef75595f267280e895ea249bab4b62b76841410ceb8539c416363"},"schema_version":"1.0"},"canonical_sha256":"47f91d00dfb8500f54ae6fd9646b5db5d493f35263f09b1f40ae1ff277eb9cce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:50:26.739157Z","signature_b64":"Db3MZIBt5ubFVu0XNeU2HUhrFoVnbOjcgEIqenOL+5DQzqoA0EQhmdF9lxiob38GvW1oK9PD+VzYVvQCE494Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47f91d00dfb8500f54ae6fd9646b5db5d493f35263f09b1f40ae1ff277eb9cce","last_reissued_at":"2026-07-05T11:50:26.738590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:50:26.738590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.06457","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:50:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24SAY4ZQe+joWvaxSdAxPsGQJ2QE/SRkKbjgRdg9qBDsa0Gvr95cdyvhguUzU7HDemZSKsyTKP47SdlniD82Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:53:59.189650Z"},"content_sha256":"eafc0a03d1586f2770d0c8499cbb6784932335c170524a4120856b4817a400d7","schema_version":"1.0","event_id":"sha256:eafc0a03d1586f2770d0c8499cbb6784932335c170524a4120856b4817a400d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:I74R2AG7XBIA6VFON7MWI225WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hoeffding and Bernstein inequalities for weighted sums of exchangeable random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Rina Foygel Barber","submitted_at":"2024-04-09T16:56:48Z","abstract_excerpt":"The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from some distribution (and are therefore exchangeable). In contrast to the existing literature on this problem, our results provide a natural unified view of both the i.i.d. and the exchangeable setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06457","kind":"arxiv","version":3},"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/2404.06457/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":"2026-07-05T11:50:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rC6yahuclmcY5PCzqi3bu+/exLZomfpX0pt4OhXahShlEX4nYo4/8PUl4JGtc0lvWu5YQXHw2Guv0BcwZDIbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:53:59.190327Z"},"content_sha256":"23b708aa0362d3f14206bbe41b1cf5ae88eb532ac2115db291c694301f78066f","schema_version":"1.0","event_id":"sha256:23b708aa0362d3f14206bbe41b1cf5ae88eb532ac2115db291c694301f78066f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I74R2AG7XBIA6VFON7MWI225WX/bundle.json","state_url":"https://pith.science/pith/I74R2AG7XBIA6VFON7MWI225WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I74R2AG7XBIA6VFON7MWI225WX/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":"2026-08-06T07:53:59Z","links":{"resolver":"https://pith.science/pith/I74R2AG7XBIA6VFON7MWI225WX","bundle":"https://pith.science/pith/I74R2AG7XBIA6VFON7MWI225WX/bundle.json","state":"https://pith.science/pith/I74R2AG7XBIA6VFON7MWI225WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I74R2AG7XBIA6VFON7MWI225WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I74R2AG7XBIA6VFON7MWI225WX","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":"462583eab21ef75595f267280e895ea249bab4b62b76841410ceb8539c416363","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-04-09T16:56:48Z","title_canon_sha256":"6415797fc3280624544dbd7235e2a85d5347fc22db88e8f2a5238f880fc5578e"},"schema_version":"1.0","source":{"id":"2404.06457","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.06457","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"arxiv_version","alias_value":"2404.06457v3","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06457","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_12","alias_value":"I74R2AG7XBIA","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_16","alias_value":"I74R2AG7XBIA6VFO","created_at":"2026-07-05T11:50:26Z"},{"alias_kind":"pith_short_8","alias_value":"I74R2AG7","created_at":"2026-07-05T11:50:26Z"}],"graph_snapshots":[{"event_id":"sha256:23b708aa0362d3f14206bbe41b1cf5ae88eb532ac2115db291c694301f78066f","target":"graph","created_at":"2026-07-05T11:50:26Z","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/2404.06457/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from some distribution (and are therefore exchangeable). In contrast to the existing literature on this problem, our results provide a natural unified view of both the i.i.d. and the exchangeable setting.","authors_text":"Rina Foygel Barber","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-04-09T16:56:48Z","title":"Hoeffding and Bernstein inequalities for weighted sums of exchangeable random variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06457","kind":"arxiv","version":3},"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:eafc0a03d1586f2770d0c8499cbb6784932335c170524a4120856b4817a400d7","target":"record","created_at":"2026-07-05T11:50:26Z","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":"462583eab21ef75595f267280e895ea249bab4b62b76841410ceb8539c416363","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-04-09T16:56:48Z","title_canon_sha256":"6415797fc3280624544dbd7235e2a85d5347fc22db88e8f2a5238f880fc5578e"},"schema_version":"1.0","source":{"id":"2404.06457","kind":"arxiv","version":3}},"canonical_sha256":"47f91d00dfb8500f54ae6fd9646b5db5d493f35263f09b1f40ae1ff277eb9cce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47f91d00dfb8500f54ae6fd9646b5db5d493f35263f09b1f40ae1ff277eb9cce","first_computed_at":"2026-07-05T11:50:26.738590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:50:26.738590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Db3MZIBt5ubFVu0XNeU2HUhrFoVnbOjcgEIqenOL+5DQzqoA0EQhmdF9lxiob38GvW1oK9PD+VzYVvQCE494Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:50:26.739157Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.06457","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eafc0a03d1586f2770d0c8499cbb6784932335c170524a4120856b4817a400d7","sha256:23b708aa0362d3f14206bbe41b1cf5ae88eb532ac2115db291c694301f78066f"],"state_sha256":"88835add2d4f87f77981c12a2e6319d359225ff224ad576cae0848a413fff4aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xd6UD2r+2i3mYoUscZmgWM+qKoLpvtNm1sT5J9JHU2SPkzQ+G01jnqxntkki6Z2TA4o8sLSLOQ4bcDDEnfLlAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T07:53:59.196084Z","bundle_sha256":"a465fcfc9d8e180de550f3f2bc0dec5839a25355552f907db769b07be1da506c"}}