{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FUNVUPXOCRQKPCXWNYN2L2LSYW","short_pith_number":"pith:FUNVUPXO","canonical_record":{"source":{"id":"2410.10418","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T12:10:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1ee85b38a4d2af1b525823779d623a334ef481bf494beaca083ce4e009c15ea9","abstract_canon_sha256":"a7c772f42982a6e3b6c20d3cb4fd5c00513c3aa63a64edbde92d17b5638f1d7d"},"schema_version":"1.0"},"canonical_sha256":"2d1b5a3eee1460a78af66e1ba5e972c59f068eefce25678fb38ccccf5fb0722c","source":{"kind":"arxiv","id":"2410.10418","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.10418","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.10418v3","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10418","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_12","alias_value":"FUNVUPXOCRQK","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_16","alias_value":"FUNVUPXOCRQKPCXW","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_8","alias_value":"FUNVUPXO","created_at":"2026-07-05T11:19:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FUNVUPXOCRQKPCXWNYN2L2LSYW","target":"record","payload":{"canonical_record":{"source":{"id":"2410.10418","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T12:10:52Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"1ee85b38a4d2af1b525823779d623a334ef481bf494beaca083ce4e009c15ea9","abstract_canon_sha256":"a7c772f42982a6e3b6c20d3cb4fd5c00513c3aa63a64edbde92d17b5638f1d7d"},"schema_version":"1.0"},"canonical_sha256":"2d1b5a3eee1460a78af66e1ba5e972c59f068eefce25678fb38ccccf5fb0722c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:19:21.650021Z","signature_b64":"GXmJnFi5+7ZW9MIgkenZ2anYkyhjwGOqmuc/rG2DUHIPvjU+bpCQ4YiFWkmroJYhgxw9RzN1EdI2kdi58zZ5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d1b5a3eee1460a78af66e1ba5e972c59f068eefce25678fb38ccccf5fb0722c","last_reissued_at":"2026-07-05T11:19:21.649493Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:19:21.649493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.10418","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":"2026-07-05T11:19:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mTno3seGvDvCiJfHwEgaUhoQKwCXD8qCe82wxTXKp4a+Oan73G7wSem5YKyWxXNrDw6uzorDQPMu/r/3p43HBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:20:49.135351Z"},"content_sha256":"f77ac363f19370cb67865489489e45cf4cb25d526cbc3ce4e9041fb57d06396a","schema_version":"1.0","event_id":"sha256:f77ac363f19370cb67865489489e45cf4cb25d526cbc3ce4e9041fb57d06396a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FUNVUPXOCRQKPCXWNYN2L2LSYW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unified Breakdown Analysis for Byzantine Robust Gossip","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Aymeric Dieuleveut, Hadrien Hendrikx, Renaud Gaucher","submitted_at":"2024-10-14T12:10:52Z","abstract_excerpt":"In decentralized machine learning, different devices communicate in a peer-to-peer manner to collaboratively learn from each other's data. Such approaches are vulnerable to misbehaving (or Byzantine) devices. We introduce F-RG, a general framework for building robust decentralized algorithms with guarantees arising from robust-sum-like aggregation rules F. We then investigate the notion of *breakdown point*, and show an upper bound on the number of adversaries that decentralized algorithms can tolerate. We introduce a practical robust aggregation rule, coined CS+, such that CS+-RG has a near-o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10418","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/2410.10418/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":"2026-07-05T11:19:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m1ej/IcHZf/mTozRNPo4Utb4E1Q+6G8W+eye/urDNXnFsM2vwYDbF8RYeHNsewGsvPLeedNzMjh16EvU43dIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:20:49.135861Z"},"content_sha256":"da84b1df62349747898e3cef06f3eac71e5ed7c52565dc83f3698afec49ac592","schema_version":"1.0","event_id":"sha256:da84b1df62349747898e3cef06f3eac71e5ed7c52565dc83f3698afec49ac592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/bundle.json","state_url":"https://pith.science/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/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":"2026-08-09T14:20:49Z","links":{"resolver":"https://pith.science/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW","bundle":"https://pith.science/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/bundle.json","state":"https://pith.science/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FUNVUPXOCRQKPCXWNYN2L2LSYW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FUNVUPXOCRQKPCXWNYN2L2LSYW","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":"a7c772f42982a6e3b6c20d3cb4fd5c00513c3aa63a64edbde92d17b5638f1d7d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T12:10:52Z","title_canon_sha256":"1ee85b38a4d2af1b525823779d623a334ef481bf494beaca083ce4e009c15ea9"},"schema_version":"1.0","source":{"id":"2410.10418","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.10418","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.10418v3","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.10418","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_12","alias_value":"FUNVUPXOCRQK","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_16","alias_value":"FUNVUPXOCRQKPCXW","created_at":"2026-07-05T11:19:21Z"},{"alias_kind":"pith_short_8","alias_value":"FUNVUPXO","created_at":"2026-07-05T11:19:21Z"}],"graph_snapshots":[{"event_id":"sha256:da84b1df62349747898e3cef06f3eac71e5ed7c52565dc83f3698afec49ac592","target":"graph","created_at":"2026-07-05T11:19:21Z","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/2410.10418/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In decentralized machine learning, different devices communicate in a peer-to-peer manner to collaboratively learn from each other's data. Such approaches are vulnerable to misbehaving (or Byzantine) devices. We introduce F-RG, a general framework for building robust decentralized algorithms with guarantees arising from robust-sum-like aggregation rules F. We then investigate the notion of *breakdown point*, and show an upper bound on the number of adversaries that decentralized algorithms can tolerate. We introduce a practical robust aggregation rule, coined CS+, such that CS+-RG has a near-o","authors_text":"Aymeric Dieuleveut, Hadrien Hendrikx, Renaud Gaucher","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T12:10:52Z","title":"Unified Breakdown Analysis for Byzantine Robust Gossip"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.10418","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:f77ac363f19370cb67865489489e45cf4cb25d526cbc3ce4e9041fb57d06396a","target":"record","created_at":"2026-07-05T11:19:21Z","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":"a7c772f42982a6e3b6c20d3cb4fd5c00513c3aa63a64edbde92d17b5638f1d7d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-10-14T12:10:52Z","title_canon_sha256":"1ee85b38a4d2af1b525823779d623a334ef481bf494beaca083ce4e009c15ea9"},"schema_version":"1.0","source":{"id":"2410.10418","kind":"arxiv","version":3}},"canonical_sha256":"2d1b5a3eee1460a78af66e1ba5e972c59f068eefce25678fb38ccccf5fb0722c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d1b5a3eee1460a78af66e1ba5e972c59f068eefce25678fb38ccccf5fb0722c","first_computed_at":"2026-07-05T11:19:21.649493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:19:21.649493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GXmJnFi5+7ZW9MIgkenZ2anYkyhjwGOqmuc/rG2DUHIPvjU+bpCQ4YiFWkmroJYhgxw9RzN1EdI2kdi58zZ5CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:19:21.650021Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.10418","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f77ac363f19370cb67865489489e45cf4cb25d526cbc3ce4e9041fb57d06396a","sha256:da84b1df62349747898e3cef06f3eac71e5ed7c52565dc83f3698afec49ac592"],"state_sha256":"f4981e555bfe7643122c68d334adbc6f67521c9830dad2b3821584083e84839d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NhgtB8omZ/Dzgfp/VCcLB61/QhZo6gXAd1aiox+Ux4Px14Itwl16402iddBac2C4L8oLo87NNXc56gl9vQvCDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:20:49.139150Z","bundle_sha256":"70073639fbab64b729caf0e6c696ae4e0d27b581f0cb495eb5b90906ddc3c329"}}