{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CBU5NJUAGP6IB5YGIZLAUFW2SG","short_pith_number":"pith:CBU5NJUA","canonical_record":{"source":{"id":"2106.08315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T17:45:51Z","cross_cats_sorted":["cs.DC","cs.LG"],"title_canon_sha256":"796ac81ab30b7d3b6e24dac92b62b8a88495743c216a3b017a113efa6c97c35a","abstract_canon_sha256":"eefd2d0be0f7f509cef45c0b8b5578c6a8d661687fb7f8b627c82b9265d13d92"},"schema_version":"1.0"},"canonical_sha256":"1069d6a68033fc80f70646560a16da91a4068f4142e709ec5473d72b1f1a00b4","source":{"kind":"arxiv","id":"2106.08315","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.08315","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"arxiv_version","alias_value":"2106.08315v3","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.08315","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_12","alias_value":"CBU5NJUAGP6I","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_16","alias_value":"CBU5NJUAGP6IB5YG","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_8","alias_value":"CBU5NJUA","created_at":"2026-07-05T05:57:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CBU5NJUAGP6IB5YGIZLAUFW2SG","target":"record","payload":{"canonical_record":{"source":{"id":"2106.08315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T17:45:51Z","cross_cats_sorted":["cs.DC","cs.LG"],"title_canon_sha256":"796ac81ab30b7d3b6e24dac92b62b8a88495743c216a3b017a113efa6c97c35a","abstract_canon_sha256":"eefd2d0be0f7f509cef45c0b8b5578c6a8d661687fb7f8b627c82b9265d13d92"},"schema_version":"1.0"},"canonical_sha256":"1069d6a68033fc80f70646560a16da91a4068f4142e709ec5473d72b1f1a00b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:09.277284Z","signature_b64":"VXO+WE2t8FDZdxRC6VvGErMd9H1R4fntTQFj+BlT7XAMhVt5g53grHvXn5uU1KaxWGs0QZYC9EVt4/EfruJxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1069d6a68033fc80f70646560a16da91a4068f4142e709ec5473d72b1f1a00b4","last_reissued_at":"2026-07-05T05:57:09.276897Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:09.276897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.08315","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":"2026-07-05T05:57:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+ZtXqPrtsX5TZsOmqeW/zOWoPD3d++bSoWGiFNsrEVsXqVuHEdf8Gm8ELG5LUcUjztClRF6MhTkQSTJrzH6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:43:18.505955Z"},"content_sha256":"711b3ccc900e688cc07ae48c5b27b0707db69d5723cac3780d31aa7352a98890","schema_version":"1.0","event_id":"sha256:711b3ccc900e688cc07ae48c5b27b0707db69d5723cac3780d31aa7352a98890"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CBU5NJUAGP6IB5YGIZLAUFW2SG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decentralized Local Stochastic Extra-Gradient for Variational Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.LG"],"primary_cat":"math.OC","authors_text":"Aleksandr Beznosikov, Alexander Gasnikov, Anastasia Koloskova, Pavel Dvurechensky, Sebastian U Stich, Valentin Samokhin","submitted_at":"2021-06-15T17:45:51Z","abstract_excerpt":"We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentralized calculations with time-varying networks and centralized topologies commonly used in Federated Learning. Moreover, multiple local updates on the workers can be made for reducing the communication frequency between the workers. We extend the stochastic extragradient method to this very general se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08315","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/2106.08315/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":"2026-07-05T05:57:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K84AfnOUa3L29fF7jtHVE1Tvy1kmPgeu0RyRtLBFx8qTy/j6BQaucYRl/Z9UqyeMOgQ3ONbmTYFQ0qeohR/SDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:43:18.506638Z"},"content_sha256":"224b141f08471faa166e75f436bdb11dc2f78819e83c0038c1f1e22033703b69","schema_version":"1.0","event_id":"sha256:224b141f08471faa166e75f436bdb11dc2f78819e83c0038c1f1e22033703b69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/bundle.json","state_url":"https://pith.science/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/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":"2026-08-11T03:43:18Z","links":{"resolver":"https://pith.science/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG","bundle":"https://pith.science/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/bundle.json","state":"https://pith.science/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBU5NJUAGP6IB5YGIZLAUFW2SG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CBU5NJUAGP6IB5YGIZLAUFW2SG","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":"eefd2d0be0f7f509cef45c0b8b5578c6a8d661687fb7f8b627c82b9265d13d92","cross_cats_sorted":["cs.DC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T17:45:51Z","title_canon_sha256":"796ac81ab30b7d3b6e24dac92b62b8a88495743c216a3b017a113efa6c97c35a"},"schema_version":"1.0","source":{"id":"2106.08315","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.08315","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"arxiv_version","alias_value":"2106.08315v3","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.08315","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_12","alias_value":"CBU5NJUAGP6I","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_16","alias_value":"CBU5NJUAGP6IB5YG","created_at":"2026-07-05T05:57:09Z"},{"alias_kind":"pith_short_8","alias_value":"CBU5NJUA","created_at":"2026-07-05T05:57:09Z"}],"graph_snapshots":[{"event_id":"sha256:224b141f08471faa166e75f436bdb11dc2f78819e83c0038c1f1e22033703b69","target":"graph","created_at":"2026-07-05T05:57:09Z","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/2106.08315/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider distributed stochastic variational inequalities (VIs) on unbounded domains with the problem data that is heterogeneous (non-IID) and distributed across many devices. We make a very general assumption on the computational network that, in particular, covers the settings of fully decentralized calculations with time-varying networks and centralized topologies commonly used in Federated Learning. Moreover, multiple local updates on the workers can be made for reducing the communication frequency between the workers. We extend the stochastic extragradient method to this very general se","authors_text":"Aleksandr Beznosikov, Alexander Gasnikov, Anastasia Koloskova, Pavel Dvurechensky, Sebastian U Stich, Valentin Samokhin","cross_cats":["cs.DC","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T17:45:51Z","title":"Decentralized Local Stochastic Extra-Gradient for Variational Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08315","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":"sha256:711b3ccc900e688cc07ae48c5b27b0707db69d5723cac3780d31aa7352a98890","target":"record","created_at":"2026-07-05T05:57:09Z","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":"eefd2d0be0f7f509cef45c0b8b5578c6a8d661687fb7f8b627c82b9265d13d92","cross_cats_sorted":["cs.DC","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T17:45:51Z","title_canon_sha256":"796ac81ab30b7d3b6e24dac92b62b8a88495743c216a3b017a113efa6c97c35a"},"schema_version":"1.0","source":{"id":"2106.08315","kind":"arxiv","version":3}},"canonical_sha256":"1069d6a68033fc80f70646560a16da91a4068f4142e709ec5473d72b1f1a00b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1069d6a68033fc80f70646560a16da91a4068f4142e709ec5473d72b1f1a00b4","first_computed_at":"2026-07-05T05:57:09.276897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:57:09.276897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXO+WE2t8FDZdxRC6VvGErMd9H1R4fntTQFj+BlT7XAMhVt5g53grHvXn5uU1KaxWGs0QZYC9EVt4/EfruJxBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:57:09.277284Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.08315","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:711b3ccc900e688cc07ae48c5b27b0707db69d5723cac3780d31aa7352a98890","sha256:224b141f08471faa166e75f436bdb11dc2f78819e83c0038c1f1e22033703b69"],"state_sha256":"a6f5ca18d53dd76f52db1191d7c637868172fbdd6c1f580040fb9a6ea2cc9544"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhghCzqSH3ZtJoE816Vb3f/feEKVZ82C6iddY4coY+ekI+AMfCY0wGwGrkwye0//Dxi1QPyx6j+IxCRNLubEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:43:18.515660Z","bundle_sha256":"41b20c993497b106f2257d62c616a18f872a7a9c119205f0cce58e141d6ccc73"}}