{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:K6R55ICWPSRGXX2ELEOFGZXZ6W","short_pith_number":"pith:K6R55ICW","canonical_record":{"source":{"id":"1806.00291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-01T11:26:51Z","cross_cats_sorted":[],"title_canon_sha256":"32d3d2fb4e1cbd7fd999f469965eabfbd6fb56129f56f544afb738f6e201fcc7","abstract_canon_sha256":"2a6c700a5f534bbd0949bab08b88f162fc3c40b0ba8966b8c19e679267a42687"},"schema_version":"1.0"},"canonical_sha256":"57a3dea0567ca26bdf44591c5366f9f5884405f42068d4261a32ee2394db2d49","source":{"kind":"arxiv","id":"1806.00291","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00291","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00291v1","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00291","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"pith_short_12","alias_value":"K6R55ICWPSRG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K6R55ICWPSRGXX2E","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K6R55ICW","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:K6R55ICWPSRGXX2ELEOFGZXZ6W","target":"record","payload":{"canonical_record":{"source":{"id":"1806.00291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-01T11:26:51Z","cross_cats_sorted":[],"title_canon_sha256":"32d3d2fb4e1cbd7fd999f469965eabfbd6fb56129f56f544afb738f6e201fcc7","abstract_canon_sha256":"2a6c700a5f534bbd0949bab08b88f162fc3c40b0ba8966b8c19e679267a42687"},"schema_version":"1.0"},"canonical_sha256":"57a3dea0567ca26bdf44591c5366f9f5884405f42068d4261a32ee2394db2d49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:24.133730Z","signature_b64":"qOtt8i0+KeeXM1nm0sX0FXYMMuxRtu1FIFIObLkcoEqxq8T2BlI4rB0as/wAQ9hM6YWU3lT8x8ekSlp3Af6VCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57a3dea0567ca26bdf44591c5366f9f5884405f42068d4261a32ee2394db2d49","last_reissued_at":"2026-05-18T00:14:24.132984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:24.132984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.00291","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":"2026-05-18T00:14:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfKmMvut7vbkV2ZbgVgH09iifTkSFREISByyTSGAb1zyMe51IE8olPNKMqFiXQOYnwWy5oNCI9E+aabLvAqpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:37:03.728354Z"},"content_sha256":"c1ec3054f629247e6aa8d506161a65c56e309a4c2076a587ac0948c83ee66bf9","schema_version":"1.0","event_id":"sha256:c1ec3054f629247e6aa8d506161a65c56e309a4c2076a587ac0948c83ee66bf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:K6R55ICWPSRGXX2ELEOFGZXZ6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Algorithms for Non-Smooth Distributed Optimization in Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Francis Bach, Kevin Scaman, Laurent Massouli\\'e, S\\'ebastien Bubeck, Yin Tat Lee","submitted_at":"2018-06-01T11:26:51Z","abstract_excerpt":"In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the er"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00291","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":"2026-05-18T00:14:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qTATQfke8X8RJlc/SCFNkhJFubpYu44F6CU+NLjHSuMOYhJV30A1jK9klnUXyulQ9RkVUGbUs97EJIQkGNfDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:37:03.728707Z"},"content_sha256":"66fe8a33a7e71259dbda7b86bdeb0bf23f155e613f1ff687f84522ec236e5bf7","schema_version":"1.0","event_id":"sha256:66fe8a33a7e71259dbda7b86bdeb0bf23f155e613f1ff687f84522ec236e5bf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/bundle.json","state_url":"https://pith.science/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/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":"2026-05-30T08:37:03Z","links":{"resolver":"https://pith.science/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W","bundle":"https://pith.science/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/bundle.json","state":"https://pith.science/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6R55ICWPSRGXX2ELEOFGZXZ6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K6R55ICWPSRGXX2ELEOFGZXZ6W","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":"2a6c700a5f534bbd0949bab08b88f162fc3c40b0ba8966b8c19e679267a42687","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-01T11:26:51Z","title_canon_sha256":"32d3d2fb4e1cbd7fd999f469965eabfbd6fb56129f56f544afb738f6e201fcc7"},"schema_version":"1.0","source":{"id":"1806.00291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.00291","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"arxiv_version","alias_value":"1806.00291v1","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00291","created_at":"2026-05-18T00:14:24Z"},{"alias_kind":"pith_short_12","alias_value":"K6R55ICWPSRG","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K6R55ICWPSRGXX2E","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K6R55ICW","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:66fe8a33a7e71259dbda7b86bdeb0bf23f155e613f1ff687f84522ec236e5bf7","target":"graph","created_at":"2026-05-18T00:14:24Z","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":"In this work, we consider the distributed optimization of non-smooth convex functions using a network of computing units. We investigate this problem under two regularity assumptions: (1) the Lipschitz continuity of the global objective function, and (2) the Lipschitz continuity of local individual functions. Under the local regularity assumption, we provide the first optimal first-order decentralized algorithm called multi-step primal-dual (MSPD) and its corresponding optimal convergence rate. A notable aspect of this result is that, for non-smooth functions, while the dominant term of the er","authors_text":"Francis Bach, Kevin Scaman, Laurent Massouli\\'e, S\\'ebastien Bubeck, Yin Tat Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-01T11:26:51Z","title":"Optimal Algorithms for Non-Smooth Distributed Optimization in Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00291","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:c1ec3054f629247e6aa8d506161a65c56e309a4c2076a587ac0948c83ee66bf9","target":"record","created_at":"2026-05-18T00:14:24Z","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":"2a6c700a5f534bbd0949bab08b88f162fc3c40b0ba8966b8c19e679267a42687","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-01T11:26:51Z","title_canon_sha256":"32d3d2fb4e1cbd7fd999f469965eabfbd6fb56129f56f544afb738f6e201fcc7"},"schema_version":"1.0","source":{"id":"1806.00291","kind":"arxiv","version":1}},"canonical_sha256":"57a3dea0567ca26bdf44591c5366f9f5884405f42068d4261a32ee2394db2d49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57a3dea0567ca26bdf44591c5366f9f5884405f42068d4261a32ee2394db2d49","first_computed_at":"2026-05-18T00:14:24.132984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:24.132984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qOtt8i0+KeeXM1nm0sX0FXYMMuxRtu1FIFIObLkcoEqxq8T2BlI4rB0as/wAQ9hM6YWU3lT8x8ekSlp3Af6VCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:24.133730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.00291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1ec3054f629247e6aa8d506161a65c56e309a4c2076a587ac0948c83ee66bf9","sha256:66fe8a33a7e71259dbda7b86bdeb0bf23f155e613f1ff687f84522ec236e5bf7"],"state_sha256":"d41145bf30ce8b573519e8a1c4d8632c87d2cb91713584dbbb7c9b261729ae66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Odp5mQZ6VMmz+v6x+HVCIAWVs/fM/YTYSMsrq+uCbJhVySTqfoHsFcl2JstR1PNMNjyBzF9Qg+chiRCqrSiFCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:37:03.730629Z","bundle_sha256":"5ab82cedaf35feca4593bb195dd8b4bd3d95f57978436c20c01646a338ab3c68"}}