{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:J3KTKKQPDBSUOP2DB2RYXCIMM5","short_pith_number":"pith:J3KTKKQP","canonical_record":{"source":{"id":"2008.12946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-29T09:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"0e9c79a1d69e1f83a802cf9c02e4fc0774676bec1cc1deec98a97ec8c64b8f2a","abstract_canon_sha256":"d510b123b0f00baaadcc8c881dfc7a98ede190a5f672ceeeae59a2edec5a473f"},"schema_version":"1.0"},"canonical_sha256":"4ed5352a0f1865473f430ea38b890c674c8d384b6a6b2fb69b5a6af22632ac59","source":{"kind":"arxiv","id":"2008.12946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.12946","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"arxiv_version","alias_value":"2008.12946v1","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.12946","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_12","alias_value":"J3KTKKQPDBSU","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_16","alias_value":"J3KTKKQPDBSUOP2D","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_8","alias_value":"J3KTKKQP","created_at":"2026-07-05T01:31:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:J3KTKKQPDBSUOP2DB2RYXCIMM5","target":"record","payload":{"canonical_record":{"source":{"id":"2008.12946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-29T09:47:55Z","cross_cats_sorted":[],"title_canon_sha256":"0e9c79a1d69e1f83a802cf9c02e4fc0774676bec1cc1deec98a97ec8c64b8f2a","abstract_canon_sha256":"d510b123b0f00baaadcc8c881dfc7a98ede190a5f672ceeeae59a2edec5a473f"},"schema_version":"1.0"},"canonical_sha256":"4ed5352a0f1865473f430ea38b890c674c8d384b6a6b2fb69b5a6af22632ac59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:31:32.794937Z","signature_b64":"t6cvcIS5wJkHlfNirjjf/fyA6H9xQLxQ/Xoal9poYi8l2TQX63KVhz78NdCy7yPgEXx7Jz1ZBgYpw16AhHhsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ed5352a0f1865473f430ea38b890c674c8d384b6a6b2fb69b5a6af22632ac59","last_reissued_at":"2026-07-05T01:31:32.794544Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:31:32.794544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.12946","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":"2026-07-05T01:31:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TybrDTyyBTDmpd/eroXzHccAYqfVH86w/SRqyAXAdX7mqI4jESf5jTbT5BXIL2i9Zrpt4i2VpvsF/c9PP37OBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:43:34.764450Z"},"content_sha256":"d2d23772d0fc64cbf6598b527d3a67fd26c6f5cfd4f360e8260e3389f8465d50","schema_version":"1.0","event_id":"sha256:d2d23772d0fc64cbf6598b527d3a67fd26c6f5cfd4f360e8260e3389f8465d50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:J3KTKKQPDBSUOP2DB2RYXCIMM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Convergence of Randomized Primal-Dual Coordinate Method for Large-scale Linear Constrained Convex Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daoli Zhu, Lei Zhao","submitted_at":"2020-08-29T09:47:55Z","abstract_excerpt":"Linear constrained convex programming has many practical applications, including support vector machine and machine learning portfolio problems. We propose the randomized primal-dual coordinate (RPDC) method, a randomized coordinate extension of the first-order primal-dual method by Cohen and Zhu, 1984 and Zhao and Zhu, 2019, to solve linear constrained convex programming. We randomly choose a block of variables based on a uniform distribution, linearize, and apply a Bregman-like function (core function) to the selected block to obtain simple parallel primal-dual decomposition. We then establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.12946","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2008.12946/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":"2026-07-05T01:31:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEZoX2cAGJLXlMBlXiDtp0ANCFSo4niA9+FUFfDgBz/o3pZGBFH5u5PwQOIO/wCKldyeZlYLrnWH+zYx4rCNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:43:34.764987Z"},"content_sha256":"0e2e87aaa0c14f03837cc9a94ec85d36c82f0526bd2bc07a01d65a88ee85716a","schema_version":"1.0","event_id":"sha256:0e2e87aaa0c14f03837cc9a94ec85d36c82f0526bd2bc07a01d65a88ee85716a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/bundle.json","state_url":"https://pith.science/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/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":"2026-08-12T16:43:34Z","links":{"resolver":"https://pith.science/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5","bundle":"https://pith.science/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/bundle.json","state":"https://pith.science/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3KTKKQPDBSUOP2DB2RYXCIMM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:J3KTKKQPDBSUOP2DB2RYXCIMM5","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":"d510b123b0f00baaadcc8c881dfc7a98ede190a5f672ceeeae59a2edec5a473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-29T09:47:55Z","title_canon_sha256":"0e9c79a1d69e1f83a802cf9c02e4fc0774676bec1cc1deec98a97ec8c64b8f2a"},"schema_version":"1.0","source":{"id":"2008.12946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.12946","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"arxiv_version","alias_value":"2008.12946v1","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.12946","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_12","alias_value":"J3KTKKQPDBSU","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_16","alias_value":"J3KTKKQPDBSUOP2D","created_at":"2026-07-05T01:31:32Z"},{"alias_kind":"pith_short_8","alias_value":"J3KTKKQP","created_at":"2026-07-05T01:31:32Z"}],"graph_snapshots":[{"event_id":"sha256:0e2e87aaa0c14f03837cc9a94ec85d36c82f0526bd2bc07a01d65a88ee85716a","target":"graph","created_at":"2026-07-05T01:31:32Z","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/2008.12946/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Linear constrained convex programming has many practical applications, including support vector machine and machine learning portfolio problems. We propose the randomized primal-dual coordinate (RPDC) method, a randomized coordinate extension of the first-order primal-dual method by Cohen and Zhu, 1984 and Zhao and Zhu, 2019, to solve linear constrained convex programming. We randomly choose a block of variables based on a uniform distribution, linearize, and apply a Bregman-like function (core function) to the selected block to obtain simple parallel primal-dual decomposition. We then establi","authors_text":"Daoli Zhu, Lei Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-29T09:47:55Z","title":"Linear Convergence of Randomized Primal-Dual Coordinate Method for Large-scale Linear Constrained Convex Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.12946","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:d2d23772d0fc64cbf6598b527d3a67fd26c6f5cfd4f360e8260e3389f8465d50","target":"record","created_at":"2026-07-05T01:31:32Z","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":"d510b123b0f00baaadcc8c881dfc7a98ede190a5f672ceeeae59a2edec5a473f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-08-29T09:47:55Z","title_canon_sha256":"0e9c79a1d69e1f83a802cf9c02e4fc0774676bec1cc1deec98a97ec8c64b8f2a"},"schema_version":"1.0","source":{"id":"2008.12946","kind":"arxiv","version":1}},"canonical_sha256":"4ed5352a0f1865473f430ea38b890c674c8d384b6a6b2fb69b5a6af22632ac59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ed5352a0f1865473f430ea38b890c674c8d384b6a6b2fb69b5a6af22632ac59","first_computed_at":"2026-07-05T01:31:32.794544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:31:32.794544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6cvcIS5wJkHlfNirjjf/fyA6H9xQLxQ/Xoal9poYi8l2TQX63KVhz78NdCy7yPgEXx7Jz1ZBgYpw16AhHhsAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:31:32.794937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.12946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2d23772d0fc64cbf6598b527d3a67fd26c6f5cfd4f360e8260e3389f8465d50","sha256:0e2e87aaa0c14f03837cc9a94ec85d36c82f0526bd2bc07a01d65a88ee85716a"],"state_sha256":"d3ed675d4ad139082d8ce773fa534f646e67dbd567841d3a971f44938be09c23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWchJLi7RIFR4AiXZHE4eWONDyd0LLM/NaM77HIRMIAwg3lxSR5KJIIu9/sYpgimo7Jmvu10mwCJ5d7+egmHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:43:34.770688Z","bundle_sha256":"875a28cb65f522bb587d7df6d28990cbbec0e8deb7d48825fc269e776cbc433a"}}