{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TQY4KUVNPPW6LKJSLRKGE43LSP","short_pith_number":"pith:TQY4KUVN","canonical_record":{"source":{"id":"2401.07096","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-13T15:15:44Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"be8d6a97a2a8e22635a5894f69448c33ce2335d6489b519878cb7eec785a444c","abstract_canon_sha256":"897cb410d9280b5f85afb820ee081a444d6bfae848552983b358a4637fa941dc"},"schema_version":"1.0"},"canonical_sha256":"9c31c552ad7bede5a9325c5462736b93dcefc61b150b6fd8e0f8dea04cf17109","source":{"kind":"arxiv","id":"2401.07096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.07096","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"2401.07096v1","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.07096","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"TQY4KUVNPPW6","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_16","alias_value":"TQY4KUVNPPW6LKJS","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_8","alias_value":"TQY4KUVN","created_at":"2026-07-05T07:33:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TQY4KUVNPPW6LKJSLRKGE43LSP","target":"record","payload":{"canonical_record":{"source":{"id":"2401.07096","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-13T15:15:44Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"be8d6a97a2a8e22635a5894f69448c33ce2335d6489b519878cb7eec785a444c","abstract_canon_sha256":"897cb410d9280b5f85afb820ee081a444d6bfae848552983b358a4637fa941dc"},"schema_version":"1.0"},"canonical_sha256":"9c31c552ad7bede5a9325c5462736b93dcefc61b150b6fd8e0f8dea04cf17109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:33:31.794059Z","signature_b64":"7XvMWvz2ViUWxAKTGlczJQ9Gm+VGcGTCTWulswYOySvGEukuDiaZUHFYw61QbLm6eBgfwO8dGndj6lwChNccBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c31c552ad7bede5a9325c5462736b93dcefc61b150b6fd8e0f8dea04cf17109","last_reissued_at":"2026-07-05T07:33:31.793583Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:33:31.793583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.07096","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":"2026-07-05T07:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MX7CiEhFUMxamXOmgXhxrA3TQEwCB9YIMOSmeak8F/0TtWSbenU3kMqp4w7UFLSyGXsOKfpAm9qaPtuzSq5PBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:26.363604Z"},"content_sha256":"2cdcb44d94e05ec1135a446bf20d1a86b15206120cf18bd47515aef639918a4c","schema_version":"1.0","event_id":"sha256:2cdcb44d94e05ec1135a446bf20d1a86b15206120cf18bd47515aef639918a4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TQY4KUVNPPW6LKJSLRKGE43LSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Understanding the ADMM Algorithm via High-Resolution Differential Equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Bin Shi, Bowen Li","submitted_at":"2024-01-13T15:15:44Z","abstract_excerpt":"In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this challenge, the alternating direction method of multipliers (ADMM) has emerged as a widely used approach, particularly well-suited to distributed convex optimization. However, the iterative behavior of ADMM has not been well understood. In this paper, we employ dimensional analysis to derive a system of high-resolution ordinary differential equations (ODEs) for ADMM."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07096","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/2401.07096/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":"2026-07-05T07:33:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EmO6BNZD5NpT7Yi5xngEaSIabkeZPok7tlC/knwmEgPv9ZDV/6ypJ5WyIQcxD3YZUE0X0/Z5CaTgGTff6b4hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:09:26.364140Z"},"content_sha256":"eabbf5cdc370d3518bc19639ea4be3ee89ca75171d53f9411faa1e0e5643e012","schema_version":"1.0","event_id":"sha256:eabbf5cdc370d3518bc19639ea4be3ee89ca75171d53f9411faa1e0e5643e012"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/bundle.json","state_url":"https://pith.science/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/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":"2026-08-09T12:09:26Z","links":{"resolver":"https://pith.science/pith/TQY4KUVNPPW6LKJSLRKGE43LSP","bundle":"https://pith.science/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/bundle.json","state":"https://pith.science/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQY4KUVNPPW6LKJSLRKGE43LSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TQY4KUVNPPW6LKJSLRKGE43LSP","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":"897cb410d9280b5f85afb820ee081a444d6bfae848552983b358a4637fa941dc","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-13T15:15:44Z","title_canon_sha256":"be8d6a97a2a8e22635a5894f69448c33ce2335d6489b519878cb7eec785a444c"},"schema_version":"1.0","source":{"id":"2401.07096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.07096","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"arxiv_version","alias_value":"2401.07096v1","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.07096","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_12","alias_value":"TQY4KUVNPPW6","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_16","alias_value":"TQY4KUVNPPW6LKJS","created_at":"2026-07-05T07:33:31Z"},{"alias_kind":"pith_short_8","alias_value":"TQY4KUVN","created_at":"2026-07-05T07:33:31Z"}],"graph_snapshots":[{"event_id":"sha256:eabbf5cdc370d3518bc19639ea4be3ee89ca75171d53f9411faa1e0e5643e012","target":"graph","created_at":"2026-07-05T07:33:31Z","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/2401.07096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the fields of statistics, machine learning, image science, and related areas, there is an increasing demand for decentralized collection or storage of large-scale datasets, as well as distributed solution methods. To tackle this challenge, the alternating direction method of multipliers (ADMM) has emerged as a widely used approach, particularly well-suited to distributed convex optimization. However, the iterative behavior of ADMM has not been well understood. In this paper, we employ dimensional analysis to derive a system of high-resolution ordinary differential equations (ODEs) for ADMM.","authors_text":"Bin Shi, Bowen Li","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-13T15:15:44Z","title":"Understanding the ADMM Algorithm via High-Resolution Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07096","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":"sha256:2cdcb44d94e05ec1135a446bf20d1a86b15206120cf18bd47515aef639918a4c","target":"record","created_at":"2026-07-05T07:33:31Z","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":"897cb410d9280b5f85afb820ee081a444d6bfae848552983b358a4637fa941dc","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2024-01-13T15:15:44Z","title_canon_sha256":"be8d6a97a2a8e22635a5894f69448c33ce2335d6489b519878cb7eec785a444c"},"schema_version":"1.0","source":{"id":"2401.07096","kind":"arxiv","version":1}},"canonical_sha256":"9c31c552ad7bede5a9325c5462736b93dcefc61b150b6fd8e0f8dea04cf17109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c31c552ad7bede5a9325c5462736b93dcefc61b150b6fd8e0f8dea04cf17109","first_computed_at":"2026-07-05T07:33:31.793583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:31.793583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7XvMWvz2ViUWxAKTGlczJQ9Gm+VGcGTCTWulswYOySvGEukuDiaZUHFYw61QbLm6eBgfwO8dGndj6lwChNccBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:31.794059Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.07096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cdcb44d94e05ec1135a446bf20d1a86b15206120cf18bd47515aef639918a4c","sha256:eabbf5cdc370d3518bc19639ea4be3ee89ca75171d53f9411faa1e0e5643e012"],"state_sha256":"de4f6d7794c0f0b0adad81dc0c556e2dd2ca51ce5ba4eac02b485e1d71859450"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+O+HiTh4+p/i57SFpRj1A4RXMghzKGgB/XBTEHRDv4i/Nj6lMqODYaoYfym5fpPWetwkfsNGBLd0P/yUrq1yCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:09:26.369721Z","bundle_sha256":"394d345603cad6862e0eefeb4c1bd90bc04444f4b5ac54c95cb1953ed9ddb8a8"}}