{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MWTNZBPB67ISY34FCOSG3P7NAT","short_pith_number":"pith:MWTNZBPB","canonical_record":{"source":{"id":"1706.02654","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-08T15:52:55Z","cross_cats_sorted":[],"title_canon_sha256":"f3a2fa503bd99a27469010c09149c1531e64c6fdc4234d7ab6ba3245638b151f","abstract_canon_sha256":"0da26d1616cc860e9bc1f7888773a527ebfba8e5f15269ccbedaa88080b6f4dd"},"schema_version":"1.0"},"canonical_sha256":"65a6dc85e1f7d12c6f8513a46dbfed04c2c762b83a650dff80c69d558fdf3975","source":{"kind":"arxiv","id":"1706.02654","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02654","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02654v3","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02654","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"MWTNZBPB67IS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MWTNZBPB67ISY34F","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MWTNZBPB","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MWTNZBPB67ISY34FCOSG3P7NAT","target":"record","payload":{"canonical_record":{"source":{"id":"1706.02654","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-08T15:52:55Z","cross_cats_sorted":[],"title_canon_sha256":"f3a2fa503bd99a27469010c09149c1531e64c6fdc4234d7ab6ba3245638b151f","abstract_canon_sha256":"0da26d1616cc860e9bc1f7888773a527ebfba8e5f15269ccbedaa88080b6f4dd"},"schema_version":"1.0"},"canonical_sha256":"65a6dc85e1f7d12c6f8513a46dbfed04c2c762b83a650dff80c69d558fdf3975","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:19.281952Z","signature_b64":"L93F74Y1bN7SJYgy/i/X+VsiORgA4tuM98g0xF5Vz7ncuawi+pytB4RWY+NJpH6LzVLm/79ZYIEsHBenMcluAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65a6dc85e1f7d12c6f8513a46dbfed04c2c762b83a650dff80c69d558fdf3975","last_reissued_at":"2026-05-18T00:31:19.280850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:19.280850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.02654","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":"2026-05-18T00:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h3x24hHjkl16PIvWiNaacs2g3jc6iJoB/uk61+WtFNNL8s6Bea3PQCsSOH4UluHXSoDY5ATLi932QLSFkkU6CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:26:21.645241Z"},"content_sha256":"af47a61c79f32b628ebe898522a7ad56b0993a0aa7fcbad01deb7b93df5d7a04","schema_version":"1.0","event_id":"sha256:af47a61c79f32b628ebe898522a7ad56b0993a0aa7fcbad01deb7b93df5d7a04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MWTNZBPB67ISY34FCOSG3P7NAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Richard Heusdens, Thomas Sherson, W. Bastiaan Kleijn","submitted_at":"2017-06-08T15:52:55Z","abstract_excerpt":"In this paper we present a novel derivation for an existing node-based algorithm for distributed optimisation termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, in this work monotone operator theory is used to connect PDMM with other first-order methods such as Douglas-Rachford splitting and the alternating direction method of multipliers thus providing insight to the operation of the scheme. In particular, we show how PDMM combines a lifted dual form in conjunction with Peaceman-Rachford splitting to remove the need for collaboration between nodes per "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02654","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":""},"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":"2026-05-18T00:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qUTUgDEHKSw9vmtRnnVqrSDfoJPBtQCNaEH6nN2LoWw3gWlk88NvqBOTMpefiygEHWZXiHQKsNUGVvW508v2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T19:26:21.645664Z"},"content_sha256":"aed6ed928d1e91ad0f387d8e3ad5444179418ce648000a2105df82d96f8e300d","schema_version":"1.0","event_id":"sha256:aed6ed928d1e91ad0f387d8e3ad5444179418ce648000a2105df82d96f8e300d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MWTNZBPB67ISY34FCOSG3P7NAT/bundle.json","state_url":"https://pith.science/pith/MWTNZBPB67ISY34FCOSG3P7NAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MWTNZBPB67ISY34FCOSG3P7NAT/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":"2026-05-20T19:26:21Z","links":{"resolver":"https://pith.science/pith/MWTNZBPB67ISY34FCOSG3P7NAT","bundle":"https://pith.science/pith/MWTNZBPB67ISY34FCOSG3P7NAT/bundle.json","state":"https://pith.science/pith/MWTNZBPB67ISY34FCOSG3P7NAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MWTNZBPB67ISY34FCOSG3P7NAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MWTNZBPB67ISY34FCOSG3P7NAT","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":"0da26d1616cc860e9bc1f7888773a527ebfba8e5f15269ccbedaa88080b6f4dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-08T15:52:55Z","title_canon_sha256":"f3a2fa503bd99a27469010c09149c1531e64c6fdc4234d7ab6ba3245638b151f"},"schema_version":"1.0","source":{"id":"1706.02654","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.02654","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.02654v3","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.02654","created_at":"2026-05-18T00:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"MWTNZBPB67IS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MWTNZBPB67ISY34F","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MWTNZBPB","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:aed6ed928d1e91ad0f387d8e3ad5444179418ce648000a2105df82d96f8e300d","target":"graph","created_at":"2026-05-18T00:31:19Z","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 paper we present a novel derivation for an existing node-based algorithm for distributed optimisation termed the primal-dual method of multipliers (PDMM). In contrast to its initial derivation, in this work monotone operator theory is used to connect PDMM with other first-order methods such as Douglas-Rachford splitting and the alternating direction method of multipliers thus providing insight to the operation of the scheme. In particular, we show how PDMM combines a lifted dual form in conjunction with Peaceman-Rachford splitting to remove the need for collaboration between nodes per ","authors_text":"Richard Heusdens, Thomas Sherson, W. Bastiaan Kleijn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-08T15:52:55Z","title":"Derivation and Analysis of the Primal-Dual Method of Multipliers Based on Monotone Operator Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.02654","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:af47a61c79f32b628ebe898522a7ad56b0993a0aa7fcbad01deb7b93df5d7a04","target":"record","created_at":"2026-05-18T00:31:19Z","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":"0da26d1616cc860e9bc1f7888773a527ebfba8e5f15269ccbedaa88080b6f4dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-08T15:52:55Z","title_canon_sha256":"f3a2fa503bd99a27469010c09149c1531e64c6fdc4234d7ab6ba3245638b151f"},"schema_version":"1.0","source":{"id":"1706.02654","kind":"arxiv","version":3}},"canonical_sha256":"65a6dc85e1f7d12c6f8513a46dbfed04c2c762b83a650dff80c69d558fdf3975","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a6dc85e1f7d12c6f8513a46dbfed04c2c762b83a650dff80c69d558fdf3975","first_computed_at":"2026-05-18T00:31:19.280850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:19.280850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L93F74Y1bN7SJYgy/i/X+VsiORgA4tuM98g0xF5Vz7ncuawi+pytB4RWY+NJpH6LzVLm/79ZYIEsHBenMcluAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:19.281952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.02654","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af47a61c79f32b628ebe898522a7ad56b0993a0aa7fcbad01deb7b93df5d7a04","sha256:aed6ed928d1e91ad0f387d8e3ad5444179418ce648000a2105df82d96f8e300d"],"state_sha256":"6546c4abd55f89ebc39058f92c323b466f9a4d20c30ece06f4d76f9ed062a399"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXQQyfMPQIVOfVjrrRBIxioHTu+hEF+lwc+qByutl2+zarL1ydXtdw6ETd4HS34UT2ncXwZU9uY2eoXMLxm5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T19:26:21.647887Z","bundle_sha256":"8d653e72869445b5eb84b972cdb3aa07ecdd5c88c5316b5fc225343165ae8338"}}