{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OJT3XBD2CUOK4WG43H2RQQYM3P","short_pith_number":"pith:OJT3XBD2","schema_version":"1.0","canonical_sha256":"7267bb847a151cae58dcd9f518430cdbc3c23741bf7bdcd6cfdd29774e764dcf","source":{"kind":"arxiv","id":"2507.20386","version":2},"attestation_state":"computed","paper":{"title":"The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angelika Wiegele, Daniel Brosch, Jan Schwiddessen","submitted_at":"2025-07-27T19:03:54Z","abstract_excerpt":"The Burer-Monteiro factorization has become a powerful tool for solving large-scale semidefinite programs (SDPs), enabling recently developed low-rank solvers to tackle problems previously beyond reach. However, existing methods are typically designed to prioritize scalability over solution accuracy. We introduce the Augmented Mixing Method, a new algorithm that combines the Burer-Monteiro factorization with an inexact augmented Lagrangian framework and a block coordinate descent scheme. Our method emphasizes solving low-dimensional subproblems efficiently and to high precision. Inequality con"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.20386","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-07-27T19:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"a61c838dbf6f4ff5d9f2988fd34f0321f854ffbfce0ec8046c7831cfbf1637cd","abstract_canon_sha256":"21dfeef36ee9fcaa05d02fe68f5b9a98ed7d2edb4859169091689df241b58c3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:53.678948Z","signature_b64":"ckPNexb0UgY67nx96aJd98RlrEvHox9SHe04WtpLd6Nqzz5HTZgT0QMQowXTN9Sav667mCSnA5Wc62KDDZLyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7267bb847a151cae58dcd9f518430cdbc3c23741bf7bdcd6cfdd29774e764dcf","last_reissued_at":"2026-06-19T16:10:53.678538Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:53.678538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Angelika Wiegele, Daniel Brosch, Jan Schwiddessen","submitted_at":"2025-07-27T19:03:54Z","abstract_excerpt":"The Burer-Monteiro factorization has become a powerful tool for solving large-scale semidefinite programs (SDPs), enabling recently developed low-rank solvers to tackle problems previously beyond reach. However, existing methods are typically designed to prioritize scalability over solution accuracy. We introduce the Augmented Mixing Method, a new algorithm that combines the Burer-Monteiro factorization with an inexact augmented Lagrangian framework and a block coordinate descent scheme. Our method emphasizes solving low-dimensional subproblems efficiently and to high precision. Inequality con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20386","kind":"arxiv","version":2},"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/2507.20386/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.20386","created_at":"2026-06-19T16:10:53.678598+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.20386v2","created_at":"2026-06-19T16:10:53.678598+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20386","created_at":"2026-06-19T16:10:53.678598+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJT3XBD2CUOK","created_at":"2026-06-19T16:10:53.678598+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJT3XBD2CUOK4WG4","created_at":"2026-06-19T16:10:53.678598+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJT3XBD2","created_at":"2026-06-19T16:10:53.678598+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P","json":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P.json","graph_json":"https://pith.science/api/pith-number/OJT3XBD2CUOK4WG43H2RQQYM3P/graph.json","events_json":"https://pith.science/api/pith-number/OJT3XBD2CUOK4WG43H2RQQYM3P/events.json","paper":"https://pith.science/paper/OJT3XBD2"},"agent_actions":{"view_html":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P","download_json":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P.json","view_paper":"https://pith.science/paper/OJT3XBD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.20386&json=true","fetch_graph":"https://pith.science/api/pith-number/OJT3XBD2CUOK4WG43H2RQQYM3P/graph.json","fetch_events":"https://pith.science/api/pith-number/OJT3XBD2CUOK4WG43H2RQQYM3P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P/action/storage_attestation","attest_author":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P/action/author_attestation","sign_citation":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P/action/citation_signature","submit_replication":"https://pith.science/pith/OJT3XBD2CUOK4WG43H2RQQYM3P/action/replication_record"}},"created_at":"2026-06-19T16:10:53.678598+00:00","updated_at":"2026-06-19T16:10:53.678598+00:00"}