{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MPCHSJTFT56A3MZDN26LQZQ7JY","short_pith_number":"pith:MPCHSJTF","canonical_record":{"source":{"id":"2502.08835","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T22:52:15Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"47e8c66c18a2e8f8dd1242e41aad3b075d96646b7da7a3227e9e80effc8bdc4f","abstract_canon_sha256":"231c9157ab8dd3f989608cd82669ba974e42d85e14e25eb9a01d95428c7e1ad7"},"schema_version":"1.0"},"canonical_sha256":"63c47926659f7c0db3236ebcb8661f4e20b74e094a188bf6703907a55938c854","source":{"kind":"arxiv","id":"2502.08835","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08835","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08835v1","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08835","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"MPCHSJTFT56A","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_16","alias_value":"MPCHSJTFT56A3MZD","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_8","alias_value":"MPCHSJTF","created_at":"2026-07-05T10:13:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MPCHSJTFT56A3MZDN26LQZQ7JY","target":"record","payload":{"canonical_record":{"source":{"id":"2502.08835","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T22:52:15Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"47e8c66c18a2e8f8dd1242e41aad3b075d96646b7da7a3227e9e80effc8bdc4f","abstract_canon_sha256":"231c9157ab8dd3f989608cd82669ba974e42d85e14e25eb9a01d95428c7e1ad7"},"schema_version":"1.0"},"canonical_sha256":"63c47926659f7c0db3236ebcb8661f4e20b74e094a188bf6703907a55938c854","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:30.431444Z","signature_b64":"iOPMEwJGHzqVJ0h37pTg+jLD9knMjCVgs+ckmmQmPYWMwxTpStbciYZd3ZBIsoGqunEaCW2G+r7XPfx1wO2/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63c47926659f7c0db3236ebcb8661f4e20b74e094a188bf6703907a55938c854","last_reissued_at":"2026-07-05T10:13:30.430944Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:30.430944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.08835","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":"2026-07-05T10:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"icUcMSgagELznPv+QRvdXop1C9UeruoNMGjFIOytTCxzgVYHM2EAyhqdR6sn3AaOokq2rCUtup0K4PCWj4XPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:43:53.515416Z"},"content_sha256":"26147a2441bcb461c1e64893ab53801fd4bc20e271303134d82c64c0fba4355f","schema_version":"1.0","event_id":"sha256:26147a2441bcb461c1e64893ab53801fd4bc20e271303134d82c64c0fba4355f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MPCHSJTFT56A3MZDN26LQZQ7JY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bundle-based Augmented Lagrangian Framework: Algorithm, Convergence, and Primal-dual Principles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Feng-Yi Liao, Yang Zheng","submitted_at":"2025-02-12T22:52:15Z","abstract_excerpt":"We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a $\\textit{single-loop}$ process. Motivated by the proximal bundle method (PBM), we use a $\\textit{bundle}$ of past iterates to approximate the subproblem in ALM to get a computationally efficient update at each iteration. We establish sub-linear convergences for primal feasibility, primal cost values, and dual iterates under mild assumptions. With further regularity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08835","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/2502.08835/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":"2026-07-05T10:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GG7xeNY2aqH0jM9C+g58EhzxbrNVLREeqaypSc3XHRQllExKNhGjn/rW7dPpLGOm4vwTXlbC40ofolKexAQPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:43:53.516319Z"},"content_sha256":"a198b8a8c07bc7b7b6d06fcb9fd67dcc107e7a006ec71187dc93aa2f9fef1c8e","schema_version":"1.0","event_id":"sha256:a198b8a8c07bc7b7b6d06fcb9fd67dcc107e7a006ec71187dc93aa2f9fef1c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/bundle.json","state_url":"https://pith.science/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/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":"2026-08-09T03:43:53Z","links":{"resolver":"https://pith.science/pith/MPCHSJTFT56A3MZDN26LQZQ7JY","bundle":"https://pith.science/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/bundle.json","state":"https://pith.science/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPCHSJTFT56A3MZDN26LQZQ7JY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MPCHSJTFT56A3MZDN26LQZQ7JY","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":"231c9157ab8dd3f989608cd82669ba974e42d85e14e25eb9a01d95428c7e1ad7","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T22:52:15Z","title_canon_sha256":"47e8c66c18a2e8f8dd1242e41aad3b075d96646b7da7a3227e9e80effc8bdc4f"},"schema_version":"1.0","source":{"id":"2502.08835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08835","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08835v1","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08835","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"MPCHSJTFT56A","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_16","alias_value":"MPCHSJTFT56A3MZD","created_at":"2026-07-05T10:13:30Z"},{"alias_kind":"pith_short_8","alias_value":"MPCHSJTF","created_at":"2026-07-05T10:13:30Z"}],"graph_snapshots":[{"event_id":"sha256:a198b8a8c07bc7b7b6d06fcb9fd67dcc107e7a006ec71187dc93aa2f9fef1c8e","target":"graph","created_at":"2026-07-05T10:13:30Z","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/2502.08835/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a new bundle-based augmented Lagrangian framework for solving constrained convex problems. Unlike the classical (inexact) augmented Lagrangian method (ALM) that has a nested double-loop structure, our framework features a $\\textit{single-loop}$ process. Motivated by the proximal bundle method (PBM), we use a $\\textit{bundle}$ of past iterates to approximate the subproblem in ALM to get a computationally efficient update at each iteration. We establish sub-linear convergences for primal feasibility, primal cost values, and dual iterates under mild assumptions. With further regularity","authors_text":"Feng-Yi Liao, Yang Zheng","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T22:52:15Z","title":"A Bundle-based Augmented Lagrangian Framework: Algorithm, Convergence, and Primal-dual Principles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08835","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":"sha256:26147a2441bcb461c1e64893ab53801fd4bc20e271303134d82c64c0fba4355f","target":"record","created_at":"2026-07-05T10:13:30Z","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":"231c9157ab8dd3f989608cd82669ba974e42d85e14e25eb9a01d95428c7e1ad7","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T22:52:15Z","title_canon_sha256":"47e8c66c18a2e8f8dd1242e41aad3b075d96646b7da7a3227e9e80effc8bdc4f"},"schema_version":"1.0","source":{"id":"2502.08835","kind":"arxiv","version":1}},"canonical_sha256":"63c47926659f7c0db3236ebcb8661f4e20b74e094a188bf6703907a55938c854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63c47926659f7c0db3236ebcb8661f4e20b74e094a188bf6703907a55938c854","first_computed_at":"2026-07-05T10:13:30.430944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:30.430944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iOPMEwJGHzqVJ0h37pTg+jLD9knMjCVgs+ckmmQmPYWMwxTpStbciYZd3ZBIsoGqunEaCW2G+r7XPfx1wO2/Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:30.431444Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26147a2441bcb461c1e64893ab53801fd4bc20e271303134d82c64c0fba4355f","sha256:a198b8a8c07bc7b7b6d06fcb9fd67dcc107e7a006ec71187dc93aa2f9fef1c8e"],"state_sha256":"c9d3fa7704df7abb3728e543dde9241cbf8908f0becfb59a4bcd03e2d787a47c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7y4l4a+pV9HqMlNavvci5VLyCusaQgIV5zSMB4AEJQH6cZAMsjRqzGGXhJN6b6zwtk5E8vxcSOeFEqkdvLTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:43:53.522233Z","bundle_sha256":"94d962e870b6b9cb8db6b136623bfa3b1d5b57102cab5ad25b535b8b96d6c974"}}