{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QBSRG7JXV5POYQ4U4QL7OYLFD2","short_pith_number":"pith:QBSRG7JX","canonical_record":{"source":{"id":"2606.06067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T12:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"ff2a759652f864d6e24aac57facd0ed0f6eab2b5905db0b8d51a9e8736abd2a5","abstract_canon_sha256":"8cdb5b9907002db46ee83f589e4fb6aacd199fb9fd9fa350be6b52022efe5c7e"},"schema_version":"1.0"},"canonical_sha256":"8065137d37af5eec4394e417f761651ea2aa100c0f27739a8b2ee0d84f2bfa59","source":{"kind":"arxiv","id":"2606.06067","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06067","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06067v1","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06067","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"QBSRG7JXV5PO","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_16","alias_value":"QBSRG7JXV5POYQ4U","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_8","alias_value":"QBSRG7JX","created_at":"2026-06-05T01:15:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QBSRG7JXV5POYQ4U4QL7OYLFD2","target":"record","payload":{"canonical_record":{"source":{"id":"2606.06067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T12:09:19Z","cross_cats_sorted":[],"title_canon_sha256":"ff2a759652f864d6e24aac57facd0ed0f6eab2b5905db0b8d51a9e8736abd2a5","abstract_canon_sha256":"8cdb5b9907002db46ee83f589e4fb6aacd199fb9fd9fa350be6b52022efe5c7e"},"schema_version":"1.0"},"canonical_sha256":"8065137d37af5eec4394e417f761651ea2aa100c0f27739a8b2ee0d84f2bfa59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:31.971808Z","signature_b64":"qbdYndDMOm6G+rYNW+C1LgET+pyDJpqWOmrXrVPByz63T2U31oPWdjuEy5y4nAr4rKQXszThzcoWI7RKMPDQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8065137d37af5eec4394e417f761651ea2aa100c0f27739a8b2ee0d84f2bfa59","last_reissued_at":"2026-06-05T01:15:31.971399Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:31.971399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.06067","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":"2026-06-05T01:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czVe+m8W5v0Qmow4CwNSezistVZgrbYQR4DeNm+lvmyCgrs2jPzBiDEobX/qE2ppqlb+UwwyqvSuTBwV6Pd9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:12:07.548488Z"},"content_sha256":"e347c925219402a52da6ea4c2856ecaa02ea353f1ffe6ecb3e1028cf83a99959","schema_version":"1.0","event_id":"sha256:e347c925219402a52da6ea4c2856ecaa02ea353f1ffe6ecb3e1028cf83a99959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QBSRG7JXV5POYQ4U4QL7OYLFD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness and stability of Lagrange multipliers and associated qualification conditions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gerd Wachsmuth, Patrick Mehlitz","submitted_at":"2026-06-04T12:09:19Z","abstract_excerpt":"This paper is concerned with uniqueness and stability of Lagrange multipliers for constrained optimization problems in abstract spaces. It is well known that validity of the strict Robinson-Zowe-Kurcyusz condition implies the so-called isolated calmness, a one-sided Lipschitz property tailored for set-valued mappings, of some Lagrange multiplier mapping associated with a perturbed version of the original optimization problem, and the latter indeed is enough to guarantee uniqueness of the Lagrange multiplier. The paper studies the isolated calmness of the Lagrange multiplier mapping in detail. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06067","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/2606.06067/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":"2026-06-05T01:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIonqFhSLaTaTj7wouPPqctrWPFtU+VXhL3yozkWQCGjYVyBhQMA0ihwimLS0ITKRYuWix0N/EyYjuWNzsj5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:12:07.549222Z"},"content_sha256":"121f07ec2ca01037cb792ea7a2661fd226f51e84b2633caa15bdbfe4d7394e7b","schema_version":"1.0","event_id":"sha256:121f07ec2ca01037cb792ea7a2661fd226f51e84b2633caa15bdbfe4d7394e7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/bundle.json","state_url":"https://pith.science/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/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":"2026-06-05T21:12:07Z","links":{"resolver":"https://pith.science/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2","bundle":"https://pith.science/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/bundle.json","state":"https://pith.science/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBSRG7JXV5POYQ4U4QL7OYLFD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QBSRG7JXV5POYQ4U4QL7OYLFD2","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":"8cdb5b9907002db46ee83f589e4fb6aacd199fb9fd9fa350be6b52022efe5c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T12:09:19Z","title_canon_sha256":"ff2a759652f864d6e24aac57facd0ed0f6eab2b5905db0b8d51a9e8736abd2a5"},"schema_version":"1.0","source":{"id":"2606.06067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06067","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06067v1","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06067","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"QBSRG7JXV5PO","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_16","alias_value":"QBSRG7JXV5POYQ4U","created_at":"2026-06-05T01:15:31Z"},{"alias_kind":"pith_short_8","alias_value":"QBSRG7JX","created_at":"2026-06-05T01:15:31Z"}],"graph_snapshots":[{"event_id":"sha256:121f07ec2ca01037cb792ea7a2661fd226f51e84b2633caa15bdbfe4d7394e7b","target":"graph","created_at":"2026-06-05T01:15:31Z","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/2606.06067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with uniqueness and stability of Lagrange multipliers for constrained optimization problems in abstract spaces. It is well known that validity of the strict Robinson-Zowe-Kurcyusz condition implies the so-called isolated calmness, a one-sided Lipschitz property tailored for set-valued mappings, of some Lagrange multiplier mapping associated with a perturbed version of the original optimization problem, and the latter indeed is enough to guarantee uniqueness of the Lagrange multiplier. The paper studies the isolated calmness of the Lagrange multiplier mapping in detail. ","authors_text":"Gerd Wachsmuth, Patrick Mehlitz","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T12:09:19Z","title":"Uniqueness and stability of Lagrange multipliers and associated qualification conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06067","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:e347c925219402a52da6ea4c2856ecaa02ea353f1ffe6ecb3e1028cf83a99959","target":"record","created_at":"2026-06-05T01:15:31Z","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":"8cdb5b9907002db46ee83f589e4fb6aacd199fb9fd9fa350be6b52022efe5c7e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-04T12:09:19Z","title_canon_sha256":"ff2a759652f864d6e24aac57facd0ed0f6eab2b5905db0b8d51a9e8736abd2a5"},"schema_version":"1.0","source":{"id":"2606.06067","kind":"arxiv","version":1}},"canonical_sha256":"8065137d37af5eec4394e417f761651ea2aa100c0f27739a8b2ee0d84f2bfa59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8065137d37af5eec4394e417f761651ea2aa100c0f27739a8b2ee0d84f2bfa59","first_computed_at":"2026-06-05T01:15:31.971399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:31.971399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qbdYndDMOm6G+rYNW+C1LgET+pyDJpqWOmrXrVPByz63T2U31oPWdjuEy5y4nAr4rKQXszThzcoWI7RKMPDQAQ==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:31.971808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e347c925219402a52da6ea4c2856ecaa02ea353f1ffe6ecb3e1028cf83a99959","sha256:121f07ec2ca01037cb792ea7a2661fd226f51e84b2633caa15bdbfe4d7394e7b"],"state_sha256":"e449fc36870488e0fdccb7efa746c15b546f3339afdb703d88be7f41199416aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47igNB2Jyu3GKX7BDETL/BnBpQLdf4EtIL2m0ugAQXtWm/CC4B1YTxA6jfi0FNBRo/ZOTV885akQU2fchVRuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:12:07.553806Z","bundle_sha256":"a185bbaa195395a17a7cd1fc52fb3955a19539e7ce5cd273e3312dcea95cb841"}}