{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:R6L6ORNKRJGN5UNIYQHCTOUPGU","short_pith_number":"pith:R6L6ORNK","canonical_record":{"source":{"id":"2606.08424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"09f44acceae64ff7aadcc0f18d323309df15d3bae460c455317487c99cfd434d","abstract_canon_sha256":"d62ee4fbcdabc0fd6683c6afd7c0dc842401d0f409c4031e717641c6af480e17"},"schema_version":"1.0"},"canonical_sha256":"8f97e745aa8a4cded1a8c40e29ba8f35019e14f6c8ea1eb16ea823629ee1df34","source":{"kind":"arxiv","id":"2606.08424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08424","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08424v1","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08424","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"R6L6ORNKRJGN","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"R6L6ORNKRJGN5UNI","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"R6L6ORNK","created_at":"2026-06-09T01:05:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:R6L6ORNKRJGN5UNIYQHCTOUPGU","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:47:50Z","cross_cats_sorted":[],"title_canon_sha256":"09f44acceae64ff7aadcc0f18d323309df15d3bae460c455317487c99cfd434d","abstract_canon_sha256":"d62ee4fbcdabc0fd6683c6afd7c0dc842401d0f409c4031e717641c6af480e17"},"schema_version":"1.0"},"canonical_sha256":"8f97e745aa8a4cded1a8c40e29ba8f35019e14f6c8ea1eb16ea823629ee1df34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:36.267052Z","signature_b64":"66VHmjWgFHOfFqq5UFBCsYqcU6ljqxhCRdNxhB7jTpyZ992ALVIhJyoK4MokJoL+EXW0k2JPdGfdlxGsidZMAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f97e745aa8a4cded1a8c40e29ba8f35019e14f6c8ea1eb16ea823629ee1df34","last_reissued_at":"2026-06-09T01:05:36.266698Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:36.266698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08424","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":"2026-06-09T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nq1KS45ZNQAAUKDU8Eu2+gKef9UB5WHCDnsXJTo9TBH6tQKA/iLHAPzJk1JmRX793uPxlAtuAHDxm0qQg+XxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:50:57.526888Z"},"content_sha256":"0dd37691250dce726107d7b5bc7208255fafc405769afbbab13e672943b525de","schema_version":"1.0","event_id":"sha256:0dd37691250dce726107d7b5bc7208255fafc405769afbbab13e672943b525de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:R6L6ORNKRJGN5UNIYQHCTOUPGU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Augmented Lagrangian methods for nonlinear semidefinite programming with complementarity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carina M. Costa, Daiana O. Santos, Evelin H. M. Krulikovski e Marina Geremia","submitted_at":"2026-06-07T02:47:50Z","abstract_excerpt":"We consider nonlinear semidefinite programming problems with complementarity constraints (SDCMPCC), a class of highly degenerate problems where classical optimality conditions typically fail. In this context, weak stationarity conditions have been developed to address their degeneracy. While these notions are well understood, their algorithmic implications remain largely unexplored in semidefinite complementarity settings. We introduce a reformulation based on the spectral decomposition of the complementarity structure, which preserves local solutions and enables a tractable analysis. Within t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08424","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/2606.08424/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":"2026-06-09T01:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dk4ZrL3LbNooiOJ3HzBwWRKITjfhxKL1PHku9Vgfp4dSFOzR7gSpUjb/jnn0Xaq0a8j8IekaXQ1cA59lce/HBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T03:50:57.527259Z"},"content_sha256":"9405633c8e69a453cd5e5eb6211554f6e7f58314835dd5b9585a479533a1fc9a","schema_version":"1.0","event_id":"sha256:9405633c8e69a453cd5e5eb6211554f6e7f58314835dd5b9585a479533a1fc9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/bundle.json","state_url":"https://pith.science/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/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":"2026-06-28T03:50:57Z","links":{"resolver":"https://pith.science/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU","bundle":"https://pith.science/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/bundle.json","state":"https://pith.science/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6L6ORNKRJGN5UNIYQHCTOUPGU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R6L6ORNKRJGN5UNIYQHCTOUPGU","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":"d62ee4fbcdabc0fd6683c6afd7c0dc842401d0f409c4031e717641c6af480e17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:47:50Z","title_canon_sha256":"09f44acceae64ff7aadcc0f18d323309df15d3bae460c455317487c99cfd434d"},"schema_version":"1.0","source":{"id":"2606.08424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08424","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08424v1","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08424","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"R6L6ORNKRJGN","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"R6L6ORNKRJGN5UNI","created_at":"2026-06-09T01:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"R6L6ORNK","created_at":"2026-06-09T01:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:9405633c8e69a453cd5e5eb6211554f6e7f58314835dd5b9585a479533a1fc9a","target":"graph","created_at":"2026-06-09T01:05:36Z","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/2606.08424/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider nonlinear semidefinite programming problems with complementarity constraints (SDCMPCC), a class of highly degenerate problems where classical optimality conditions typically fail. In this context, weak stationarity conditions have been developed to address their degeneracy. While these notions are well understood, their algorithmic implications remain largely unexplored in semidefinite complementarity settings. We introduce a reformulation based on the spectral decomposition of the complementarity structure, which preserves local solutions and enables a tractable analysis. Within t","authors_text":"Carina M. Costa, Daiana O. Santos, Evelin H. M. Krulikovski e Marina Geremia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:47:50Z","title":"Augmented Lagrangian methods for nonlinear semidefinite programming with complementarity constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08424","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":"sha256:0dd37691250dce726107d7b5bc7208255fafc405769afbbab13e672943b525de","target":"record","created_at":"2026-06-09T01:05:36Z","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":"d62ee4fbcdabc0fd6683c6afd7c0dc842401d0f409c4031e717641c6af480e17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-07T02:47:50Z","title_canon_sha256":"09f44acceae64ff7aadcc0f18d323309df15d3bae460c455317487c99cfd434d"},"schema_version":"1.0","source":{"id":"2606.08424","kind":"arxiv","version":1}},"canonical_sha256":"8f97e745aa8a4cded1a8c40e29ba8f35019e14f6c8ea1eb16ea823629ee1df34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f97e745aa8a4cded1a8c40e29ba8f35019e14f6c8ea1eb16ea823629ee1df34","first_computed_at":"2026-06-09T01:05:36.266698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:36.266698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"66VHmjWgFHOfFqq5UFBCsYqcU6ljqxhCRdNxhB7jTpyZ992ALVIhJyoK4MokJoL+EXW0k2JPdGfdlxGsidZMAg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:36.267052Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd37691250dce726107d7b5bc7208255fafc405769afbbab13e672943b525de","sha256:9405633c8e69a453cd5e5eb6211554f6e7f58314835dd5b9585a479533a1fc9a"],"state_sha256":"f1f93e7b0dc00c31d40352a59070085ec2bced3528e4fd27502300df5f12983d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wNxUmbJQQ6ePIaMz8YQ4cDXECzHxebRRIRaLzLml2WaIjsG/u+s9/horcwrk/X3aAhrnJqgIlORAXXarBeLSDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T03:50:57.529160Z","bundle_sha256":"547d6daa585b8db400b68e8f79703de45342372ac5159ffc3f949624ef745a08"}}