{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K235MSWTMYUTF5JQSW75XMG2BH","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":"fbbe66f5aad7548f4af6d866d083c7f6d63a97ecb946d8842c3f5fe0861878f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T09:55:02Z","title_canon_sha256":"bb97ee2e6dafc12ef090a881254a99c6aeeca4bcfe4ecf53c9a229b48d5ed7ec"},"schema_version":"1.0","source":{"id":"2606.01998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01998","created_at":"2026-06-02T02:05:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01998v1","created_at":"2026-06-02T02:05:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01998","created_at":"2026-06-02T02:05:03Z"},{"alias_kind":"pith_short_12","alias_value":"K235MSWTMYUT","created_at":"2026-06-02T02:05:03Z"},{"alias_kind":"pith_short_16","alias_value":"K235MSWTMYUTF5JQ","created_at":"2026-06-02T02:05:03Z"},{"alias_kind":"pith_short_8","alias_value":"K235MSWT","created_at":"2026-06-02T02:05:03Z"}],"graph_snapshots":[{"event_id":"sha256:3003afc80ce7bc013d2e805196063131dbeb9c29790f9e80d6b6e55d6591ac88","target":"graph","created_at":"2026-06-02T02:05:03Z","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/2606.01998/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate a class of sparse optimization problems in which both the objective and constraint functions are Fr\\'echet differentiable and possess locally Lipschitz continuous gradient mappings. More precisely, by utilizing the limiting (Mordukhovich) second-order subdifferential of the associated Lagrangian function, we establish new second-order necessary and sufficient optimality conditions for local optimal solutions. The obtained results are derived under mild assumptions and extend several existing results in the literature. In addition, we apply our theoretical developm","authors_text":"Liguo Jiao, Luu Thi Thu Huyen, Nguyen Van Tuyen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T09:55:02Z","title":"Second-Order Optimality Conditions for Sparse Differentiable Optimization Problems via Limiting Second-Order Subdifferentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01998","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":"sha256:134ad2a371f8d2c88cbbf78ae8e74126bd3ccd1c56859174b92fa8182ff7eacd","target":"record","created_at":"2026-06-02T02:05:03Z","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":"fbbe66f5aad7548f4af6d866d083c7f6d63a97ecb946d8842c3f5fe0861878f1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-06-01T09:55:02Z","title_canon_sha256":"bb97ee2e6dafc12ef090a881254a99c6aeeca4bcfe4ecf53c9a229b48d5ed7ec"},"schema_version":"1.0","source":{"id":"2606.01998","kind":"arxiv","version":1}},"canonical_sha256":"56b7d64ad3662932f53095bfdbb0da09e97248feddcaec6bba9a0afc1488f314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56b7d64ad3662932f53095bfdbb0da09e97248feddcaec6bba9a0afc1488f314","first_computed_at":"2026-06-02T02:05:03.189144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:05:03.189144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xq0Db3yFJvldBGWpS3OQLyS+NZJbTTdgGY4DeilPktc0tLuNGK28Q3HnUYIdGxs3nMQUqnxwpGqlGmpCC5IxBQ==","signature_status":"signed_v1","signed_at":"2026-06-02T02:05:03.189532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:134ad2a371f8d2c88cbbf78ae8e74126bd3ccd1c56859174b92fa8182ff7eacd","sha256:3003afc80ce7bc013d2e805196063131dbeb9c29790f9e80d6b6e55d6591ac88"],"state_sha256":"b5a374fa9ec3807a9082880ebe3fb83471b42b06eafb071801a48aa85e4f45dc"}