{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:KITA52Q4Z67DEDCZ2D3GJC3Y43","short_pith_number":"pith:KITA52Q4","canonical_record":{"source":{"id":"2312.16277","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-26T17:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"92445ad31c78ca5a5c7cf4a6ef59a727280e0212b955b7a2ea3c09e978a94863","abstract_canon_sha256":"b81ef1267981b77a03acbefb8310fbf92ec60cbc2ae781a71f17d563fac2cff6"},"schema_version":"1.0"},"canonical_sha256":"52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af","source":{"kind":"arxiv","id":"2312.16277","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.16277","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"2312.16277v2","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.16277","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"KITA52Q4Z67D","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_16","alias_value":"KITA52Q4Z67DEDCZ","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_8","alias_value":"KITA52Q4","created_at":"2026-07-05T09:56:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:KITA52Q4Z67DEDCZ2D3GJC3Y43","target":"record","payload":{"canonical_record":{"source":{"id":"2312.16277","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-26T17:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"92445ad31c78ca5a5c7cf4a6ef59a727280e0212b955b7a2ea3c09e978a94863","abstract_canon_sha256":"b81ef1267981b77a03acbefb8310fbf92ec60cbc2ae781a71f17d563fac2cff6"},"schema_version":"1.0"},"canonical_sha256":"52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:49.078229Z","signature_b64":"MhuVIvq0H4gu7nT8UCURujQFge693Bjmz9MU8y+uLnElfiUlBrI81JRucohFhzwSjViXK4wwQhoIW99lWLzICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af","last_reissued_at":"2026-07-05T09:56:49.077754Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:49.077754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.16277","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iBgVB4Z7PHMT0bJor/qATUZNmqXN1LHwof1zR4Y6Ds7WKy8887dke4U/0aOBQDp1YaedBALtHUt6Q46hSL2qCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:57:03.684839Z"},"content_sha256":"608fb0cee1353f2a248eb859a9622d07e4d8779ff5341d73f0ac6d44ddada1b2","schema_version":"1.0","event_id":"sha256:608fb0cee1353f2a248eb859a9622d07e4d8779ff5341d73f0ac6d44ddada1b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:KITA52Q4Z67DEDCZ2D3GJC3Y43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Boris S. Mordukhovich, Pham Duy Khanh, Vo Thanh Phat, Vu Vinh Huy Khoa","submitted_at":"2023-12-26T17:58:53Z","abstract_excerpt":"The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern prox-regular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16277","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/2312.16277/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":"2026-07-05T09:56:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MeaqDpIHUMbw3ZdmW4092De2tlC3Jqj/S29HR69UCC9wNq0aYQxs45QDmYVb0mYK6piUYap255Eaqh8xyYpiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:57:03.685352Z"},"content_sha256":"136e150c2082ebbd9187fb9abd875a650ecd28b47f1444ee6a12f5f0e33ab48d","schema_version":"1.0","event_id":"sha256:136e150c2082ebbd9187fb9abd875a650ecd28b47f1444ee6a12f5f0e33ab48d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/bundle.json","state_url":"https://pith.science/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/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":"2026-08-10T05:57:03Z","links":{"resolver":"https://pith.science/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43","bundle":"https://pith.science/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/bundle.json","state":"https://pith.science/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KITA52Q4Z67DEDCZ2D3GJC3Y43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:KITA52Q4Z67DEDCZ2D3GJC3Y43","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":"b81ef1267981b77a03acbefb8310fbf92ec60cbc2ae781a71f17d563fac2cff6","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-26T17:58:53Z","title_canon_sha256":"92445ad31c78ca5a5c7cf4a6ef59a727280e0212b955b7a2ea3c09e978a94863"},"schema_version":"1.0","source":{"id":"2312.16277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.16277","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"arxiv_version","alias_value":"2312.16277v2","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.16277","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_12","alias_value":"KITA52Q4Z67D","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_16","alias_value":"KITA52Q4Z67DEDCZ","created_at":"2026-07-05T09:56:49Z"},{"alias_kind":"pith_short_8","alias_value":"KITA52Q4","created_at":"2026-07-05T09:56:49Z"}],"graph_snapshots":[{"event_id":"sha256:136e150c2082ebbd9187fb9abd875a650ecd28b47f1444ee6a12f5f0e33ab48d","target":"graph","created_at":"2026-07-05T09:56:49Z","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/2312.16277/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern prox-regular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained ge","authors_text":"Boris S. Mordukhovich, Pham Duy Khanh, Vo Thanh Phat, Vu Vinh Huy Khoa","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-26T17:58:53Z","title":"Second-Order Subdifferential Optimality Conditions in Nonsmooth Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16277","kind":"arxiv","version":2},"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":"sha256:608fb0cee1353f2a248eb859a9622d07e4d8779ff5341d73f0ac6d44ddada1b2","target":"record","created_at":"2026-07-05T09:56:49Z","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":"b81ef1267981b77a03acbefb8310fbf92ec60cbc2ae781a71f17d563fac2cff6","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-26T17:58:53Z","title_canon_sha256":"92445ad31c78ca5a5c7cf4a6ef59a727280e0212b955b7a2ea3c09e978a94863"},"schema_version":"1.0","source":{"id":"2312.16277","kind":"arxiv","version":2}},"canonical_sha256":"52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52260eea1ccfbe320c59d0f6648b78e6ec0142c1c97962ecf34131b88d4b80af","first_computed_at":"2026-07-05T09:56:49.077754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:56:49.077754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MhuVIvq0H4gu7nT8UCURujQFge693Bjmz9MU8y+uLnElfiUlBrI81JRucohFhzwSjViXK4wwQhoIW99lWLzICg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:56:49.078229Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.16277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:608fb0cee1353f2a248eb859a9622d07e4d8779ff5341d73f0ac6d44ddada1b2","sha256:136e150c2082ebbd9187fb9abd875a650ecd28b47f1444ee6a12f5f0e33ab48d"],"state_sha256":"17bb54809b4a85ae1852619524947e0b6554a79e8d547c2acfec3d099921b44f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTpfvfbD5SsuB6wYRZdpJ7/A7v6gJcGH02ptYMgL/VjrY14WYlloeejQhucuFbVy5wMpKGr9QMXZxR2HtdfVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T05:57:03.689799Z","bundle_sha256":"6bc83de444f966ec55db3e8adcbb141a20497b3eac91b983b0166ce7390e1b29"}}