{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:4VOU4FTDBZGPR57W7W6YXK3DYC","short_pith_number":"pith:4VOU4FTD","canonical_record":{"source":{"id":"2311.03604","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-06T23:16:38Z","cross_cats_sorted":[],"title_canon_sha256":"31f686b210e428a0b661fd1869defc6c60760dd99792de28278acaa903ea5f8f","abstract_canon_sha256":"030499f4050cf489b08a9f86ccd277bda724703ea9870c59d81fb44e4694ed2a"},"schema_version":"1.0"},"canonical_sha256":"e55d4e16630e4cf8f7f6fdbd8bab63c09ac946d40c5ec4a39185aee6b77c3272","source":{"kind":"arxiv","id":"2311.03604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03604","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03604v1","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03604","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"4VOU4FTDBZGP","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VOU4FTDBZGPR57W","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VOU4FTD","created_at":"2026-07-05T07:10:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:4VOU4FTDBZGPR57W7W6YXK3DYC","target":"record","payload":{"canonical_record":{"source":{"id":"2311.03604","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-06T23:16:38Z","cross_cats_sorted":[],"title_canon_sha256":"31f686b210e428a0b661fd1869defc6c60760dd99792de28278acaa903ea5f8f","abstract_canon_sha256":"030499f4050cf489b08a9f86ccd277bda724703ea9870c59d81fb44e4694ed2a"},"schema_version":"1.0"},"canonical_sha256":"e55d4e16630e4cf8f7f6fdbd8bab63c09ac946d40c5ec4a39185aee6b77c3272","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:10:00.987773Z","signature_b64":"GKGnb7CnDXWDjLpP3fmpnkq1zjkHM73pVZSUPiCxMuD+E8AkLVoH2c5+z7mIGcfAOW5IWaUFqWE0SBbwDS9FAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e55d4e16630e4cf8f7f6fdbd8bab63c09ac946d40c5ec4a39185aee6b77c3272","last_reissued_at":"2026-07-05T07:10:00.987257Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:10:00.987257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.03604","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":"2026-07-05T07:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k2hvbBs6jKvb0f+NoO4/9F7WKUKV0GEhtjRjSLGzCGdyKCORaJu1DhPLO8Z+//9VnLI7YSILwmmiC3U+FDdxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:52:15.671014Z"},"content_sha256":"1d4cd1012eb99b2ca01557dbff304606bf64b290bc27f9a4fd01af405cea8eb4","schema_version":"1.0","event_id":"sha256:1d4cd1012eb99b2ca01557dbff304606bf64b290bc27f9a4fd01af405cea8eb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:4VOU4FTDBZGPR57W7W6YXK3DYC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directional derivative of the value function for parametric set-constrained optimization problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jane Ye, Kuang Bai","submitted_at":"2023-11-06T23:16:38Z","abstract_excerpt":"This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and lower Dini directional derivative of the value function respectively, from which we obtain Hadamard directional differentiability of the value function when the set of multipliers is a singleton. Our results do not require convexity of the set involved. Even in the case of a parametric nonlinear program, our results improve the classical ones in that our regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03604","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/2311.03604/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":"2026-07-05T07:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TA4P0uK15ArQEZrieL5CtK7RnFyUGt7KEODrbKXk7Vwm6+YYYCsWGzSCeA2e7NKl8257HWPtaN0cpl3hsuuZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T01:52:15.671392Z"},"content_sha256":"f92ccd56e76470acfb12a2f8d8dd81928a80f8e261cf97b61f20b7a2e1cba942","schema_version":"1.0","event_id":"sha256:f92ccd56e76470acfb12a2f8d8dd81928a80f8e261cf97b61f20b7a2e1cba942"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/bundle.json","state_url":"https://pith.science/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/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":"2026-08-06T01:52:15Z","links":{"resolver":"https://pith.science/pith/4VOU4FTDBZGPR57W7W6YXK3DYC","bundle":"https://pith.science/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/bundle.json","state":"https://pith.science/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VOU4FTDBZGPR57W7W6YXK3DYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4VOU4FTDBZGPR57W7W6YXK3DYC","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":"030499f4050cf489b08a9f86ccd277bda724703ea9870c59d81fb44e4694ed2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-06T23:16:38Z","title_canon_sha256":"31f686b210e428a0b661fd1869defc6c60760dd99792de28278acaa903ea5f8f"},"schema_version":"1.0","source":{"id":"2311.03604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03604","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03604v1","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03604","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"4VOU4FTDBZGP","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_16","alias_value":"4VOU4FTDBZGPR57W","created_at":"2026-07-05T07:10:00Z"},{"alias_kind":"pith_short_8","alias_value":"4VOU4FTD","created_at":"2026-07-05T07:10:00Z"}],"graph_snapshots":[{"event_id":"sha256:f92ccd56e76470acfb12a2f8d8dd81928a80f8e261cf97b61f20b7a2e1cba942","target":"graph","created_at":"2026-07-05T07:10:00Z","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/2311.03604/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and lower Dini directional derivative of the value function respectively, from which we obtain Hadamard directional differentiability of the value function when the set of multipliers is a singleton. Our results do not require convexity of the set involved. Even in the case of a parametric nonlinear program, our results improve the classical ones in that our regul","authors_text":"Jane Ye, Kuang Bai","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-06T23:16:38Z","title":"Directional derivative of the value function for parametric set-constrained optimization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03604","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":"sha256:1d4cd1012eb99b2ca01557dbff304606bf64b290bc27f9a4fd01af405cea8eb4","target":"record","created_at":"2026-07-05T07:10:00Z","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":"030499f4050cf489b08a9f86ccd277bda724703ea9870c59d81fb44e4694ed2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2023-11-06T23:16:38Z","title_canon_sha256":"31f686b210e428a0b661fd1869defc6c60760dd99792de28278acaa903ea5f8f"},"schema_version":"1.0","source":{"id":"2311.03604","kind":"arxiv","version":1}},"canonical_sha256":"e55d4e16630e4cf8f7f6fdbd8bab63c09ac946d40c5ec4a39185aee6b77c3272","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e55d4e16630e4cf8f7f6fdbd8bab63c09ac946d40c5ec4a39185aee6b77c3272","first_computed_at":"2026-07-05T07:10:00.987257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:10:00.987257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GKGnb7CnDXWDjLpP3fmpnkq1zjkHM73pVZSUPiCxMuD+E8AkLVoH2c5+z7mIGcfAOW5IWaUFqWE0SBbwDS9FAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:10:00.987773Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.03604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d4cd1012eb99b2ca01557dbff304606bf64b290bc27f9a4fd01af405cea8eb4","sha256:f92ccd56e76470acfb12a2f8d8dd81928a80f8e261cf97b61f20b7a2e1cba942"],"state_sha256":"b033bfe4f36bc5b6b2d4cd1431eb4ea86cc9ac8a2c29936bc36624763f6c51ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86AwxoInzeLWh033m3MVbcZwTHh9aLTm6A7iwv9EpPG+sBNSs+z6udCw5fuwAnT5TFcbFfg0Vx3FSVIwnvrpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T01:52:15.674086Z","bundle_sha256":"5b214a253216d98977e098c8ec7b29ce5a3c576e80f81a64e0d01279d6d30d65"}}