{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z5QBDNQ6LKW4GAW7ID5R22HPWM","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":"e62af284ec37c8c4d7531c30d5454bc4349ada3abb076983c8eb6dd766a3ee2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-10-01T22:00:51Z","title_canon_sha256":"e7013036403169d53ec474faee53ce1f127d0ec6cff3fb0990f8c9ec3fe14756"},"schema_version":"1.0","source":{"id":"2510.01487","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.01487","created_at":"2026-05-28T02:04:43Z"},{"alias_kind":"arxiv_version","alias_value":"2510.01487v2","created_at":"2026-05-28T02:04:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.01487","created_at":"2026-05-28T02:04:43Z"},{"alias_kind":"pith_short_12","alias_value":"Z5QBDNQ6LKW4","created_at":"2026-05-28T02:04:43Z"},{"alias_kind":"pith_short_16","alias_value":"Z5QBDNQ6LKW4GAW7","created_at":"2026-05-28T02:04:43Z"},{"alias_kind":"pith_short_8","alias_value":"Z5QBDNQ6","created_at":"2026-05-28T02:04:43Z"}],"graph_snapshots":[{"event_id":"sha256:983acd827edff174af1daeb9441a4e20e0848246f29c07cdcb85ba5830d3d26c","target":"graph","created_at":"2026-05-28T02:04:43Z","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/2510.01487/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal solution as an implicit, locally differentiable function of the upper-level variables, thereby avoiding classical single-level reformulations. Under standard regularity assumptions on the lower level, an adjoint-based representation of the reduced upper-level gradient is derived, replacing explicit construction of the sensitivity Jacobian with a single linear adjo","authors_text":"Eduardo Nolasco, Ross D. King, Vassilios S. Vassiliadis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-10-01T22:00:51Z","title":"A sensitivity-based method for bilevel optimization problems: Theoretical analysis and computational performance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.01487","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":"sha256:20d67f1c0a7cbe81e1374da147d5126e63f8fa836df047605029d0bc833d3f67","target":"record","created_at":"2026-05-28T02:04:43Z","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":"e62af284ec37c8c4d7531c30d5454bc4349ada3abb076983c8eb6dd766a3ee2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-10-01T22:00:51Z","title_canon_sha256":"e7013036403169d53ec474faee53ce1f127d0ec6cff3fb0990f8c9ec3fe14756"},"schema_version":"1.0","source":{"id":"2510.01487","kind":"arxiv","version":2}},"canonical_sha256":"cf6011b61e5aadc302df40fb1d68efb3043bbd4a3cb15b8b8c4c87006d7539ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf6011b61e5aadc302df40fb1d68efb3043bbd4a3cb15b8b8c4c87006d7539ae","first_computed_at":"2026-05-28T02:04:43.206383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T02:04:43.206383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZkQAcOIo8iZQQZIzfresv21K2bQqgE+m6uBvQabBR1gbOsJAlWI+GOmdVQH08b3Dehvhh9dAJpuReiexF1kwDQ==","signature_status":"signed_v1","signed_at":"2026-05-28T02:04:43.207488Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.01487","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20d67f1c0a7cbe81e1374da147d5126e63f8fa836df047605029d0bc833d3f67","sha256:983acd827edff174af1daeb9441a4e20e0848246f29c07cdcb85ba5830d3d26c"],"state_sha256":"c78627d2ee6207a82180ece37ec18eea8cc018aaff174250097489dca80babf1"}