{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EKH6Q4B6FWTIDESRXZP33GJDK6","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":"2eb5dda0e238b9514f704720fdb9d76e7b9bb3a2672dbe9f2602e397a322995c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-27T15:05:06Z","title_canon_sha256":"24b646b931932e964b7e7b3b98076dca4d4d47facbb98014b6cfe2da6a8d8784"},"schema_version":"1.0","source":{"id":"2606.28965","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.28965","created_at":"2026-06-30T01:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.28965v1","created_at":"2026-06-30T01:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28965","created_at":"2026-06-30T01:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"EKH6Q4B6FWTI","created_at":"2026-06-30T01:17:47Z"},{"alias_kind":"pith_short_16","alias_value":"EKH6Q4B6FWTIDESR","created_at":"2026-06-30T01:17:47Z"},{"alias_kind":"pith_short_8","alias_value":"EKH6Q4B6","created_at":"2026-06-30T01:17:47Z"}],"graph_snapshots":[{"event_id":"sha256:5a09d6b59da00646e521e872c3b5c2e765143904acbe299198cce9f4e51ed6b2","target":"graph","created_at":"2026-06-30T01:17:47Z","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/2606.28965/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop a second-order sensitivity theory for the efficient solution map \\(S\\) of a parametric vector optimization problem \\(\\min_C f(p,x)\\) subject to \\(x\\in H(p)\\). The main point is the passage from efficient values to efficient decisions. Under a value-to-decision error bound (VDB), second-order information for the marginal map \\(\\Phi\\) lifts to a second-order Dini formula for \\(S\\). We first work in the abstract inclusion model \\(x\\in H(p)\\), where outer and inner estimates yield second-order semi-derivability of \\(S\\). We then specialize to structured feasible maps \\(H(p)=\\{x\\in\\Omega","authors_text":"N. X. D. Bao, Tan H. Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-27T15:05:06Z","title":"Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28965","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":"sha256:6d5b041b239a6cc28c5317ca50cbf6bb5703c455880a63342572d53e25461d6e","target":"record","created_at":"2026-06-30T01:17:47Z","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":"2eb5dda0e238b9514f704720fdb9d76e7b9bb3a2672dbe9f2602e397a322995c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-27T15:05:06Z","title_canon_sha256":"24b646b931932e964b7e7b3b98076dca4d4d47facbb98014b6cfe2da6a8d8784"},"schema_version":"1.0","source":{"id":"2606.28965","kind":"arxiv","version":1}},"canonical_sha256":"228fe8703e2da6819251be5fbd9923579d81b8381a1cfd9bf43fc0888af37bb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"228fe8703e2da6819251be5fbd9923579d81b8381a1cfd9bf43fc0888af37bb0","first_computed_at":"2026-06-30T01:17:47.483349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:47.483349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N4h+0DPoGCptqvLVQI2dv+N+bwYospOOaGX0dyMve3XcSWTuyq7C/3GlnNoV47XUFhvH7BUyxadUspt/1XgtCQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:47.483831Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.28965","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d5b041b239a6cc28c5317ca50cbf6bb5703c455880a63342572d53e25461d6e","sha256:5a09d6b59da00646e521e872c3b5c2e765143904acbe299198cce9f4e51ed6b2"],"state_sha256":"09669cee3269b7ceadb7b5ffab67b25acdd74a15d41f6808c7e05272c0946844"}