{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:EKH6Q4B6FWTIDESRXZP33GJDK6","short_pith_number":"pith:EKH6Q4B6","schema_version":"1.0","canonical_sha256":"228fe8703e2da6819251be5fbd9923579d81b8381a1cfd9bf43fc0888af37bb0","source":{"kind":"arxiv","id":"2606.28965","version":1},"attestation_state":"computed","paper":{"title":"Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"N. X. D. Bao, Tan H. Cao","submitted_at":"2026-06-27T15:05:06Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.28965","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-06-27T15:05:06Z","cross_cats_sorted":[],"title_canon_sha256":"24b646b931932e964b7e7b3b98076dca4d4d47facbb98014b6cfe2da6a8d8784","abstract_canon_sha256":"2eb5dda0e238b9514f704720fdb9d76e7b9bb3a2672dbe9f2602e397a322995c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:47.483831Z","signature_b64":"N4h+0DPoGCptqvLVQI2dv+N+bwYospOOaGX0dyMve3XcSWTuyq7C/3GlnNoV47XUFhvH7BUyxadUspt/1XgtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"228fe8703e2da6819251be5fbd9923579d81b8381a1cfd9bf43fc0888af37bb0","last_reissued_at":"2026-06-30T01:17:47.483349Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:47.483349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"N. X. D. Bao, Tan H. Cao","submitted_at":"2026-06-27T15:05:06Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28965","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/2606.28965/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.28965","created_at":"2026-06-30T01:17:47.483415+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28965v1","created_at":"2026-06-30T01:17:47.483415+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28965","created_at":"2026-06-30T01:17:47.483415+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKH6Q4B6FWTI","created_at":"2026-06-30T01:17:47.483415+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKH6Q4B6FWTIDESR","created_at":"2026-06-30T01:17:47.483415+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKH6Q4B6","created_at":"2026-06-30T01:17:47.483415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6","json":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6.json","graph_json":"https://pith.science/api/pith-number/EKH6Q4B6FWTIDESRXZP33GJDK6/graph.json","events_json":"https://pith.science/api/pith-number/EKH6Q4B6FWTIDESRXZP33GJDK6/events.json","paper":"https://pith.science/paper/EKH6Q4B6"},"agent_actions":{"view_html":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6","download_json":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6.json","view_paper":"https://pith.science/paper/EKH6Q4B6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28965&json=true","fetch_graph":"https://pith.science/api/pith-number/EKH6Q4B6FWTIDESRXZP33GJDK6/graph.json","fetch_events":"https://pith.science/api/pith-number/EKH6Q4B6FWTIDESRXZP33GJDK6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6/action/storage_attestation","attest_author":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6/action/author_attestation","sign_citation":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6/action/citation_signature","submit_replication":"https://pith.science/pith/EKH6Q4B6FWTIDESRXZP33GJDK6/action/replication_record"}},"created_at":"2026-06-30T01:17:47.483415+00:00","updated_at":"2026-06-30T01:17:47.483415+00:00"}