{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3AHZJCFRVZOUVY7K2XG3M5RGSC","short_pith_number":"pith:3AHZJCFR","schema_version":"1.0","canonical_sha256":"d80f9488b1ae5d4ae3ead5cdb67626908b935ec043d42690e0cfed3e8368e543","source":{"kind":"arxiv","id":"1403.2898","version":1},"attestation_state":"computed","paper":{"title":"A Minty variational principle for set optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas H. Hamel, Carola Schrage, Giovanni P. Crespi","submitted_at":"2014-03-12T12:10:39Z","abstract_excerpt":"Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. L\\\"ohne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity as"},"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":"1403.2898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-12T12:10:39Z","cross_cats_sorted":[],"title_canon_sha256":"1eec791897085f87120cee7638769a46e0078bdefbf5b2ba5a215deded5edcae","abstract_canon_sha256":"b7dbebffddb1a6ba1f55e4b1a169f75bea90b5308471452733bd89641bfecc27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:06.706565Z","signature_b64":"DJW4OaS4jeyRFtnyMC7RorLoCZ6omnE3vsgK4qTRRIzoIMMhrioYefn9/S0ZrntHAKlzvZQoGRjIh1kLHSDCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d80f9488b1ae5d4ae3ead5cdb67626908b935ec043d42690e0cfed3e8368e543","last_reissued_at":"2026-05-18T00:56:06.706054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:06.706054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Minty variational principle for set optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas H. Hamel, Carola Schrage, Giovanni P. Crespi","submitted_at":"2014-03-12T12:10:39Z","abstract_excerpt":"Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution concept for such problems, introduced by F. Heyde and A. L\\\"ohne, comprises the attainment of the infimum as well as a minimality property. The main result is a Minty type variational inequality for set optimization problems which provides a sufficient optimality condition under lower semicontinuity assumptions and a necessary condition under appropriate generalized convexity as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2898","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":""},"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":"1403.2898","created_at":"2026-05-18T00:56:06.706130+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.2898v1","created_at":"2026-05-18T00:56:06.706130+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2898","created_at":"2026-05-18T00:56:06.706130+00:00"},{"alias_kind":"pith_short_12","alias_value":"3AHZJCFRVZOU","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3AHZJCFRVZOUVY7K","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3AHZJCFR","created_at":"2026-05-18T12:28:11.866339+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/3AHZJCFRVZOUVY7K2XG3M5RGSC","json":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC.json","graph_json":"https://pith.science/api/pith-number/3AHZJCFRVZOUVY7K2XG3M5RGSC/graph.json","events_json":"https://pith.science/api/pith-number/3AHZJCFRVZOUVY7K2XG3M5RGSC/events.json","paper":"https://pith.science/paper/3AHZJCFR"},"agent_actions":{"view_html":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC","download_json":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC.json","view_paper":"https://pith.science/paper/3AHZJCFR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.2898&json=true","fetch_graph":"https://pith.science/api/pith-number/3AHZJCFRVZOUVY7K2XG3M5RGSC/graph.json","fetch_events":"https://pith.science/api/pith-number/3AHZJCFRVZOUVY7K2XG3M5RGSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC/action/storage_attestation","attest_author":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC/action/author_attestation","sign_citation":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC/action/citation_signature","submit_replication":"https://pith.science/pith/3AHZJCFRVZOUVY7K2XG3M5RGSC/action/replication_record"}},"created_at":"2026-05-18T00:56:06.706130+00:00","updated_at":"2026-05-18T00:56:06.706130+00:00"}