{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T3JSISAKFO63PFFSGJFMRICBSF","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":"6bb73763cec64f2b65c1c1168b8aa795c1f42c14eff941000931fb805396eab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-11T10:53:14Z","title_canon_sha256":"dbd04ddd85d3cf122265266efc70c48b0ba9b1d00c92d1c14e8164f890f1b5a1"},"schema_version":"1.0","source":{"id":"1409.3383","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.3383","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"arxiv_version","alias_value":"1409.3383v2","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.3383","created_at":"2026-05-18T00:56:06Z"},{"alias_kind":"pith_short_12","alias_value":"T3JSISAKFO63","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T3JSISAKFO63PFFS","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T3JSISAK","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:b8f80e805f342b3dda43cd5e2d8cfe9639d9d5e3f7c9c8e94355f37fe8a0e404","target":"graph","created_at":"2026-05-18T00:56:06Z","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"},"paper":{"abstract_excerpt":"In the literature, necessary and sufficient conditions in terms of variational inequalities are introduced to characterize minimizers of convex set valued functions with values in a conlinear space. Similar results are proved for a weaker concept of minimizers and weaker variational inequalities. The implications are proved using scalarization techniques that eventually provide original problems, not fully equivalent to the set-valued counterparts. Therefore, we try, in the course of this note, to close the network among the various notions proposed. More specifically, we prove that a minimize","authors_text":"Carola Schrage, Giovanni P. Crespi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-11T10:53:14Z","title":"Weak Minimizers, Minimizers and Variational Inequalities for set valued Functions. A blooming wreath?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3383","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":"sha256:993cf500e974137c0b3591c07e7995175a5d1666e831260e9f8a8314d2a4036a","target":"record","created_at":"2026-05-18T00:56:06Z","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":"6bb73763cec64f2b65c1c1168b8aa795c1f42c14eff941000931fb805396eab7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-11T10:53:14Z","title_canon_sha256":"dbd04ddd85d3cf122265266efc70c48b0ba9b1d00c92d1c14e8164f890f1b5a1"},"schema_version":"1.0","source":{"id":"1409.3383","kind":"arxiv","version":2}},"canonical_sha256":"9ed324480a2bbdb794b2324ac8a041914f9852ac9a27aabab20c5e9b156aef7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ed324480a2bbdb794b2324ac8a041914f9852ac9a27aabab20c5e9b156aef7a","first_computed_at":"2026-05-18T00:56:06.664915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:06.664915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqrHtgqe4F4dbARrOqwRcx2L/8gHypz+JEHA0P9RvT04P5EdeVDBJgmInsYKoHYqwU6M08iN12zUyD0/UKz4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:06.665586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.3383","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:993cf500e974137c0b3591c07e7995175a5d1666e831260e9f8a8314d2a4036a","sha256:b8f80e805f342b3dda43cd5e2d8cfe9639d9d5e3f7c9c8e94355f37fe8a0e404"],"state_sha256":"312934aeea4b53bd914aca62775f96292dc7e26364e8a55ca0abc07b56e69ed1"}