{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DBMAWPFEW5OF7AU54K7BUEURHL","short_pith_number":"pith:DBMAWPFE","schema_version":"1.0","canonical_sha256":"18580b3ca4b75c5f829de2be1a12913acd02e972953f10c2091672da5574282c","source":{"kind":"arxiv","id":"1501.00307","version":1},"attestation_state":"computed","paper":{"title":"Coderivative characterizations of maximal monotonicity for set-valued mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"B. S. Mordukhovich, G. M. Lee, N. H. Chieu, T. T. A. Nghia","submitted_at":"2015-01-01T20:29:35Z","abstract_excerpt":"This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which seem to be the first infinitesimal characterizations of maximal monotonicity outside the single-valued case. We also present second-order necessary and sufficient conditions for lower-${\\mathcal C}^2$ functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions."},"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":"1501.00307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-01-01T20:29:35Z","cross_cats_sorted":[],"title_canon_sha256":"dd4c47a05d6065c062f55358c77ba64c43eb52a84b2fdb06f14636deb9a9d9f0","abstract_canon_sha256":"fc2fa8767be2feff601e2f83bc6cd0680a7c600e8fc9dea8926feae280881d91"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:09.638553Z","signature_b64":"9bZNpe2BNSQxkUNC6naiCJQ0Htnb2fe8HEplzdAFNZAMkm59YOhtyJ6y9nVmnrGE3srvShaP+mMSFctV1IloCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18580b3ca4b75c5f829de2be1a12913acd02e972953f10c2091672da5574282c","last_reissued_at":"2026-05-18T02:30:09.638109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:09.638109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coderivative characterizations of maximal monotonicity for set-valued mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"B. S. Mordukhovich, G. M. Lee, N. H. Chieu, T. T. A. Nghia","submitted_at":"2015-01-01T20:29:35Z","abstract_excerpt":"This paper concerns generalized differential characterizations of maximal monotone set-valued mappings. Using advanced tools of variational analysis, we establish coderivative criteria for maximal monotonicity of set-valued mappings, which seem to be the first infinitesimal characterizations of maximal monotonicity outside the single-valued case. We also present second-order necessary and sufficient conditions for lower-${\\mathcal C}^2$ functions to be convex and strongly convex. Examples are provided to illustrate the obtained results and the imposed assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00307","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":"1501.00307","created_at":"2026-05-18T02:30:09.638162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00307v1","created_at":"2026-05-18T02:30:09.638162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00307","created_at":"2026-05-18T02:30:09.638162+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBMAWPFEW5OF","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBMAWPFEW5OF7AU5","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBMAWPFE","created_at":"2026-05-18T12:29:17.054201+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/DBMAWPFEW5OF7AU54K7BUEURHL","json":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL.json","graph_json":"https://pith.science/api/pith-number/DBMAWPFEW5OF7AU54K7BUEURHL/graph.json","events_json":"https://pith.science/api/pith-number/DBMAWPFEW5OF7AU54K7BUEURHL/events.json","paper":"https://pith.science/paper/DBMAWPFE"},"agent_actions":{"view_html":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL","download_json":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL.json","view_paper":"https://pith.science/paper/DBMAWPFE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00307&json=true","fetch_graph":"https://pith.science/api/pith-number/DBMAWPFEW5OF7AU54K7BUEURHL/graph.json","fetch_events":"https://pith.science/api/pith-number/DBMAWPFEW5OF7AU54K7BUEURHL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL/action/storage_attestation","attest_author":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL/action/author_attestation","sign_citation":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL/action/citation_signature","submit_replication":"https://pith.science/pith/DBMAWPFEW5OF7AU54K7BUEURHL/action/replication_record"}},"created_at":"2026-05-18T02:30:09.638162+00:00","updated_at":"2026-05-18T02:30:09.638162+00:00"}