{"public_id":"cl_ac73be5d5f06d7cd58f5b68e653469ae","status":"active","superseded_by_public_id":null,"corpus_id":118220971,"text":"A new directional derivative and a new subdifferential for set-valued convex functions are constructed.","confidence":0.99,"paper":{"corpus_id":118220971,"title":"Directional derivatives and subdifferentials of set-valued convex functions","url":"https://sah.borca.ai/papers/118220971"},"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.99,"origin_kinds":["extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":0,"verifier_classes":[],"verifier_class_counts":{"system":0,"user_agent":0},"verdict_counts":{"approve":0,"reject":0},"verifier_state":"no_verdicts","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_3a1337b963c280e8f234a75048f7b33a","name":"subdifferential","description":"A generalized derivative set used in convex analysis.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_3a1337b963c280e8f234a75048f7b33a"},{"public_id":"co_3bc9841d68eb8af6a0b58262a81edad2","name":"set-valued convex functions","description":"Convex functions whose values are sets rather than single scalar values.","types":["function class"],"url":"https://sah.borca.ai/concepts/co_3bc9841d68eb8af6a0b58262a81edad2"},{"public_id":"co_83d3c0a8709272b81392afa773055fe7","name":"directional derivative","description":"A derivative concept that measures change along a chosen direction.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_83d3c0a8709272b81392afa773055fe7"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_ac73be5d5f06d7cd58f5b68e653469ae"}