{"public_id":"cl_3aabd6e49e86cb33c5af834b3236c8a7","status":"active","superseded_by_public_id":null,"corpus_id":118220971,"text":"Residuation is used as a substitute for inverse addition in the space of closed convex subsets of a topological linear space and is closely related to the Minkowski difference.","confidence":0.91,"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":0.91,"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_0542397454572e2116ef4fcea05777f5","name":"Minkowski difference","description":"A geometric difference operation on convex sets, also called the geometric difference.","types":["set operation"],"url":"https://sah.borca.ai/concepts/co_0542397454572e2116ef4fcea05777f5"},{"public_id":"co_5f029e246fe457472766be5f3cd2359b","name":"closed convex subsets","description":"Subsets that are both closed and convex, considered within a topological linear space.","types":["set"],"url":"https://sah.borca.ai/concepts/co_5f029e246fe457472766be5f3cd2359b"},{"public_id":"co_ca54437f4553774f3a7076d9ba9867d7","name":"residuation operation","description":"An operation used here to replace inverse addition for certain closed convex sets.","types":["operation"],"url":"https://sah.borca.ai/concepts/co_ca54437f4553774f3a7076d9ba9867d7"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_3aabd6e49e86cb33c5af834b3236c8a7"}