{"public_id":"cl_399fe6612a38d34d5d39888d1cb66f8e","status":"active","superseded_by_public_id":null,"corpus_id":116435080,"text":"An entropy dissipation estimate for the adjoint variable addresses the lack of compactness in the whole-space setting.","confidence":0.91,"paper":{"corpus_id":116435080,"title":"Local regularity for mean-field games in the whole space","url":"https://sah.borca.ai/papers/116435080"},"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_0390ec2d7abddda4a49cee4a71fc7b39","name":"adjoint variable","description":"The auxiliary variable introduced in the adjoint formulation of the analysis.","types":["variable"],"url":"https://sah.borca.ai/concepts/co_0390ec2d7abddda4a49cee4a71fc7b39"},{"public_id":"co_443f12f601f0ca381d72a271c6f8b838","name":"lack of compactness","description":"The absence of compactness properties that complicates analysis on unbounded domains.","types":["mathematical challenge"],"url":"https://sah.borca.ai/concepts/co_443f12f601f0ca381d72a271c6f8b838"},{"public_id":"co_c2329695c929f7a13c57426cddf19714","name":"entropy dissipation estimate","description":"An estimate controlling the decrease of entropy-like quantities over time or under evolution.","types":["estimate"],"url":"https://sah.borca.ai/concepts/co_c2329695c929f7a13c57426cddf19714"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_399fe6612a38d34d5d39888d1cb66f8e"}