{"id":"W3111985369","doi":"10.1007/s00526-023-02442-5","title":"Constant rank theorems for curvature problems via a viscosity approach","year":2023,"lang":"en","type":"article","venue":"Calculus of Variations and Partial Differential Equations","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Australian Research Council; Deutsche Forschungsgemeinschaft; Fields Institute for Research in Mathematical Sciences","keywords":"Mathematics; Curvature; Constant (computer programming); Generalization; Mathematical proof; Eigenvalues and eigenvectors; Rank (graph theory); Mean curvature; Lipschitz continuity; Mathematical analysis; Simple (philosophy); Pure mathematics; Applied mathematics; Combinatorics; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004723013,0.001561555,0.001231258,0.005023716,0.001355438,0.003775695,0.001826865,0.001596109,0.009738794],"category_scores_gemma":[0.01450083,0.0006158882,0.001812355,0.00118439,0.004912822,0.00887917,0.005663441,0.005421279,0.001109131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002128369,"about_ca_system_score_gemma":0.0009962826,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001204971,"about_ca_topic_score_gemma":0.0009882677,"domain_scores_codex":[0.997581,0.0009218089,0.00009632916,0.0003285322,0.0007953753,0.0002769557],"domain_scores_gemma":[0.9894756,0.006091399,0.001114644,0.0007055036,0.001494177,0.001118623],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00001120286,0.00001269067,0.0002373946,0.00006209799,0.00001124833,0.00007270106,0.0001004596,0.00235618,0.0008708384,0.9920053,0.001313498,0.002946468],"study_design_scores_gemma":[0.00001200191,0.0000375675,0.0004175361,0.00003923804,0.00001551594,0.0001299337,0.00008695716,0.05106309,0.0007536989,0.9439049,0.003512251,0.00002716269],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.07932869,0.003839458,0.8302937,0.004738958,0.0004042545,0.0001213083,0.0003502677,0.0004291463,0.0804942],"genre_scores_gemma":[0.852427,0.003070224,0.1021682,0.001669915,0.001520054,0.0002498495,0.0004099973,0.0005914549,0.03789324],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009738794,"threshold_uncertainty_score":0.03257954,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07630753973518908,"score_gpt":0.3215816552051362,"score_spread":0.2452741154699471,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}