{"id":"W4296608948","doi":"10.1007/s12220-022-01041-8","title":"Regularity of Critical Points of the Volume Functional for Lagrangian Submanifolds","year":2022,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Lagrangian; Differential geometry; Mathematics; Hamiltonian (control theory); Mathematical analysis; Partial differential equation; Mathematical optimization","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001679229,0.001112082,0.001436424,0.007123124,0.001680543,0.003607944,0.001691055,0.001570079,0.004084222],"category_scores_gemma":[0.009368383,0.0008572172,0.0008591036,0.0009409972,0.004161675,0.00305929,0.002781789,0.001894773,0.0004416755],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002686944,"about_ca_system_score_gemma":0.0007917174,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002248813,"about_ca_topic_score_gemma":0.001651064,"domain_scores_codex":[0.9994702,0.0001564327,0.00003082067,0.0001013295,0.0001174196,0.0001237206],"domain_scores_gemma":[0.9957702,0.001615212,0.0007596388,0.0001926681,0.0005911826,0.001071217],"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":[0.0003264345,0.0001239149,0.004858051,0.0001250596,0.00006574119,0.0005047835,0.0005959616,0.01530076,0.007178276,0.9637276,0.002054524,0.005138811],"study_design_scores_gemma":[0.00005795604,0.00008849284,0.004616439,0.00007358295,0.00002607997,0.0003339978,0.0003646811,0.1336018,0.00176166,0.8575836,0.001428545,0.00006310177],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9298337,0.0009243567,0.04956941,0.001500515,0.0001367121,0.0000582848,0.0002955371,0.0001848221,0.01749676],"genre_scores_gemma":[0.9885429,0.0003205204,0.004984716,0.0001001503,0.0001781992,0.0000487613,0.0003814748,0.0001249587,0.005318321],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007123124,"threshold_uncertainty_score":0.01949525,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03457035432352551,"score_gpt":0.2863785122032134,"score_spread":0.2518081578796879,"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."}}