{"id":"W4416917285","doi":"10.1090/proc/17495","title":"A simple proof of curvature estimates for the 𝑛-1 Hessian equation","year":2025,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Curvature; Simple (philosophy); Hessian matrix; Hessian equation; Mean curvature; Center of curvature","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":[0.001558692,0.002142061,0.001113468,0.002685166,0.0009436274,0.001265425,0.001848306,0.001379497,0.01468621],"category_scores_gemma":[0.006511332,0.000717539,0.00262845,0.001147207,0.001885291,0.00389373,0.00454846,0.004938646,0.004001245],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001592173,"about_ca_system_score_gemma":0.000834809,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002983609,"about_ca_topic_score_gemma":0.002905031,"domain_scores_codex":[0.9992213,0.0001418064,0.00005054128,0.0001384194,0.0003754022,0.0000724968],"domain_scores_gemma":[0.9984407,0.0006061504,0.0001128181,0.0001707024,0.0005176747,0.0001520212],"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":[0.00004455399,0.00005839156,0.0005760315,0.0005156493,0.00009223237,0.0005310391,0.000601019,0.003507188,0.01029369,0.899269,0.03911008,0.04540104],"study_design_scores_gemma":[0.00003396397,0.00007813528,0.002169845,0.0001010802,0.00008921891,0.0007111575,0.0001189126,0.0265086,0.004656796,0.8981198,0.06729063,0.0001219555],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02757832,0.008647175,0.7963501,0.01303551,0.00473813,0.0002531958,0.001631532,0.001578326,0.1461878],"genre_scores_gemma":[0.539371,0.01008005,0.2983427,0.006608882,0.004492619,0.0006548505,0.00183333,0.002034298,0.1365824],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01468621,"threshold_uncertainty_score":0.04913032,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04114189775162259,"score_gpt":0.3484521836506466,"score_spread":0.307310285899024,"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."}}