{"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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005469343,0.0001611745,0.0004491202,0.00002212983,0.0001967631,0.00003342305,0.0005435823,0.00005586354,0.00002055633],"category_scores_gemma":[0.00308449,0.00008801086,0.0004564862,0.0006108134,0.0006122213,0.00007341179,0.0001786277,0.0001612354,9.100197e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003885562,"about_ca_system_score_gemma":0.00006055524,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000111778,"about_ca_topic_score_gemma":0.000001654565,"domain_scores_codex":[0.9987523,0.000009821451,0.0005181765,0.0001737652,0.0003222674,0.0002236739],"domain_scores_gemma":[0.996873,0.001793778,0.0007007535,0.0002226157,0.0003785336,0.00003127063],"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":[0.00005236672,0.000531319,0.001114463,0.002371378,0.0005239748,7.396708e-9,0.001922698,0.00001600657,0.01974124,0.9608384,0.01055832,0.002329875],"study_design_scores_gemma":[0.00021876,0.00005903795,0.0007592869,0.0001973129,0.0004431421,4.033536e-7,0.001121011,0.05489038,0.05856819,0.8835167,0.0001327777,0.00009296538],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4109212,0.0001427378,0.5707458,0.01017361,0.0001262267,0.004232856,0.0001018313,0.0001487102,0.003407014],"genre_scores_gemma":[0.9050782,0.000003535726,0.09422017,0.0001556661,0.00005186403,0.0002058035,0.000002034429,0.00002482383,0.0002578628],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.494157,"threshold_uncertainty_score":0.3692646,"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."}}