{"id":"W4411805975","doi":"10.1007/s40818-025-00215-1","title":"Interior $$C^2$$ Estimate for Hessian Quotient Equation in General Dimension","year":2025,"lang":"en","type":"article","venue":"Annals of PDE","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"","keywords":"Quotient; Dimension (graph theory); Hessian matrix; Mathematics; Mathematical analysis; Pure mathematics; Applied mathematics","routes":{"ca_aff":true,"ca_fund":false,"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":[0.002059451,0.002367379,0.00210064,0.005428184,0.001479241,0.002539177,0.002714159,0.002004055,0.01689227],"category_scores_gemma":[0.007651835,0.0006297223,0.001578577,0.001239222,0.003548192,0.007801717,0.005183294,0.005873861,0.001538118],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002199894,"about_ca_system_score_gemma":0.001236776,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003499627,"about_ca_topic_score_gemma":0.003355768,"domain_scores_codex":[0.9993657,0.0002320569,0.0000285413,0.0001225151,0.0001656648,0.00008534212],"domain_scores_gemma":[0.9969022,0.001499892,0.0002461014,0.0002076239,0.0005815974,0.0005625773],"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":[0.00008347607,0.00006613693,0.000613747,0.0003185092,0.00003896155,0.0002037994,0.0001993714,0.003833617,0.002779289,0.9735175,0.009041437,0.009304192],"study_design_scores_gemma":[0.0000226671,0.00003685354,0.001135243,0.0000753596,0.00004480192,0.0002214879,0.00009043808,0.08703861,0.0009445035,0.9015616,0.008779448,0.00004894301],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1621584,0.01532957,0.4986372,0.02336535,0.004662977,0.0001931065,0.001797804,0.00123155,0.292624],"genre_scores_gemma":[0.7589343,0.008013363,0.08821634,0.003753426,0.005626474,0.0003546926,0.001525598,0.001672431,0.1319034],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01689227,"threshold_uncertainty_score":0.05651021,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1219892561282288,"score_gpt":0.4204497475323027,"score_spread":0.2984604914040739,"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."}}