{"id":"W4388650776","doi":"10.48550/arxiv.2311.05835","title":"Interior $C^2$ estimate for Hessian quotient equation in dimension three","year":2023,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Physics Problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Quotient; Hessian matrix; Dimension (graph theory); Sigma; Mathematics; Hessian equation; Pure mathematics; Mathematical analysis; Combinatorics; Applied mathematics; Physics","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":[0.001096544,0.00105672,0.0008351209,0.00222479,0.001154453,0.00124983,0.001322661,0.0008712976,0.0132543],"category_scores_gemma":[0.003121395,0.0002633041,0.001029279,0.0005022067,0.002240701,0.00343303,0.003454437,0.003793021,0.001578212],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001038791,"about_ca_system_score_gemma":0.0006505229,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002869702,"about_ca_topic_score_gemma":0.002457805,"domain_scores_codex":[0.9995073,0.000101512,0.00001939485,0.00007480552,0.0001952702,0.0001016505],"domain_scores_gemma":[0.9987896,0.0004569092,0.0001156514,0.00009580709,0.000302737,0.0002393612],"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":[0.00003830016,0.00002188872,0.000760835,0.0001879794,0.00001490625,0.0002729614,0.0002248146,0.002284876,0.004127121,0.9759493,0.007558695,0.008558382],"study_design_scores_gemma":[0.00001693103,0.00004302946,0.001669639,0.00006774974,0.00002552901,0.0003947147,0.0001311731,0.05870888,0.002309409,0.9220657,0.01451666,0.00005055143],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1492074,0.007463457,0.5153333,0.009992878,0.002376292,0.0001253988,0.001121117,0.0008682376,0.3135119],"genre_scores_gemma":[0.8416449,0.00381318,0.0715146,0.002606066,0.002131032,0.0002050257,0.001009037,0.0008605982,0.07621557],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0132543,"threshold_uncertainty_score":0.04434007,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2841746990204183,"score_gpt":0.2869191867293552,"score_spread":0.002744487708936927,"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."}}