{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0005466151,0.0003780747,0.000589453,0.0002716998,0.00008696311,0.00003776321,0.0004861347,0.0002807141,0.00001632267],"category_scores_gemma":[0.0005217622,0.0004153308,0.0002359978,0.0003333285,0.00008866678,0.0001892236,0.0009590937,0.0004719343,0.0001018149],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000440103,"about_ca_system_score_gemma":0.00008057021,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004899129,"about_ca_topic_score_gemma":0.0003231375,"domain_scores_codex":[0.998073,0.0000713699,0.0004532734,0.0008642745,0.0001115103,0.0004265884],"domain_scores_gemma":[0.9975291,0.000971561,0.0004303796,0.0008268653,0.0001324286,0.0001096836],"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":[0.0001546555,0.0002247677,0.000253961,0.001625424,0.00007589807,0.00005817244,0.0004091163,0.1160333,0.0002512108,0.8804104,0.0002321545,0.0002710372],"study_design_scores_gemma":[0.0004739582,0.00004348833,0.00008367926,0.000606328,0.00007418527,3.60806e-7,0.00005585242,0.3102029,0.0001968468,0.6879674,0.00001038556,0.0002846858],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2284515,0.000006685042,0.769089,0.00009850861,0.0003503047,0.001306707,0.00003533439,0.0002923851,0.000369589],"genre_scores_gemma":[0.972997,0.00001135011,0.0259099,0.00001716347,0.00004856153,0.00002448198,0.00005666216,0.0001050652,0.0008298701],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7445455,"threshold_uncertainty_score":0.9998298,"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."}}