{"id":"W2483917811","doi":"10.1090/surv/187/18","title":"Trudinger-Moser-Onofri inequality on 𝕊²","year":2013,"lang":"en","type":"book-chapter","venue":"Mathematical surveys and monographs","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Inequality; Mathematics; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.003707478,0.000711126,0.001115982,0.0002840912,0.0002174223,0.0001514273,0.0002707649,0.0006244187,0.003575929],"category_scores_gemma":[0.001574796,0.0005745629,0.0004242512,0.0001040474,0.0003472163,0.0001185175,0.000173698,0.000660616,0.0009167995],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008430928,"about_ca_system_score_gemma":0.00004835449,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000220169,"about_ca_topic_score_gemma":0.00004297755,"domain_scores_codex":[0.9964773,0.0003653749,0.0011679,0.0007865299,0.0007608226,0.0004420397],"domain_scores_gemma":[0.9934205,0.004565575,0.0004158426,0.001014134,0.0002627728,0.0003211771],"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":[0.00002166954,0.0002548568,0.00004735673,0.0006321101,0.0001945542,0.000003979199,0.0001642397,5.753067e-7,0.000004515084,0.9825172,0.005805328,0.01035357],"study_design_scores_gemma":[0.0004244325,0.0002353459,0.0004259003,0.0003747985,0.0001222101,0.000008581778,0.00002348767,0.0002090495,0.00001396397,0.9871137,0.01043299,0.0006155326],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01381919,0.0002098151,0.01539675,0.0006096977,0.0003374548,0.002015445,0.0006104509,0.0004266654,0.9665745],"genre_scores_gemma":[0.1535715,0.0005516731,0.03811147,0.0005807657,0.0008380591,0.0007104443,0.0007547908,0.0008010654,0.8040802],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1624943,"threshold_uncertainty_score":0.9998611,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1124351906251344,"score_gpt":0.3074897788017391,"score_spread":0.1950545881766047,"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."}}