{"id":"W2793493848","doi":"10.1093/imrn/rny152","title":"An Extension of Polynomial Integrability to Dual Quermassintegrals","year":2018,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Extension (predicate logic); Generalization; Smoothness; Mathematics; Polynomial; Dual (grammatical number); Integrable system; Characterization (materials science); Function (biology); Section (typography); Pure mathematics; Combinatorics; Mathematical analysis; Physics; Computer science; Optics","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":["metaresearch","metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.008449548,0.0004700259,0.0009633315,0.00182316,0.0001572099,0.0004589771,0.002227039,0.0004644084,0.001203246],"category_scores_gemma":[0.02702818,0.0003842007,0.000293845,0.0006055249,0.0005439719,0.0003547355,0.002176091,0.001276305,0.0001646657],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003747224,"about_ca_system_score_gemma":0.0005589825,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006717456,"about_ca_topic_score_gemma":0.0001942673,"domain_scores_codex":[0.9931497,0.0004858935,0.001649501,0.0009124175,0.003120444,0.0006820717],"domain_scores_gemma":[0.986673,0.005179235,0.000743138,0.001593911,0.005477943,0.0003327619],"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":[0.002024026,0.01777371,0.000792007,0.02828153,0.002799253,0.000166388,0.07659227,0.0009209238,0.0131974,0.7349027,0.1054527,0.017097],"study_design_scores_gemma":[0.0004846457,0.0009518587,0.0002354978,0.003306031,0.00009648944,0.00001447375,0.005578044,0.03072247,0.02037205,0.9350101,0.002411508,0.0008167995],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9597066,0.00008815726,0.0209978,0.001757689,0.001839777,0.001300747,0.0006866034,0.0001579302,0.01346466],"genre_scores_gemma":[0.8869986,0.00002673814,0.1099104,0.0000481725,0.001081213,0.0001377281,0.00007932867,0.00008015738,0.001637641],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2001074,"threshold_uncertainty_score":0.999861,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3221132817494082,"score_gpt":0.5206016454730705,"score_spread":0.1984883637236623,"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."}}