{"id":"W2514782409","doi":"10.1002/cpa.21736","title":"Ricci Curvature and Bochner Formulas for Martingales","year":2018,"lang":"en","type":"preprint","venue":"Communications on Pure and Applied Mathematics","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Ricci curvature; Mathematics; Riemann curvature tensor; Curvature; Bounded function; Scalar curvature; Ricci flow; Formalism (music); Hessian matrix; Path (computing); Mathematical proof; Mathematical analysis; Pure mathematics; Applied mathematics; Geometry; Computer science","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"],"consensus_categories":[],"category_scores_codex":[0.0009105105,0.0004661109,0.0008335896,0.0002634316,0.0005065005,0.0002617922,0.0009682381,0.0005820962,0.0000222331],"category_scores_gemma":[0.0005366335,0.0003784502,0.0001851182,0.0002826391,0.0002570304,0.00004594868,0.001519638,0.0007890885,0.00001155037],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003185226,"about_ca_system_score_gemma":0.00004595014,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001171947,"about_ca_topic_score_gemma":0.00002242082,"domain_scores_codex":[0.9982154,0.00003537329,0.0007054079,0.0004681386,0.0002704426,0.0003052163],"domain_scores_gemma":[0.9944981,0.001563449,0.0006670365,0.002911574,0.0002356385,0.0001242195],"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":[0.00001948867,0.000660422,0.00002580272,0.002157445,0.0004696231,2.312087e-7,0.001743938,0.000004563375,0.00006785016,0.93911,0.04805754,0.00768309],"study_design_scores_gemma":[0.0004240846,0.00006139313,0.00003630649,0.0003751027,0.0008323641,0.000005330186,0.0006714305,0.003646305,0.0001890284,0.9628085,0.03042093,0.0005292397],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.3259462,0.03080155,0.3493496,0.02393197,0.0009653052,0.02112963,0.001812701,0.002012167,0.2440509],"genre_scores_gemma":[0.3363732,0.001423473,0.6590885,0.0003427322,0.0002407653,0.0009542301,0.0002957261,0.0001213228,0.001160095],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3097388,"threshold_uncertainty_score":0.9998667,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08467329869625244,"score_gpt":0.3410223718468822,"score_spread":0.2563490731506298,"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."}}