{"id":"W2779515341","doi":"10.1515/crelle-2019-0014","title":"Brownian motion on Perelman’s almost Ricci-flat manifold","year":2019,"lang":"de","type":"preprint","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Ricci curvature; Mathematics; Ricci flow; Brownian motion; Parallel transport; Riemannian manifold; Laplace operator; Mathematical analysis; Manifold (fluid mechanics); Pure mathematics; Orthonormal basis; Martingale (probability theory); Combinatorics; Curvature; Geometry; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007764539,0.0008773792,0.000486753,0.001734479,0.001047738,0.001266909,0.0008564044,0.0008971145,0.003750878],"category_scores_gemma":[0.001882082,0.0003330755,0.000847592,0.0005978337,0.001599427,0.001847068,0.001064317,0.001280122,0.0005882981],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001520757,"about_ca_system_score_gemma":0.0008638704,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004313869,"about_ca_topic_score_gemma":0.001912177,"domain_scores_codex":[0.9995748,0.0000840956,0.00001428643,0.000104645,0.000134189,0.0000879869],"domain_scores_gemma":[0.9991052,0.0001372219,0.0001744385,0.0000736179,0.0002126336,0.0002968392],"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":[0.00006950768,0.0000480694,0.0009142893,0.00004835796,0.00003093446,0.0002897162,0.0002169739,0.02219802,0.006960078,0.9623664,0.001372786,0.005484977],"study_design_scores_gemma":[0.00003172384,0.0002392012,0.003688379,0.00003568465,0.00002675457,0.0003225122,0.0002064465,0.3216975,0.003835317,0.6638773,0.005956965,0.00008233211],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7646158,0.0005937432,0.2086009,0.0009445165,0.0002032936,0.00007179762,0.0002568309,0.0003395478,0.02437358],"genre_scores_gemma":[0.9536173,0.0004500873,0.02523656,0.0001940137,0.0001359181,0.00006185943,0.0003810616,0.0001101125,0.01981307],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004313869,"threshold_uncertainty_score":0.01254797,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03511853042744309,"score_gpt":0.3090285644074512,"score_spread":0.2739100339800081,"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."}}