{"id":"W3216473862","doi":"10.1016/j.spa.2023.104292","title":"Heat kernel bounds and Ricci curvature for Lipschitz manifolds","year":2024,"lang":"en","type":"article","venue":"Stochastic Processes and their Applications","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"European Research Council; Rheinische Friedrich-Wilhelms-Universität Bonn; Austrian Science Fund","keywords":"Mathematics; Ricci curvature; Lipschitz continuity; Riemannian manifold; Lebesgue measure; Measure (data warehouse); Bounded function; Pure mathematics; Heat kernel; Lebesgue integration; Mathematical analysis; Curvature; Combinatorics; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.0001805913,0.0002029981,0.0002524523,0.000141593,0.0002764854,0.0002615163,0.0001253034,0.0001076391,0.00001812361],"category_scores_gemma":[0.0001391957,0.0001421273,0.00006591318,0.00079984,0.0000661114,0.0001062162,0.00005439082,0.0001444578,0.000004928933],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001284404,"about_ca_system_score_gemma":0.00007320306,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006096257,"about_ca_topic_score_gemma":0.00002385109,"domain_scores_codex":[0.9990664,0.000006256304,0.0002151166,0.0003974772,0.0001012276,0.0002135341],"domain_scores_gemma":[0.998884,0.0006229644,0.0000291908,0.0002193476,0.0001432172,0.0001013397],"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":[0.00001710458,0.0001642489,0.000009107056,0.003072638,0.0003752299,6.179919e-7,0.001352058,0.000006780007,0.0002712493,0.9698073,0.003986885,0.02093679],"study_design_scores_gemma":[0.0002266228,0.00007090211,0.00001692235,0.0001315038,0.0003431751,0.00004211583,0.0007379031,0.00890213,0.00005071641,0.9599672,0.02921441,0.0002964105],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.002513474,0.01620421,0.9785941,0.000872088,0.00005107235,0.0006710228,0.0001108383,0.0001458925,0.0008373474],"genre_scores_gemma":[0.9948521,0.00009431854,0.002817254,0.00008106261,0.0002812155,0.0009913917,0.0000434693,0.0000353317,0.0008038954],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9923386,"threshold_uncertainty_score":0.5795782,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01964965891618981,"score_gpt":0.2853416441461506,"score_spread":0.2656919852299608,"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."}}