{"id":"W2146638188","doi":"10.1515/crelle-2013-0009","title":"Energy inequalities for cutoff functions and some applications","year":2013,"lang":"en","type":"article","venue":"Journal für die reine und angewandte Mathematik (Crelles Journal)","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":38,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Trinity College, University of Cambridge; Natural Sciences and Engineering Research Council of Canada","keywords":"Dirichlet form; Bounded function; Cutoff; Heat kernel; Completeness (order theory); Measure (data warehouse); Sobolev inequality; Metric (unit); Dirichlet distribution; Poincaré inequality","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":["metaepi_narrow","scholarly_communication"],"consensus_categories":[],"category_scores_codex":[0.001201657,0.0004451826,0.0008684319,0.0007802409,0.001256908,0.001074355,0.0003941115,0.0002062568,0.0005331289],"category_scores_gemma":[0.0005033281,0.0003138452,0.0006022099,0.0005018383,0.0001059873,0.0009382936,0.0001054558,0.0006488222,0.00004274365],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001158974,"about_ca_system_score_gemma":0.0001061354,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001797404,"about_ca_topic_score_gemma":0.00002060809,"domain_scores_codex":[0.996964,0.0001381947,0.001359267,0.0003113355,0.0006130084,0.0006141458],"domain_scores_gemma":[0.995977,0.001094022,0.00114053,0.0004008763,0.0008541996,0.0005334135],"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":[0.0001032684,0.001517302,0.000229717,0.001043653,0.00450577,0.00006020084,0.002420495,0.0001091351,0.002839761,0.481759,0.3981166,0.1072951],"study_design_scores_gemma":[0.001101488,0.0002216001,0.00002464961,0.0001974179,0.0007305613,0.001023244,0.002778198,0.0008192716,0.0002888006,0.7201554,0.2722168,0.0004425128],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04338831,0.06382497,0.8734958,0.009973989,0.0007397551,0.001198567,0.0000789973,0.0001902518,0.007109325],"genre_scores_gemma":[0.5165496,0.07617066,0.1756063,0.002479498,0.02083525,0.001720128,0.0001265693,0.0008171956,0.2056949],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6978896,"threshold_uncertainty_score":0.9999626,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03269703751891293,"score_gpt":0.3039680788096154,"score_spread":0.2712710412907025,"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."}}