{"id":"W4392679303","doi":"10.1007/s12220-024-01569-x","title":"Toward Weighted Lorentz–Sobolev Capacities from Caffarelli–Silvestre Extensions","year":2024,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":false,"ca_institutions":"Memorial University of Newfoundland","funders":"National Natural Science Foundation of China","keywords":"Sobolev space; Lorentz transformation; Mathematics; Sobolev inequality; Lebesgue integration; Pure mathematics; Laplace transform; Type (biology); Mathematical analysis; Physics; Geology","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":[0.003157267,0.00166839,0.001044323,0.003565811,0.001133076,0.002606713,0.001774235,0.001693264,0.007947854],"category_scores_gemma":[0.01182289,0.0007970834,0.001001594,0.001723197,0.00337613,0.008243385,0.005219806,0.003845246,0.001114766],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0016215,"about_ca_system_score_gemma":0.0008770684,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001103042,"about_ca_topic_score_gemma":0.001277642,"domain_scores_codex":[0.9992394,0.0003254738,0.00003688072,0.0001177748,0.0001770572,0.0001033577],"domain_scores_gemma":[0.9962448,0.001683259,0.0004670961,0.0003524292,0.0005874838,0.000664844],"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":[0.00001206575,0.000007545296,0.00006915873,0.0000210164,0.000005164125,0.00002260654,0.00006196529,0.003161324,0.0003390708,0.9925,0.0006105798,0.003189476],"study_design_scores_gemma":[0.000003208009,0.00001057331,0.00008139068,0.00001529309,0.000003448802,0.00002690143,0.0000283244,0.01919279,0.0002153826,0.978736,0.001672809,0.00001382456],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1363887,0.001394091,0.8013449,0.002110467,0.0004268985,0.00007095122,0.0004344933,0.0002794822,0.05754992],"genre_scores_gemma":[0.8126772,0.002899705,0.1416776,0.001141219,0.001045799,0.0001988705,0.0007686992,0.0006003301,0.03899046],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007947854,"threshold_uncertainty_score":0.02658826,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08391062876588291,"score_gpt":0.3333198890948973,"score_spread":0.2494092603290144,"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."}}