{"id":"W4412935841","doi":"10.1007/s00229-025-01656-5","title":"On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry","year":2025,"lang":"en","type":"article","venue":"manuscripta mathematica","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Cape Breton University","funders":"National Science Foundation","keywords":"Mathematics; Algebraic geometry; Sobolev space; Measure (data warehouse); Geometry and topology; Metric space; Metric (unit); Homogeneous; Number theory; Mathematical analysis; Interpolation space; Geometry; Sobolev inequality; Pure mathematics; Functional analysis; Combinatorics; 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":[0.001721453,0.000435713,0.001987655,0.003439138,0.00009009655,0.00008035488,0.0005945856,0.000276173,0.0004158196],"category_scores_gemma":[0.004780617,0.0003324063,0.000602109,0.006141458,0.0001410862,0.0001282645,0.0001359738,0.0003598512,0.0000372205],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001024863,"about_ca_system_score_gemma":0.0001444293,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009903911,"about_ca_topic_score_gemma":0.0001524517,"domain_scores_codex":[0.9963973,0.0001851435,0.001541811,0.0004517479,0.0009595193,0.0004644746],"domain_scores_gemma":[0.9959331,0.001688034,0.0007704998,0.001066474,0.0004388333,0.0001030285],"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":[0.001126617,0.005953521,0.003409408,0.004420702,0.003181378,0.00004500812,0.001202537,0.0009979653,0.001659117,0.925379,0.04788259,0.004742195],"study_design_scores_gemma":[0.0257815,0.002133036,0.006310587,0.00511711,0.006302584,0.00004204355,0.01481201,0.0199476,0.009053879,0.9017127,0.006515828,0.002271183],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7981526,0.004397886,0.08894384,0.001680456,0.000767217,0.002418219,0.00007166785,0.0001673217,0.1034008],"genre_scores_gemma":[0.9793345,0.00004249758,0.004700053,0.00007972439,0.00002751132,0.00007866786,0.000007357919,0.00003717247,0.0156925],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1811819,"threshold_uncertainty_score":0.9999128,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02475568912358126,"score_gpt":0.2654750549582051,"score_spread":0.2407193658346238,"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."}}