{"id":"W2949075883","doi":"10.48550/arxiv.math/0001125","title":"Topological obstructions to nonnegative curvature","year":2000,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Sectional curvature; Mathematics; Curvature; Metric (unit); Pure mathematics; Construct (python library); Topology (electrical circuits); Riemann curvature tensor; Scalar curvature; Vector bundle; Ricci curvature; Mathematical analysis; Geometry; Combinatorics; Computer science; Engineering","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","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0002746307,0.0005081034,0.0008855187,0.0003651473,0.0002103041,0.00009280076,0.0006848238,0.0008709829,0.003960147],"category_scores_gemma":[0.00104111,0.0004058048,0.00054631,0.001107879,0.00009177641,0.00007396203,0.000583659,0.00168354,0.000818093],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001248644,"about_ca_system_score_gemma":0.00008595168,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007473217,"about_ca_topic_score_gemma":0.0000846075,"domain_scores_codex":[0.9974399,0.0001347355,0.0006087884,0.0008828435,0.0004450511,0.0004887003],"domain_scores_gemma":[0.9977545,0.0003450148,0.0002636759,0.001140421,0.000231055,0.0002653066],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.0003461047,0.003390541,0.530699,0.001021881,0.006674612,0.0004351691,0.01196385,0.004318933,0.0005317148,0.09343788,0.3235036,0.02367678],"study_design_scores_gemma":[0.0009156907,0.000316442,0.4422851,0.0005052753,0.002067311,0.00005297994,0.001836347,0.0002609776,0.0006956842,0.3998055,0.1482738,0.00298489],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9776512,0.0003355557,0.002203858,0.002096883,0.0008781931,0.0005206707,0.00007897088,0.0002229809,0.01601173],"genre_scores_gemma":[0.9793662,0.00008212739,0.01077966,0.0006464428,0.0009309499,0.0001274067,0.00007980823,0.00005059388,0.007936743],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3063676,"threshold_uncertainty_score":0.9999599,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1179399700432206,"score_gpt":0.3494787917473443,"score_spread":0.2315388217041237,"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."}}