{"id":"W2051229458","doi":"10.1016/j.geomphys.2010.05.010","title":"Topological properties of manifolds admitting a <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" display=\"inline\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>Y</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:math>-Riemannian metric","year":2010,"lang":"lv","type":"article","venue":"Journal of Geometry and Physics","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Manifold (fluid mechanics); Geodesic; Mathematics; Riemannian manifold; Combinatorics; Cohomology; Topology (electrical circuits); Pure mathematics; Mathematical analysis","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","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":["research_integrity"],"category_scores_codex":[0.002672068,0.0007887507,0.0006216519,0.0007993887,0.001170904,0.001128598,0.001664055,0.001979991,0.1030981],"category_scores_gemma":[0.003627816,0.001139455,0.002301091,0.002746724,0.001088434,0.001418258,0.001313056,0.002591253,0.0004316131],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001311225,"about_ca_system_score_gemma":0.0009923113,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004750836,"about_ca_topic_score_gemma":0.0002233257,"domain_scores_codex":[0.9919272,0.0003523174,0.002328721,0.001062111,0.002648518,0.001681103],"domain_scores_gemma":[0.9918999,0.001741849,0.003446141,0.001564595,0.0003899017,0.0009575959],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.00158936,0.001205576,0.0001792279,0.002822148,0.004090047,0.001415645,0.002798239,0.001192602,0.004066408,0.9078765,0.06729362,0.005470621],"study_design_scores_gemma":[0.002851751,0.003931405,0.0005791705,0.001746953,0.004856408,0.002809206,0.005267815,0.1102052,0.861369,0.000819566,0.00374784,0.001815692],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8775831,0.002522912,0.001274903,0.0005448168,0.001892384,0.00003676719,0.0001295529,0.00006266004,0.1159529],"genre_scores_gemma":[0.9898274,0.001411368,0.003717775,0.0006777206,0.003369396,0.0001261398,0.0001610975,0.0003539331,0.0003551677],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9070569,"threshold_uncertainty_score":0.9999083,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02198804316193199,"score_gpt":0.2493294264782922,"score_spread":0.2273413833163602,"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."}}