{"id":"W2964189267","doi":"10.1016/j.topol.2013.08.014","title":"Extending finite group actions on surfaces over<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>","year":2013,"lang":"lv","type":"article","venue":"Topology and its Applications","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":15,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"National Natural Science Foundation of China; Peking University; Centre de Recherches Mathématiques","keywords":"Mathematics; Homogeneous space; Abelian group; Embedding; Combinatorics; Order (exchange); Group (periodic table); Discrete mathematics; Geometry; Artificial intelligence; Computer science; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001043431,0.0007113202,0.0003810532,0.0006025685,0.002213506,0.0006344207,0.001361232,0.002226218,0.3667283],"category_scores_gemma":[0.001477428,0.001217076,0.0009027115,0.001206708,0.001727883,0.0009494567,0.001182823,0.001542405,0.005115024],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001699671,"about_ca_system_score_gemma":0.0006527315,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001348792,"about_ca_topic_score_gemma":0.0006342516,"domain_scores_codex":[0.9938049,0.000330413,0.001450875,0.001504889,0.001034877,0.001873994],"domain_scores_gemma":[0.992393,0.003326474,0.001453598,0.001896124,0.0001546373,0.000776208],"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":[0.0002550417,0.0004329442,0.00001880802,0.0005597908,0.0009067679,0.0001461413,0.001277869,0.0003002364,0.001080758,0.8609279,0.1319379,0.00215584],"study_design_scores_gemma":[0.004115303,0.003652066,0.001260718,0.0008891046,0.003378285,0.002773659,0.008211593,0.1421707,0.774578,0.005632976,0.05007376,0.003263931],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6037639,0.001686556,0.001867178,0.002053128,0.001452886,0.00009556812,0.0003478283,0.0002286901,0.3885042],"genre_scores_gemma":[0.9872974,0.002548139,0.002359464,0.001553421,0.001371037,0.002087808,0.0007643361,0.0003743673,0.00164407],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.8552949,"threshold_uncertainty_score":0.9990855,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02504334200024509,"score_gpt":0.2641735618235947,"score_spread":0.2391302198233496,"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."}}