{"id":"W2055762794","doi":"10.3934/era.2009.16.44","title":"Research announcement: The structure of groups with a quasiconvex hierarchy","year":2009,"lang":"en","type":"article","venue":"Electronic Research Announcements","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":99,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Hebrew University of Jerusalem","keywords":"Quasiconvex function; Mathematics; Hierarchy; Separable space; Group (periodic table); Pure mathematics; Combinatorics; Regular polygon; Convex analysis; Mathematical analysis; Geometry; Convex optimization","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":[],"consensus_categories":[],"category_scores_codex":[0.006202997,0.0002654773,0.0004177177,0.0009133938,0.0008149029,0.0001011569,0.001394322,0.0001551288,0.0005167287],"category_scores_gemma":[0.0009330242,0.0001606665,0.0000809889,0.004340943,0.001046627,0.0002060255,0.0002138281,0.002255175,0.00003992629],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004933818,"about_ca_system_score_gemma":0.001066903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008494462,"about_ca_topic_score_gemma":0.0001388668,"domain_scores_codex":[0.9914314,0.001275161,0.0005291811,0.0006207509,0.003580606,0.002562955],"domain_scores_gemma":[0.9958807,0.001338121,0.00015753,0.001124588,0.001320374,0.000178652],"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":[0.000877576,0.0009394016,0.001463246,0.0001094355,0.0003478011,0.00003211139,0.002439452,0.000007672313,0.01581491,0.9402235,0.02286914,0.01487573],"study_design_scores_gemma":[0.001853567,0.007817572,0.001583275,0.00008180705,0.00002169192,0.00003897721,0.002404944,0.0000569245,0.003584898,0.9366249,0.04566483,0.0002665458],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9773238,0.001635601,0.000714438,0.006035175,0.00007713861,0.001901782,0.00005501408,0.00006103434,0.01219603],"genre_scores_gemma":[0.9955582,0.0002534994,0.0003362221,0.000128995,0.0001874265,0.00003477249,0.00003947044,0.0000276169,0.003433813],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02279569,"threshold_uncertainty_score":0.9797738,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08201714973938616,"score_gpt":0.4108827430477721,"score_spread":0.3288655933083859,"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."}}