{"id":"W2916265538","doi":"10.1016/j.disc.2020.112025","title":"On the existence of dense substructures in finite groups","year":2020,"lang":"en","type":"preprint","venue":"Discrete Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Quadratic growth; Conjecture; Mathematics; Quadratic equation; Combinatorics; Span (engineering); Group (periodic table); Set (abstract data type); Upper and lower bounds; Finite set; Pure mathematics; Mathematical analysis; Geometry; Physics; 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":[0.0007522399,0.0005616056,0.00104146,0.0001688249,0.0001262854,0.00006347481,0.001342508,0.0003884452,0.0001551218],"category_scores_gemma":[0.003651219,0.0003417071,0.000433737,0.000248512,0.0003693733,0.00003191812,0.001200049,0.001270784,0.000007240635],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004631788,"about_ca_system_score_gemma":0.00005722832,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009175121,"about_ca_topic_score_gemma":0.00001917901,"domain_scores_codex":[0.9971035,0.000235499,0.001127589,0.0004971743,0.0006792566,0.0003570454],"domain_scores_gemma":[0.9931651,0.004161073,0.000890695,0.001610076,0.00008777045,0.00008525993],"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":[0.00004330949,0.00005614348,0.0000550134,0.001967302,0.0001055529,0.00002401139,0.01490676,0.0001599987,0.00004684709,0.9821691,0.0003915982,0.00007435796],"study_design_scores_gemma":[0.000211533,0.00005063981,0.0002129295,0.001198211,0.0001017447,0.000006164848,0.00116158,0.003371631,0.000843914,0.9924634,0.00001682451,0.0003614656],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9805464,0.000265579,0.004248008,0.000654788,0.0005488369,0.00125695,0.000221335,0.0001039944,0.01215414],"genre_scores_gemma":[0.9821156,0.00006432077,0.01723945,0.0002401784,0.00009958366,0.00006447164,0.000013729,0.00008979192,0.00007292122],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01374518,"threshold_uncertainty_score":0.9999035,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06572966962262852,"score_gpt":0.3080353981631448,"score_spread":0.2423057285405163,"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."}}