{"id":"W2067086851","doi":"10.1016/j.ejc.2013.05.027","title":"Roth-type theorems in finite groups","year":2013,"lang":"en","type":"article","venue":"European Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Lemma (botany); Type (biology); Combinatorics; Discrete mathematics","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":[],"consensus_categories":[],"category_scores_codex":[0.001698175,0.0001560595,0.0002912483,0.0002119414,0.00008328196,0.00005693813,0.0005242994,0.00003565812,0.0001922655],"category_scores_gemma":[0.0009737131,0.0001138052,0.0001174985,0.0003308851,0.00007476677,0.0002115554,0.0001192056,0.0005183626,0.00004486987],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003787271,"about_ca_system_score_gemma":0.00002287713,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.409532e-7,"about_ca_topic_score_gemma":1.908564e-7,"domain_scores_codex":[0.9981006,0.0006107173,0.0006513306,0.0000994724,0.0003130409,0.0002248402],"domain_scores_gemma":[0.998342,0.0005429098,0.0004264136,0.0002803912,0.0002924219,0.0001159064],"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":[0.00003532682,0.0001411494,0.003470324,0.00003930063,0.00003841732,0.0002150068,0.001639195,0.00001905413,0.00008947319,0.9877011,0.004631857,0.001979808],"study_design_scores_gemma":[0.0009024817,0.0003160209,0.008131589,0.00007671929,0.00001634621,0.00007696282,0.0001794193,0.00004104212,0.00007994589,0.9857724,0.004258209,0.0001488916],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9499155,0.0004532601,0.001143983,0.00014779,0.001879007,0.0001278429,5.834368e-7,0.00002221029,0.04630978],"genre_scores_gemma":[0.9982316,0.000118539,0.0009736,0.0001243241,0.0001600695,3.852034e-7,2.766157e-7,0.00004482652,0.0003463575],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04831608,"threshold_uncertainty_score":0.4640842,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02469061789435342,"score_gpt":0.2530964903757491,"score_spread":0.2284058724813956,"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."}}