{"id":"W4407238997","doi":"10.1142/s1793042125500691","title":"Multiplicative groups avoiding a fixed group","year":2025,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Finite Group Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia; Vancouver Island University","funders":"","keywords":"Mathematics; Group (periodic table); Multiplicative group; Multiplicative function; Fixed point; Pure mathematics; Combinatorics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000740015,0.0005604746,0.0005259081,0.002246374,0.001181875,0.00189041,0.001065137,0.0007402273,0.003799221],"category_scores_gemma":[0.005898314,0.0002592413,0.0005180296,0.0007219233,0.002274957,0.003076538,0.001670036,0.001047389,0.000749175],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009786796,"about_ca_system_score_gemma":0.0003979476,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004397683,"about_ca_topic_score_gemma":0.000391296,"domain_scores_codex":[0.9993124,0.0001224083,0.00002753421,0.0001709081,0.0002533076,0.0001135207],"domain_scores_gemma":[0.998184,0.0008117875,0.0002480349,0.0002649679,0.0002639555,0.000227307],"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":[0.00008674947,0.00002731479,0.001547769,0.00008124574,0.00001504141,0.0002643322,0.0003027444,0.001089861,0.005583184,0.9766175,0.001156103,0.01322815],"study_design_scores_gemma":[0.00002285824,0.0001058025,0.001767706,0.0000752968,0.00004098508,0.001508899,0.0002072204,0.02138012,0.01073853,0.949501,0.01461986,0.00003162419],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8086266,0.001951769,0.09744414,0.0009671159,0.00032165,0.00005855054,0.0001353694,0.0009253437,0.08956943],"genre_scores_gemma":[0.9676338,0.0006273319,0.01867288,0.0002304761,0.0003280863,0.00006198545,0.0001979711,0.0001170109,0.0121305],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003799221,"threshold_uncertainty_score":0.01270968,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04254302291910207,"score_gpt":0.4004587122845852,"score_spread":0.3579156893654831,"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."}}