{"id":"W7110882245","doi":"10.4995/agt.24202","title":"Simple polynomial equations over (2x2)-matrices","year":2025,"lang":"en","type":"article","venue":"Applied General Topology","topic":"Matrix Theory and Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Nipissing University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Polynomial; Simple (philosophy); Euclidean geometry; Matrix polynomial; Set (abstract data type); Identity (music); Square-free polynomial; Alternating polynomial","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0001844769,0.00012491,0.0001719137,0.0001518056,0.0002217806,0.00006540868,0.0006839148,0.0001005658,0.0002040061],"category_scores_gemma":[0.00001824015,0.0001181221,0.00005715412,0.000413828,0.00008676192,0.00009897325,0.0003157396,0.0001166643,0.0001165995],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000262423,"about_ca_system_score_gemma":0.00007840541,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00007847927,"about_ca_topic_score_gemma":0.00001867237,"domain_scores_codex":[0.998988,0.000054235,0.0002097281,0.0003507654,0.00008522296,0.0003119986],"domain_scores_gemma":[0.9992493,0.0001815052,0.00005860318,0.0004373835,0.00002026508,0.00005292724],"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":[0.000006819322,0.00002639333,0.00005080219,0.000004037137,0.00001723163,0.000002322408,0.00005756143,0.0002203444,0.002496887,0.9682521,0.008071058,0.02079444],"study_design_scores_gemma":[0.001261733,0.00007233956,0.001114163,0.000003293658,0.00003002563,0.000006801991,0.00004247045,0.04448805,0.01574202,0.7044647,0.2323097,0.000464742],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03705679,0.0002255862,0.8901945,0.002083841,0.001219452,0.0002202071,0.000006922647,0.0002540891,0.06873856],"genre_scores_gemma":[0.9718817,0.00001474993,0.01998841,0.00318397,0.0004315476,0.00005241314,0.00001180114,0.000006643698,0.004428687],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.934825,"threshold_uncertainty_score":0.4816881,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009536382067077478,"score_gpt":0.2706029723466217,"score_spread":0.2610665902795443,"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."}}