{"id":"W6903558018","doi":"10.1155/2024/9942234","title":"The Matrix Representations of Centroids for Low-Dimensional Mock-Lie Algebras","year":2024,"lang":"en","type":"article","venue":"RePEc: Research Papers in Economics","topic":"Advanced Topics in Algebra","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Centroid; Representation (politics); Algebra over a field; Matrix (chemical analysis); Commutative property; Matrix representation; Algebraic number; Matrix algebra","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":[0.001419086,0.0001417423,0.0002422077,0.0001973549,0.0002426185,0.0000830568,0.0004179195,0.0001062634,0.00006566072],"category_scores_gemma":[0.002175207,0.0001176449,0.0001599906,0.00019869,0.000340549,0.00013034,0.0002239489,0.0004366935,0.00001183193],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003214069,"about_ca_system_score_gemma":0.000277887,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005145259,"about_ca_topic_score_gemma":0.00005944208,"domain_scores_codex":[0.9980541,0.0001129108,0.0006072914,0.0004220365,0.0002649337,0.0005386633],"domain_scores_gemma":[0.9931113,0.00587118,0.00008653103,0.0007078542,0.0001348811,0.00008827066],"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":[0.000076,0.00009617711,0.0002255244,0.000230735,0.0001052168,0.00001083348,0.000250487,0.0005153166,0.0008486009,0.9552891,0.001224141,0.04112783],"study_design_scores_gemma":[0.0004649571,0.00006748117,0.0001766395,0.0001297371,0.00001174666,0.00001159138,0.0005338915,0.01399236,0.001927864,0.9564573,0.02606503,0.0001613519],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9382805,0.001413938,0.0006210959,0.004128616,0.001566395,0.003033957,0.0002190988,0.0002007245,0.05053571],"genre_scores_gemma":[0.9234818,0.002973556,0.03696846,0.00005642153,0.0006577977,0.0007333091,0.00004438156,0.0001952648,0.03488907],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04096648,"threshold_uncertainty_score":0.4797421,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03968206154733765,"score_gpt":0.3915635698723694,"score_spread":0.3518815083250317,"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."}}