{"id":"W2037142942","doi":"10.1216/rmjm/1181070040","title":"Commutative Endomorphism Algebras of Torsion-Free, Rank-Two Kronecker Modules with Singular Height Functions","year":2002,"lang":"en","type":"article","venue":"Rocky Mountain Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Endomorphism; Kronecker delta; Torsion (gastropod); Pure mathematics; Commutative property; Rank (graph theory); Algebra over a field; Combinatorics","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":[0.0006175199,0.0003875973,0.001008317,0.0002295163,0.0002263473,0.0000517562,0.0006754707,0.0001399241,0.0006342492],"category_scores_gemma":[0.0007010846,0.0002730183,0.0002982514,0.0003134036,0.0001850023,0.0002908654,0.0001389506,0.0004870748,0.00001154502],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001438237,"about_ca_system_score_gemma":0.00006275607,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009843278,"about_ca_topic_score_gemma":0.000008050307,"domain_scores_codex":[0.996927,0.0001610543,0.001295198,0.0001903549,0.001071754,0.0003546041],"domain_scores_gemma":[0.9957104,0.001008744,0.001635075,0.0007292861,0.0007285322,0.0001880158],"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":[0.0002507273,0.002158636,0.000265048,0.0005882322,0.001549046,0.0001477517,0.01472323,0.001287337,0.001015403,0.9671023,0.00993025,0.0009820046],"study_design_scores_gemma":[0.004577755,0.0007853335,0.00002690688,0.0006382945,0.0005952115,0.0008281986,0.003694395,0.00406968,0.003425519,0.9803171,0.0006503142,0.0003913554],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9018044,0.0008701613,0.09455279,0.000342919,0.000443479,0.0003932918,0.00002209227,0.00003337853,0.00153747],"genre_scores_gemma":[0.9059429,0.00005373687,0.09324545,0.00003862175,0.0002473034,0.000006844857,0.000002017726,0.00007319118,0.0003898989],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0132147,"threshold_uncertainty_score":0.9999722,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02611350057087106,"score_gpt":0.2561646655334294,"score_spread":0.2300511649625584,"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."}}