{"id":"W1639928264","doi":"10.1007/s10468-009-9179-9","title":"Cluster-Cyclic Quivers with Three Vertices and the Markov Equation","year":2010,"lang":"en","type":"article","venue":"Algebras and Representation Theory","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":70,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Sherbrooke; Bishop's University","funders":"","keywords":"Quiver; Cluster algebra; Mathematics; Cluster (spacecraft); Markov chain; Combinatorics; Interpretation (philosophy); Pure mathematics; Subalgebra; Discrete mathematics; Algebra over a field; Computer science; Physics; Statistical physics","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":[0.0005088962,0.0001218788,0.0001561657,0.00003623385,0.0002475184,0.00009758754,0.0001047448,0.00007239758,0.00007328467],"category_scores_gemma":[0.000261086,0.0000666372,0.00003280295,0.00008366782,0.0004173813,0.0001817738,0.00006937214,0.0001683755,0.000001772375],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000004478913,"about_ca_system_score_gemma":0.0000154009,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006908278,"about_ca_topic_score_gemma":0.00008965615,"domain_scores_codex":[0.9991499,0.0001394888,0.0001680561,0.0002201686,0.0001936786,0.0001286942],"domain_scores_gemma":[0.9981238,0.001380288,0.0001257946,0.0002678256,0.00004819852,0.00005407558],"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":[0.0004297095,0.00001096254,0.001834277,0.00001554726,0.00006016792,7.950254e-7,0.001333136,0.000001986015,0.0001375899,0.9900783,0.00005784594,0.006039631],"study_design_scores_gemma":[0.002021914,0.0000377151,0.005711566,0.00001041401,0.00009936859,0.0000175314,0.0008493997,0.0006033331,0.0002728926,0.990228,0.00004143686,0.0001064248],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9905201,0.000129279,0.00633482,0.000807524,0.0003058901,0.0003717873,8.067303e-7,0.00003763082,0.001492191],"genre_scores_gemma":[0.9985279,0.00003773315,0.0009083956,0.0001690632,0.0001256808,0.00002882832,0.000002405485,0.0000154654,0.0001845145],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008007842,"threshold_uncertainty_score":0.2717386,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01612607261878352,"score_gpt":0.2683802389075825,"score_spread":0.252254166288799,"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."}}