{"id":"W4388312826","doi":"10.1016/j.jalgebra.2023.10.019","title":"Morphisms and extensions between bricks over preprojective algebras of type A","year":2023,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université du Québec à Montréal; Université de Sherbrooke","funders":"Natural Sciences and Engineering Research Council of Canada; Mitacs; Canada Research Chairs","keywords":"Morphism; Bijection; Mathematics; Type (biology); Extension (predicate logic); Pure mathematics; Algebra over a field; Discrete mathematics; Computer science; Programming language","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":[0.000465178,0.000149576,0.0004974912,0.0002343378,0.00006428753,0.00002139826,0.0001930794,0.0001220778,0.0000748986],"category_scores_gemma":[0.0006816933,0.0001155788,0.0001477775,0.0004848412,0.00008159066,0.0001567872,0.0001334518,0.0002653468,0.000004880528],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002965984,"about_ca_system_score_gemma":0.0001106756,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001592238,"about_ca_topic_score_gemma":0.000001113416,"domain_scores_codex":[0.9985785,0.0000671642,0.0005771413,0.0001551613,0.0004217992,0.0002001702],"domain_scores_gemma":[0.9982025,0.0005564184,0.0005472525,0.0002372398,0.0003387709,0.0001178259],"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":[0.000521148,0.0002567892,0.03986228,0.0003047348,0.001690025,0.0001966159,0.008216443,0.00003578965,0.005668072,0.9019768,0.03313177,0.008139487],"study_design_scores_gemma":[0.0007334781,0.0003651821,0.05533386,0.0001036395,0.0001645292,0.0000625121,0.0002450618,0.00004671466,0.001105922,0.9415334,0.0001774505,0.0001282926],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9985017,0.0001895323,0.0001918715,0.000169571,0.0005265856,0.0001350535,0.000004637383,0.00002735271,0.0002537015],"genre_scores_gemma":[0.998403,0.0000746578,0.0009746355,0.00003441922,0.0003375334,0.000001180016,8.90232e-7,0.00002796802,0.0001457489],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03955651,"threshold_uncertainty_score":0.4713168,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05408636059683897,"score_gpt":0.3322217096173448,"score_spread":0.2781353490205059,"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."}}