{"id":"W1603045336","doi":"10.1016/j.jalgebra.2015.09.013","title":"The Hall module of an exact category with duality","year":2015,"lang":"en","type":"preprint","venue":"Journal of Algebra","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Quiver; Mathematics; Finitary; Duality (order theory); Algebra over a field; Representation theory; Pure mathematics; Dual (grammatical number); Construct (python library); Computer science; Linguistics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001787324,0.0003086967,0.000816287,0.00008355903,0.00009203379,0.0001018507,0.0009882521,0.0002921603,0.0000280443],"category_scores_gemma":[0.000334573,0.0001683115,0.0002664382,0.00008248245,0.0001591312,0.0001545416,0.0003149108,0.001079578,9.326293e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001255894,"about_ca_system_score_gemma":0.000815683,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009366025,"about_ca_topic_score_gemma":0.00004053378,"domain_scores_codex":[0.9972719,0.0002774162,0.001006275,0.0002087766,0.000984587,0.0002510297],"domain_scores_gemma":[0.9952702,0.0003211912,0.002258736,0.0008817367,0.001050413,0.0002177222],"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":[0.001180143,0.0005072517,0.0002519322,0.0005034272,0.001406029,0.0001025319,0.002955269,0.001062121,0.00006314395,0.9830207,0.005946948,0.0030005],"study_design_scores_gemma":[0.0007094915,0.0004880924,0.0004508871,0.0001567184,0.0002223787,0.0001240374,0.0003564677,0.0001392129,0.0005565929,0.9963792,0.0002145246,0.0002024239],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9952151,0.0007425148,0.0007762468,0.0003113486,0.001584672,0.0002285307,0.000008416,0.00001650796,0.001116631],"genre_scores_gemma":[0.9966565,0.00006484415,0.002345124,0.00002466595,0.0007299821,0.000003960184,0.000002349211,0.00004828127,0.0001243129],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01335847,"threshold_uncertainty_score":0.6863543,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0500476966469805,"score_gpt":0.3167970609586629,"score_spread":0.2667493643116824,"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."}}