{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009768533,0.0008881337,0.001223017,0.003168972,0.002464502,0.004207663,0.001332527,0.001458485,0.009513971],"category_scores_gemma":[0.001265013,0.000653373,0.0006978166,0.001704007,0.004873184,0.006972704,0.003991913,0.002493234,0.0008711739],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001537572,"about_ca_system_score_gemma":0.0008688329,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008603348,"about_ca_topic_score_gemma":0.0007937296,"domain_scores_codex":[0.9991823,0.000194808,0.00003983077,0.0001958861,0.0001970865,0.0001900639],"domain_scores_gemma":[0.9992478,0.0002039274,0.0001154137,0.00007075449,0.00009162819,0.0002704935],"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":[0.00003303883,0.00002447578,0.0001940409,0.00002032332,0.000006719149,0.00007841211,0.0001727367,0.0002113611,0.0005758761,0.9962174,0.0005485979,0.001917001],"study_design_scores_gemma":[0.00001808413,0.00001987423,0.0002155852,0.000006307311,0.000007142894,0.0001238284,0.00008137717,0.001038349,0.0003260885,0.9965893,0.001560536,0.00001361397],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7200279,0.002129993,0.08721394,0.005005756,0.001138327,0.00007423174,0.0006109203,0.0004900253,0.1833089],"genre_scores_gemma":[0.974608,0.0003057478,0.004682188,0.000500802,0.0006195731,0.00002845311,0.0001725491,0.00006132165,0.01902124],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009513971,"threshold_uncertainty_score":0.03182739,"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."}}