{"id":"W4406961154","doi":"10.48550/arxiv.2501.16978","title":"$\\otimes$-Frobenius functors and exact module categories","year":2025,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Norges Forskningsråd; University of Alberta","keywords":"Functor; Mathematics; Computer science; Pure mathematics; Programming language","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.000213914,0.0004963095,0.0006303398,0.0003096149,0.0002117857,0.0001023925,0.0005925536,0.0004242036,0.0001479372],"category_scores_gemma":[0.0001356897,0.0005437134,0.000233427,0.0002823031,0.000217328,0.0001918562,0.001247226,0.0006461916,0.0000336278],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001677023,"about_ca_system_score_gemma":0.0001948308,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002879116,"about_ca_topic_score_gemma":0.0001327788,"domain_scores_codex":[0.9980639,0.0001004632,0.0002766448,0.001044257,0.0001002474,0.0004145156],"domain_scores_gemma":[0.9981371,0.0002677077,0.0002588471,0.001020606,0.0001370409,0.0001787353],"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":[0.00009922107,0.0002361127,0.01257236,0.001309323,0.0005618346,0.0002573158,0.0007736883,0.004537088,0.00003437898,0.9725689,0.006443904,0.0006058555],"study_design_scores_gemma":[0.0008430748,0.00005581597,0.002632272,0.0003240335,0.0005949704,0.000006272555,0.0005173341,0.01024164,0.0005237856,0.980544,0.002731217,0.0009855275],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9604546,0.0002594893,0.0188445,0.00005870971,0.0007789116,0.0004330215,0.00007691071,0.0003475275,0.01874629],"genre_scores_gemma":[0.9701749,0.0003701529,0.0008055391,0.00004884378,0.0001403208,0.000001560928,0.00002979437,0.00003801787,0.02839084],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01803896,"threshold_uncertainty_score":0.9997014,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0716037555710653,"score_gpt":0.2057737309004042,"score_spread":0.1341699753293389,"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."}}