{"id":"W4225338647","doi":"10.48550/arxiv.2201.04606","title":"On centralizers in Azumaya domains","year":2022,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Differential Equations and Boundary Problems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Centralizer and normalizer; Modulo; Commutative property; Pure mathematics; Commutative ring; Discrete mathematics","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","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002611761,0.0002801617,0.00035354,0.0003564787,0.0001784252,0.00006855704,0.0005849886,0.0001871667,0.002051641],"category_scores_gemma":[0.0000586336,0.0003241313,0.0002232217,0.000387426,0.00008336145,0.00008015135,0.0007372031,0.0007992272,0.0000468007],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005759365,"about_ca_system_score_gemma":0.0001786625,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003867199,"about_ca_topic_score_gemma":0.0004966845,"domain_scores_codex":[0.998392,0.0001965784,0.0002515701,0.0006888006,0.0001304364,0.000340541],"domain_scores_gemma":[0.9986882,0.000231618,0.0002080994,0.0007411962,0.00003419772,0.00009667553],"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":[0.00006364358,0.0004580752,0.001104899,0.0001270046,0.00007768202,0.0003479907,0.0004605647,0.05306873,0.000006075734,0.9433543,0.000796316,0.0001347143],"study_design_scores_gemma":[0.0009562508,0.00008030871,0.0002711257,0.0001186726,0.00009339645,0.000001516222,0.000671136,0.01234759,0.000009050334,0.9831877,0.001835273,0.0004279875],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9709855,0.00001099739,0.009708445,0.00005433268,0.0005448961,0.0004788235,0.00006178153,0.0001223933,0.01803287],"genre_scores_gemma":[0.9940649,0.00007320058,0.0002621336,0.00004924963,0.00002744079,0.000003486966,0.00006462896,0.000034917,0.005420001],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04072114,"threshold_uncertainty_score":0.9999211,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1443452261480251,"score_gpt":0.2327462071047894,"score_spread":0.08840098095676427,"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."}}