{"id":"W1723157567","doi":"10.1023/a:1015665612246","title":"Almost-Commutativity in Rings","year":2002,"lang":"en","type":"article","venue":"Acta Mathematica Academiae Scientiarum Hungaricae","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Brock University","funders":"","keywords":"Mathematics; Commutative ring; Commutative property; Backslash; Zero divisor; Pure mathematics; Ring (chemistry); Zero (linguistics); Discrete mathematics","routes":{"ca_aff":true,"ca_fund":false,"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":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.002352232,0.0005133174,0.0008304182,0.0005242344,0.0003710886,0.000206067,0.001265213,0.0004276388,0.001572549],"category_scores_gemma":[0.002539402,0.0004642569,0.0002480808,0.001277253,0.0004181848,0.0008843542,0.0005155231,0.001377916,0.0008270302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001744254,"about_ca_system_score_gemma":0.00003352879,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001543312,"about_ca_topic_score_gemma":0.00002316082,"domain_scores_codex":[0.9954901,0.000228883,0.001125554,0.0008875925,0.001061518,0.001206327],"domain_scores_gemma":[0.996769,0.001215537,0.0004664958,0.001135328,0.00008575952,0.0003279155],"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":[0.00005472763,0.006293325,0.01071358,0.002555527,0.0003819335,0.0002103131,0.04960786,0.00001484404,0.03473679,0.563841,0.316188,0.01540208],"study_design_scores_gemma":[0.002051168,0.0001282896,0.005890255,0.0007635882,0.0001764671,0.0001851139,0.001272154,0.0160315,0.01175231,0.9415978,0.01840322,0.001748138],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9320143,0.000245788,0.001493981,0.005762423,0.000398446,0.0008994535,0.00001477346,0.0004740661,0.05869672],"genre_scores_gemma":[0.9750116,0.00007274197,0.01780593,0.0004033191,0.0001192483,0.00008470983,0.000003630031,0.00009143454,0.006407392],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3777568,"threshold_uncertainty_score":0.9999509,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05632988193246418,"score_gpt":0.301101439890997,"score_spread":0.2447715579585328,"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."}}