{"id":"W2963165346","doi":"10.1017/s0027763000009806","title":"Dualizing Complex of a Toric Face Ring","year":2009,"lang":"en","type":"article","venue":"Nagoya Mathematical Journal","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Affine transformation; Semigroup; Ring (chemistry); Pure mathematics; Normality; Face (sociological concept); Philosophy; Statistics","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":[],"consensus_categories":[],"category_scores_codex":[0.0005901397,0.0001581643,0.0004054534,0.0001139425,0.0001793167,0.00006270321,0.0003330038,0.00006173571,0.0006283809],"category_scores_gemma":[0.0006448227,0.000125453,0.0001670327,0.0002619876,0.00005801084,0.0001364761,0.00005163359,0.0003320218,0.00005574918],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005394571,"about_ca_system_score_gemma":0.00003466714,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.022486e-7,"about_ca_topic_score_gemma":2.69991e-7,"domain_scores_codex":[0.9984027,0.0000775708,0.0007010957,0.0001258842,0.0004235476,0.0002691707],"domain_scores_gemma":[0.99838,0.0006739396,0.0003278952,0.0003059129,0.0001566766,0.0001555728],"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":[0.00001031595,0.0003735623,0.00001752751,0.00007335844,0.00004484696,0.00001017542,0.001851232,0.000004104474,0.01114123,0.9778613,0.00259605,0.006016234],"study_design_scores_gemma":[0.0004056696,0.0001123703,0.0006161774,0.0001376466,0.00005833407,0.0003808374,0.0005528546,0.001311952,0.002011931,0.9937668,0.0004978408,0.0001476092],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4980612,0.000198834,0.4293805,0.003007129,0.00007790299,0.0004471247,0.000007919856,0.0001331966,0.06868622],"genre_scores_gemma":[0.9322292,0.00001358445,0.06731978,0.00008443242,0.0001098618,0.000004078493,7.130795e-7,0.00001652289,0.0002218007],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.434168,"threshold_uncertainty_score":0.688033,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1203615503335671,"score_gpt":0.3913101167228721,"score_spread":0.270948566389305,"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."}}