{"id":"W2796457119","doi":"10.4153/s0008439518000024","title":"Newton Complementary Duals of -Ideals","year":2018,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Dual polyhedron; Monomial; Class (philosophy); Simplicial complex; Facet (psychology); Monomial ideal; Duality (order theory)","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000494656,0.0002557737,0.0003755809,0.001348239,0.00125154,0.001694425,0.0004204764,0.0002807991,0.006677778],"category_scores_gemma":[0.0009406974,0.0003092298,0.0003756862,0.0003180144,0.002053194,0.001625379,0.001367132,0.0009412577,0.0006772236],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001171321,"about_ca_system_score_gemma":0.0005458052,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001258137,"about_ca_topic_score_gemma":0.001591809,"domain_scores_codex":[0.9994068,0.00008061519,0.00002279636,0.0001035034,0.0002266636,0.0001595753],"domain_scores_gemma":[0.9992396,0.0001242028,0.00009892022,0.00004298954,0.0002379667,0.0002563504],"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":[0.00004379298,0.00002293563,0.0005840908,0.00002423035,0.000005620876,0.00008821725,0.0002761129,0.0003270939,0.00232675,0.9920123,0.0007097682,0.003579101],"study_design_scores_gemma":[0.00004895322,0.0001044607,0.003750998,0.0000580339,0.00002416188,0.0008104671,0.001203856,0.01184791,0.01156424,0.9356927,0.03484927,0.00004481114],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7228809,0.0006729141,0.0822499,0.0007303832,0.0003160782,0.00008704742,0.0003756415,0.0002114049,0.1924757],"genre_scores_gemma":[0.9661068,0.0002124096,0.0126541,0.0001181565,0.0001873298,0.00004144721,0.0002330217,0.00005215822,0.0203945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006677778,"threshold_uncertainty_score":0.0223394,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05863965830347237,"score_gpt":0.3348202950743835,"score_spread":0.2761806367709111,"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."}}