{"id":"W2027646475","doi":"10.1016/j.aim.2012.08.009","title":"Nash resolution for binomial varieties as Euclidean division. A priori termination bound, polynomial complexity in essential dimension 2","year":2012,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":25,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Combinatorics; Euclidean geometry; Dimension (graph theory); Discrete mathematics; Upper and lower bounds; Affine space; Affine transformation; Pure mathematics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0007513192,0.0001881714,0.000278282,0.0002335344,0.0001568994,0.0001099585,0.0003941915,0.00008902804,0.000006275801],"category_scores_gemma":[0.0002511651,0.0001822406,0.0000700399,0.0003407856,0.0001026746,0.001806846,0.0002476364,0.0001394599,0.00002132599],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001739139,"about_ca_system_score_gemma":0.00006499497,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003616734,"about_ca_topic_score_gemma":0.00009025975,"domain_scores_codex":[0.99833,0.00008003281,0.0005551921,0.0002966528,0.0002956197,0.0004424772],"domain_scores_gemma":[0.998929,0.0004035755,0.0002527657,0.0002844364,0.00005462262,0.00007564961],"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":[0.000188637,0.001980695,0.005505856,0.0005905847,0.00002059028,0.00001011983,0.0217678,0.002962445,0.005277289,0.769443,0.0004533407,0.1917996],"study_design_scores_gemma":[0.002348995,0.0002297253,0.01552899,0.0002281039,0.00001422232,0.00002449536,0.0003355569,0.4426512,0.003326892,0.5312067,0.003489762,0.0006153811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5620328,0.0004404602,0.4346552,0.0002663713,0.001347406,0.0005884309,0.000004509323,0.00008800703,0.0005768216],"genre_scores_gemma":[0.9036207,0.00003095711,0.09594835,0.00005154725,0.0002139379,0.00004371583,0.00001338318,0.00001223346,0.00006523961],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4396887,"threshold_uncertainty_score":0.7431555,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02287083940093184,"score_gpt":0.3053135035405641,"score_spread":0.2824426641396323,"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."}}