{"id":"W1634163239","doi":"10.1215/ijm/1385129955","title":"Gotzmann squarefree ideals","year":2012,"lang":"en","type":"preprint","venue":"Illinois Journal of Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Killam Trusts","keywords":"Square-free integer; Mathematics; Business; Combinatorics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006355286,0.0005079357,0.0005110913,0.001812739,0.001691934,0.002255258,0.000525669,0.0004985936,0.003533718],"category_scores_gemma":[0.001685302,0.0004516205,0.0006350505,0.001215222,0.003064299,0.002992199,0.002320886,0.001421378,0.000715826],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007947922,"about_ca_system_score_gemma":0.0005620008,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006481665,"about_ca_topic_score_gemma":0.000799432,"domain_scores_codex":[0.9993107,0.00005027993,0.00003623234,0.0001212207,0.000270044,0.0002114623],"domain_scores_gemma":[0.9990295,0.0002560831,0.0002020009,0.00009793121,0.0001862412,0.0002282687],"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":[0.0003082969,0.00005022644,0.006191129,0.0002898196,0.0000461789,0.001153752,0.00178249,0.0011315,0.01001037,0.9608517,0.003240626,0.01494394],"study_design_scores_gemma":[0.00007433282,0.0001528762,0.008194393,0.0001013692,0.000112434,0.003118867,0.001308826,0.004983647,0.02042189,0.9261799,0.03528789,0.00006360273],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8844807,0.002455813,0.03416742,0.001023977,0.0002755484,0.00008288823,0.000347793,0.0003412887,0.07682458],"genre_scores_gemma":[0.9808525,0.0006755802,0.007616427,0.0001463862,0.0001870409,0.00002817381,0.0004033074,0.00003683469,0.0100536],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003533718,"threshold_uncertainty_score":0.01182145,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1037530844990443,"score_gpt":0.365348667480049,"score_spread":0.2615955829810046,"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."}}