{"id":"W2963338738","doi":"10.1353/ajm.2013.0010","title":"Geometric Auslander criterion for flatness","year":2013,"lang":"en","type":"article","venue":"American Journal of Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Fields Institute for Research in Mathematical Sciences; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Morphism; Sheaf; Flatness (cosmology); Conjecture; Pure mathematics; Algebraic number; Torsion (gastropod); Fibered knot; Mathematical analysis","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":[0.0004593257,0.0001424012,0.0004702004,0.0002683194,0.00008422509,0.00006135693,0.0003114713,0.00002753236,0.0002060032],"category_scores_gemma":[0.0007657681,0.0001057458,0.0001788127,0.0005058085,0.0001266946,0.0001881436,0.00003796024,0.0001379419,0.00003481449],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004106155,"about_ca_system_score_gemma":0.0000442311,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006799889,"about_ca_topic_score_gemma":0.00000119952,"domain_scores_codex":[0.9987411,0.00003890189,0.0006727451,0.00008833824,0.0002537981,0.0002050916],"domain_scores_gemma":[0.9962938,0.001785818,0.0009131178,0.000272894,0.0006207541,0.0001135911],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00007972989,0.003589201,0.001890257,0.001310434,0.001301057,0.00001081697,0.01849815,0.00002910913,0.009715682,0.3176615,0.1397331,0.5061809],"study_design_scores_gemma":[0.0009825487,0.001133072,0.002112506,0.0001651189,0.000258792,0.0002779699,0.007937107,0.001340997,0.001674601,0.9796627,0.004071119,0.0003834451],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6028391,0.00004455375,0.3954871,0.0007872015,0.00005790035,0.0003156051,0.000004190719,0.00001726006,0.0004471374],"genre_scores_gemma":[0.7109465,0.00002339115,0.2884987,0.0001013903,0.0001146168,0.00004557849,9.250823e-7,0.00003325663,0.000235637],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6620012,"threshold_uncertainty_score":0.4312189,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.043530943563741,"score_gpt":0.3421837439225581,"score_spread":0.2986528003588171,"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."}}