{"id":"W2539523628","doi":"10.4153/cjm-2017-035-3","title":"Degrees of Regular Sequences With a Symmetric Group Action","year":2017,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University; Royal Military College of Canada; Queen's University","funders":"","keywords":"Mathematics; Isomorphism (crystallography); Polynomial ring; Homogeneous; Action (physics); Symmetric group; Combinatorics; Group (periodic table); Polynomial; Group action; Pure mathematics; Discrete mathematics; Algebra over a field; Mathematical analysis","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":[0.0004114565,0.0001093816,0.0003084652,0.0002845951,0.0002933951,0.00008599385,0.0005491872,0.00004521347,0.0000468752],"category_scores_gemma":[0.0008421888,0.00007979137,0.00008059817,0.000160952,0.0002302881,0.0002471033,0.0000147819,0.0001550992,0.000003560223],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007598356,"about_ca_system_score_gemma":0.0003309559,"about_ca_topic_candidate":true,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006264376,"about_ca_topic_score_gemma":0.03309964,"domain_scores_codex":[0.999104,0.00002787711,0.0004192004,0.00006763798,0.0002212752,0.0001600751],"domain_scores_gemma":[0.9974469,0.0002790991,0.001193593,0.0004930301,0.0003553039,0.0002320799],"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":[0.00001573626,0.0002138769,0.01301324,0.0007198491,0.0004400745,0.000095868,0.004666361,0.00003283636,0.0006333384,0.9667056,0.00357234,0.009890917],"study_design_scores_gemma":[0.001747523,0.001188052,0.09606203,0.001745442,0.0008778543,0.001495566,0.00836107,0.001140008,0.004336951,0.8782274,0.004124271,0.0006938382],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9841841,0.0001591837,0.01266679,0.000379696,0.0000602004,0.0001491623,0.00001366456,0.000004906601,0.002382231],"genre_scores_gemma":[0.925705,0.00002067756,0.07408972,0.000007103042,0.00005036653,0.000003193061,5.540272e-7,0.00001681473,0.0001065386],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08847818,"threshold_uncertainty_score":0.9845437,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1130202323130036,"score_gpt":0.3337913673697153,"score_spread":0.2207711350567116,"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."}}