{"id":"W2554562761","doi":"10.1016/j.jalgebra.2018.05.014","title":"Togliatti systems and Galois coverings","year":2018,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":17,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni; Banff International Research Station for Mathematical Innovation and Discovery; Istituto Nazionale di Alta Matematica \"Francesco Severi\"","keywords":"Mathematics; Monomial; Diagonal; Polynomial ring; Pure mathematics; Invariant (physics); Prime power; Homogeneous; Discrete mathematics; Prime (order theory); Combinatorics; Algebra over a field; Polynomial; Mathematical analysis","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003362538,0.00008113006,0.0002048596,0.00007743509,0.00008743088,0.00006088449,0.0001423079,0.00003651635,0.00008944784],"category_scores_gemma":[0.0001864864,0.00006282021,0.00005071562,0.0001074357,0.00008876453,0.0001655306,0.00004710832,0.0001245079,0.00002512516],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002768141,"about_ca_system_score_gemma":0.00003428942,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000070256,"about_ca_topic_score_gemma":0.000003430027,"domain_scores_codex":[0.9992653,0.00003316731,0.0003464483,0.00006912776,0.0001768004,0.0001092046],"domain_scores_gemma":[0.998899,0.0002466659,0.0003230008,0.0001534498,0.0002899941,0.00008792159],"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":[0.00008923834,0.0002292747,0.004173323,0.0001773082,0.0003321155,0.00002190065,0.005138625,0.000001098046,0.01109315,0.8871759,0.08575367,0.00581443],"study_design_scores_gemma":[0.002371706,0.001734239,0.02418272,0.0004941471,0.0003498295,0.001615525,0.002385727,0.0004689135,0.01036863,0.814862,0.140585,0.0005815274],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.988689,0.0004005457,0.006633474,0.0005544687,0.0001819004,0.00009061291,0.000003021346,0.00001392878,0.003433025],"genre_scores_gemma":[0.9957955,0.00004945746,0.003282477,0.00009249865,0.0003931687,0.000002132464,1.620274e-7,0.00001352761,0.000371061],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.07231383,"threshold_uncertainty_score":0.2561734,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04130801166302817,"score_gpt":0.326885517607548,"score_spread":0.2855775059445198,"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."}}