{"id":"W2529291821","doi":"10.1016/j.jpaa.2018.11.019","title":"The symbolic defect of an ideal","year":2018,"lang":"en","type":"preprint","venue":"Journal of Pure and Applied Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Ideal (ethics); The Symbolic; Mathematics; Combinatorics; Set (abstract data type); Star (game theory); Symbolic power; Generating set of a group; Discrete mathematics; Homogeneous; Expressive power; Power (physics); Symbolic dynamics; Computer science; Pure mathematics; Physics; Geometry; Theoretical computer science; Mathematical analysis; Philosophy; Programming language; Law; Quantum mechanics","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":[0.0009936764,0.0002373636,0.0005778246,0.0001042124,0.0002073388,0.00009838019,0.0006168938,0.0001895617,0.00004172577],"category_scores_gemma":[0.0001313999,0.0001478051,0.0002475488,0.0001106318,0.0002416879,0.00005253512,0.0003553976,0.0007228427,0.000004205001],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000229308,"about_ca_system_score_gemma":0.0001508546,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000303217,"about_ca_topic_score_gemma":0.00002118643,"domain_scores_codex":[0.9983801,0.00008836472,0.0008089787,0.0001821971,0.0003481375,0.0001922645],"domain_scores_gemma":[0.9966719,0.000649987,0.001723425,0.0005357007,0.000289109,0.0001298376],"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":[0.0001488814,0.0002923819,0.0001018842,0.0003193991,0.0007614206,0.000004590263,0.003008913,0.000009849958,0.002401051,0.9521376,0.009776081,0.03103794],"study_design_scores_gemma":[0.000356989,0.0001680369,0.001579428,0.0001102967,0.0003239001,0.00004254878,0.0005441147,0.0000299546,0.003204683,0.9916384,0.001829136,0.0001725596],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9924507,0.001078211,0.001550718,0.0004679738,0.0001438177,0.0003503471,0.00001887497,0.00001474908,0.003924666],"genre_scores_gemma":[0.9946893,0.0003222141,0.004197598,0.00006113723,0.0006258845,0.00002147653,0.000004074123,0.00003375494,0.00004454658],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03950074,"threshold_uncertainty_score":0.6027316,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03081939053275576,"score_gpt":0.3160449761565843,"score_spread":0.2852255856238286,"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."}}