{"id":"W2111860191","doi":"10.1016/j.jpaa.2011.03.008","title":"The minimum distance of sets of points and the minimum socle degree","year":2011,"lang":"en","type":"article","venue":"Journal of Pure and Applied Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"Western University","funders":"","keywords":"Hyperplane; Mathematics; Degree (music); Resolution (logic); Combinatorics; Ideal (ethics); Upper and lower bounds; Class (philosophy); Field (mathematics); Discrete mathematics; Mathematical analysis; Pure mathematics; Physics","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":[0.0007360393,0.0001161774,0.000338276,0.00003411169,0.0001507226,0.0000186715,0.0002758137,0.00004657052,0.0000242548],"category_scores_gemma":[0.00009731237,0.00005874835,0.00008957512,0.0001109841,0.0004916819,0.00005876339,0.00008501934,0.0001847535,9.787748e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005736672,"about_ca_system_score_gemma":0.00003298958,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001954462,"about_ca_topic_score_gemma":0.00001774543,"domain_scores_codex":[0.9989635,0.00005731201,0.0005597468,0.00008567296,0.0002064259,0.0001273781],"domain_scores_gemma":[0.997947,0.0008757944,0.0007410389,0.0002458396,0.0001327987,0.00005746195],"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":[0.0003423748,0.0001256608,0.0002628036,0.00007012564,0.0001671143,0.000001113167,0.006813508,4.131223e-8,0.001611084,0.9774334,0.002745033,0.0104277],"study_design_scores_gemma":[0.001533354,0.00009979794,0.00527327,0.00005369204,0.0001613677,0.00003194979,0.003577479,0.00002026353,0.007271613,0.9809694,0.0009188436,0.00008898786],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9898706,0.001299356,0.001571169,0.001164192,0.00003871856,0.000259358,0.00001102668,0.000004093899,0.005781468],"genre_scores_gemma":[0.9966071,0.0002859334,0.002909329,0.00006248959,0.00003785746,0.000008439451,3.1293e-7,0.00001175666,0.0000768407],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01033871,"threshold_uncertainty_score":0.2395688,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04525376706069072,"score_gpt":0.2812527661296791,"score_spread":0.2359989990689884,"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."}}