{"id":"W1594371819","doi":"10.1016/s0021-8693(03)00232-1","title":"The Hilbert functions of ACM sets of points in Pn1×⋯×Pnk","year":2003,"lang":"en","type":"article","venue":"Journal of Algebra","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"Lakehead University","funders":"","keywords":"Mathematics; Pure mathematics; Algebra over a field","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":[0.0008462591,0.00008786931,0.0002724461,0.0001289036,0.00006958572,0.00001053788,0.0003465907,0.00004450481,0.0001449091],"category_scores_gemma":[0.002017977,0.000058323,0.0001442006,0.0003359019,0.00009544114,0.0001065202,0.00004673794,0.0002342413,0.000007477514],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003545489,"about_ca_system_score_gemma":0.0001156276,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005932988,"about_ca_topic_score_gemma":0.00004385126,"domain_scores_codex":[0.9986545,0.00014091,0.0007617829,0.000062771,0.0002510718,0.0001289065],"domain_scores_gemma":[0.9970475,0.001491849,0.0006847283,0.0004221839,0.0003038433,0.00004993167],"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":[0.0001227328,0.001133479,0.01094337,0.000105657,0.0003824109,0.000007527659,0.005252031,0.00001479848,0.006921331,0.9382519,0.02884417,0.008020613],"study_design_scores_gemma":[0.0008501596,0.0002062582,0.0174268,0.000110697,0.00008131457,0.00008000603,0.001804897,0.00001424586,0.009218533,0.9620606,0.008050864,0.00009556617],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9923421,0.0003763135,0.001114638,0.001808497,0.0001100239,0.0001345672,0.000005796867,0.000003602979,0.004104452],"genre_scores_gemma":[0.9935203,0.000095877,0.006003196,0.00003978,0.00002255525,0.000004153537,4.285661e-7,0.00001315991,0.0003005634],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02380877,"threshold_uncertainty_score":0.2415853,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04100953194256776,"score_gpt":0.3261833020406305,"score_spread":0.2851737700980627,"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."}}