{"id":"W2074289133","doi":"10.1515/forum-2012-0061","title":"On hypersurfaces containing projective varieties","year":2013,"lang":"en","type":"preprint","venue":"Forum Mathematicum","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"National Research Foundation of Korea","keywords":"Variety (cybernetics); Codimension; Mathematics; Projective variety; Lemma (botany); Pure mathematics; Generalization; Fano plane; Degree (music); Twisted cubic; Projective space; Quadratic equation; Projective test; Mathematical analysis; Complex projective space; Geometry; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008807322,0.0009935228,0.001246614,0.002884331,0.002284283,0.002904943,0.001026241,0.0009497667,0.007222996],"category_scores_gemma":[0.003060992,0.0005843003,0.001118156,0.002196108,0.003167928,0.003677233,0.002980107,0.001841159,0.0009063322],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002348402,"about_ca_system_score_gemma":0.0004868738,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002404175,"about_ca_topic_score_gemma":0.001482484,"domain_scores_codex":[0.9980472,0.0003346495,0.0001174964,0.0003740532,0.0007119937,0.000414604],"domain_scores_gemma":[0.9984452,0.0005961451,0.0003237449,0.0001591013,0.0001840317,0.0002918509],"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":[0.0001536298,0.00007051148,0.002949359,0.000147136,0.00004356013,0.001009683,0.0006621007,0.007849807,0.004740545,0.9656511,0.002821519,0.01390112],"study_design_scores_gemma":[0.00007340411,0.00008844418,0.004596858,0.0000527708,0.00003808322,0.0007276917,0.000287161,0.0313444,0.003172765,0.9467996,0.01277231,0.00004647853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8963757,0.001725644,0.0340817,0.0007972114,0.0001787102,0.00007986249,0.0005039698,0.0002149567,0.06604235],"genre_scores_gemma":[0.981392,0.000572471,0.004839876,0.00007047947,0.0002376589,0.00003355025,0.0006147809,0.00004578504,0.01219339],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007222996,"threshold_uncertainty_score":0.02416337,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02061202527224026,"score_gpt":0.2497337853076217,"score_spread":0.2291217600353815,"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."}}