{"id":"W2047612262","doi":"10.4153/cjm-2006-020-3","title":"Apolar Schemes of Algebraic Forms","year":2006,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Mathematics and Applications","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Queen's University","keywords":"Mathematics; Cardinality (data modeling); Variety (cybernetics); Algebraic variety; Subspace topology; Homogeneous; Algebraic number; Degree (music); Polyhedron; Set (abstract data type); Rational number; Combinatorics; Discrete mathematics; Pure mathematics; Algebra over a field; Computer science; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0006519102,0.0001641615,0.000475559,0.0002862002,0.00009528107,0.00004123288,0.0004169823,0.00009526797,0.0002278487],"category_scores_gemma":[0.0004175918,0.0001317876,0.0002099857,0.000245241,0.0001152966,0.0001084615,0.00001508198,0.0001770633,0.00001619684],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006869918,"about_ca_system_score_gemma":0.0004881833,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001937129,"about_ca_topic_score_gemma":0.002198391,"domain_scores_codex":[0.9982507,0.00001604729,0.001074015,0.00008243338,0.0002936722,0.0002831862],"domain_scores_gemma":[0.9977519,0.0003125545,0.0009418344,0.0003775733,0.0003455745,0.0002705524],"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":[8.93065e-7,0.000186436,0.000301513,0.0005361157,0.00007296973,0.00001545059,0.000585341,0.000006042719,0.0008892589,0.9604953,0.03661847,0.0002921948],"study_design_scores_gemma":[0.0003739124,0.00006184568,0.000086241,0.0003164199,0.0001306052,0.0002208555,0.0006437944,0.0003040911,0.007739985,0.9677708,0.02214872,0.0002027356],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9387507,0.0006033018,0.04250168,0.000579041,0.0001321183,0.0003844367,0.00007113036,0.00002081366,0.0169568],"genre_scores_gemma":[0.8182225,0.000007499711,0.1809785,0.00002559339,0.000120723,0.000004991706,0.000002767947,0.00004187891,0.0005955463],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1384768,"threshold_uncertainty_score":0.5374141,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02736052152184434,"score_gpt":0.2647960144515095,"score_spread":0.2374354929296652,"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."}}