{"id":"W2951691373","doi":"10.48550/arxiv.math/0605739","title":"Zeros of random polynomials on C^m","year":2006,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Combinatorics; Measure (data warehouse); Unit sphere; Markov chain; Distribution (mathematics); Boundary (topology); Orthogonal polynomials; Discrete mathematics; Mathematical analysis; Statistics","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":[0.001131392,0.0007528121,0.0007416331,0.001812462,0.001006132,0.00165766,0.001330755,0.0007479606,0.002915146],"category_scores_gemma":[0.006524715,0.0004009853,0.0004295955,0.0005970877,0.002773639,0.001829787,0.001853899,0.001238986,0.0003402509],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001736546,"about_ca_system_score_gemma":0.0006895343,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003205444,"about_ca_topic_score_gemma":0.001879331,"domain_scores_codex":[0.999262,0.0001812948,0.00001773193,0.0001626119,0.0001855309,0.0001908226],"domain_scores_gemma":[0.9974946,0.001041466,0.0004679797,0.0001577968,0.0003348532,0.0005032576],"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":[0.0002450728,0.00005139142,0.00333331,0.00008939441,0.00003538308,0.0004006297,0.0002738008,0.04089546,0.01036204,0.9368688,0.001615675,0.005829067],"study_design_scores_gemma":[0.00004953385,0.0001060388,0.005722581,0.00005633406,0.00002064583,0.0003756649,0.0003288032,0.667537,0.00606358,0.3177556,0.001892287,0.00009195464],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8419168,0.0004169955,0.1451785,0.0008756334,0.0000645142,0.00003229886,0.0002642059,0.0002106076,0.01104039],"genre_scores_gemma":[0.9879192,0.0002135291,0.008334908,0.00007418842,0.00006309863,0.00004518867,0.0001918967,0.00005469143,0.003103229],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003205444,"threshold_uncertainty_score":0.01259965,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1177928558542737,"score_gpt":0.3224403238421503,"score_spread":0.2046474679878766,"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."}}