{"id":"W2742503348","doi":"10.5802/aif.2411","title":"A Hilbert Lemniscate Theorem in <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>ℂ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math>","year":2008,"lang":"de","type":"article","venue":"Annales de l’institut Fourier","topic":"Algebraic and Geometric Analysis","field":"Mathematics","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Norges Forskningsråd","keywords":"Mathematics; Combinatorics; Closure (psychology); Logarithm; Domain (mathematical analysis); Regular polygon; Homogeneous; Measure (data warehouse); Several complex variables; Discrete mathematics; Mathematical analysis; Holomorphic function; Geometry","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.001854,0.001094338,0.0008183829,0.0009193703,0.001646998,0.000614223,0.001806555,0.001835283,0.005466763],"category_scores_gemma":[0.002382893,0.001464911,0.001890137,0.002224442,0.001989106,0.001148872,0.001197768,0.001768398,0.007661219],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00007300686,"about_ca_system_score_gemma":0.001690006,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008761158,"about_ca_topic_score_gemma":0.0006469293,"domain_scores_codex":[0.991573,0.0003735253,0.002015132,0.001608909,0.002079517,0.002349954],"domain_scores_gemma":[0.9935052,0.001447646,0.001452826,0.002429863,0.0002441712,0.0009202996],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0004851181,0.0006687164,0.0001362904,0.0007194045,0.00211496,0.003422054,0.005639366,0.0008110822,0.00005461483,0.9306703,0.05297141,0.002306731],"study_design_scores_gemma":[0.006222278,0.002102898,0.0003997598,0.002507925,0.006969652,0.004649645,0.006096148,0.5879549,0.02994027,0.02138087,0.3267575,0.00501819],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9233945,0.005262429,0.004303844,0.001642186,0.001381082,0.0001509063,0.0002904565,0.0002848737,0.06328975],"genre_scores_gemma":[0.9815161,0.005263571,0.005410755,0.001922427,0.001922885,0.0004359722,0.0005932198,0.0004370941,0.002497997],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9092894,"threshold_uncertainty_score":0.9996527,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02513432249160399,"score_gpt":0.2501324707773121,"score_spread":0.2249981482857081,"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."}}