{"id":"W3011491380","doi":"10.1007/s11854-021-0189-9","title":"Non-boundedness of the number of super level domains of eigenfunctions","year":2021,"lang":"fr","type":"article","venue":"Journal d Analyse Mathématique","topic":"Spectral Theory in Mathematical Physics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"Agence Nationale de la Recherche","keywords":"Mathematics; Eigenfunction; Partial differential equation; Functional analysis; Mathematical analysis; Pure mathematics; Eigenvalues and eigenvectors","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":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001579495,0.0003964717,0.001434704,0.0001263659,0.0001936772,0.00006299027,0.0007304027,0.0003266902,0.004470544],"category_scores_gemma":[0.001503968,0.0002932523,0.001511526,0.001393256,0.0007383272,0.0003074771,0.0002620709,0.0009835474,0.00005576549],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002186273,"about_ca_system_score_gemma":0.000936827,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006649638,"about_ca_topic_score_gemma":0.00006510995,"domain_scores_codex":[0.9952777,0.0006805715,0.002354542,0.0002459568,0.001000491,0.0004407295],"domain_scores_gemma":[0.9937395,0.001377498,0.001931682,0.001171175,0.001595627,0.0001845595],"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":[0.00003475765,0.002464233,0.003353768,0.003399931,0.001877629,0.00004255836,0.005688253,0.0004359574,0.04176907,0.9388153,0.001849161,0.0002693695],"study_design_scores_gemma":[0.0005875607,0.0000496128,0.003250454,0.00204709,0.001454995,0.0007949358,0.002849177,0.001125545,0.125571,0.8618389,0.0001687273,0.0002620114],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9262598,0.0004074301,0.04993787,0.001494764,0.001082272,0.0002604647,0.0001760852,0.00001026858,0.02037106],"genre_scores_gemma":[0.9464077,0.0003120645,0.04297826,0.00008802331,0.0003472661,0.00000753612,0.000003376734,0.00008886272,0.009766935],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08380193,"threshold_uncertainty_score":0.999952,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04488595353240805,"score_gpt":0.3352215504196933,"score_spread":0.2903355968872852,"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."}}