{"id":"W4417435832","doi":"10.1112/jlms.70386","title":"Conformal optimization of eigenvalues on surfaces with symmetries","year":2025,"lang":"en","type":"article","venue":"Journal of the London Mathematical Society","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"","keywords":"Conformal map; Eigenvalues and eigenvectors; Invariant (physics); Equivariant map; Homogeneous space; Maximization; Laplace operator; Laplace transform","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":[0.000697543,0.0003701895,0.0004618708,0.0007873305,0.0003940649,0.001009431,0.0004657473,0.0005502522,0.002191311],"category_scores_gemma":[0.003112869,0.000259961,0.000307105,0.0002241091,0.001480578,0.001209971,0.001224252,0.0005499924,0.0002177277],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007077894,"about_ca_system_score_gemma":0.0002292565,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004918072,"about_ca_topic_score_gemma":0.0003323197,"domain_scores_codex":[0.9996893,0.00009964624,0.00001088637,0.000055827,0.00008386351,0.00006042011],"domain_scores_gemma":[0.9992844,0.0002672821,0.0001371462,0.00006069723,0.0001215135,0.0001290323],"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":[0.00007093408,0.00004303305,0.001612287,0.00005349486,0.00002204639,0.0002353816,0.0001682704,0.04568062,0.02121371,0.921636,0.00085796,0.008406233],"study_design_scores_gemma":[0.00002951797,0.00006326281,0.002033872,0.00001667519,0.000007716012,0.0001907539,0.0001789742,0.4746864,0.005448231,0.5157289,0.001591091,0.00002463751],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7680956,0.0002307043,0.2084354,0.0007098964,0.00004149718,0.00003578017,0.00006002815,0.00008849471,0.02230254],"genre_scores_gemma":[0.9903548,0.00007004893,0.00621473,0.00003524553,0.00003398849,0.00001878548,0.00002218551,0.00003577064,0.003214432],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002191311,"threshold_uncertainty_score":0.007330656,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02911096377466096,"score_gpt":0.3114932402943658,"score_spread":0.2823822765197049,"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."}}