{"id":"W4414845207","doi":"10.4153/s0008439525101288","title":"Constructing surfaces with first Steklov eigenvalue of arbitrarily large multiplicity","year":2025,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Mathematical Approximation and Integration","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université Laval","funders":"University of Cambridge","keywords":"Multiplicity (mathematics); Eigenvalues and eigenvectors; Laplace operator; Graph; Laplacian matrix; Cayley graph; Prime (order theory)","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"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":[0.0005284456,0.0010202,0.0007561183,0.002006484,0.00140228,0.002209281,0.0006888335,0.001309325,0.006743692],"category_scores_gemma":[0.002158414,0.0006583328,0.001153364,0.0005596608,0.0025771,0.002377321,0.003069821,0.002866158,0.001472595],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001187264,"about_ca_system_score_gemma":0.0003828586,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004558768,"about_ca_topic_score_gemma":0.0004453275,"domain_scores_codex":[0.9992546,0.0001131287,0.00002442798,0.0001171493,0.0003229702,0.0001676657],"domain_scores_gemma":[0.9991813,0.0002400363,0.00008749824,0.0001647918,0.000165462,0.0001608446],"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":[0.00006927326,0.00003834435,0.0009207289,0.00005227464,0.00001599783,0.000383477,0.0004795954,0.006486264,0.01660684,0.9618834,0.002009694,0.01105423],"study_design_scores_gemma":[0.00004226412,0.0001551789,0.001186847,0.00004508597,0.00002247808,0.0007662959,0.0006919114,0.04757459,0.01781544,0.9181334,0.01350858,0.00005782515],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6338621,0.0003038177,0.2695434,0.00135281,0.0003277784,0.00008667618,0.0001611506,0.001153705,0.09320857],"genre_scores_gemma":[0.9522992,0.0001418609,0.02965209,0.0001495747,0.00007497284,0.00004502952,0.0001374625,0.000422165,0.01707766],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006743692,"threshold_uncertainty_score":0.02255994,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01895057177619353,"score_gpt":0.2621817228498287,"score_spread":0.2432311510736351,"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."}}