{"id":"W1903100294","doi":"10.4310/jdg/1236604347","title":"Counting nodal lines which touch the boundary of an analytic domain","year":2009,"lang":"en","type":"preprint","venue":"Journal of Differential Geometry","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Eigenfunction; Lambda; Boundary (topology); Mathematics; Neumann boundary condition; Domain (mathematical analysis); Mathematical analysis; Complex plane; Upper and lower bounds; Boundary value problem; Omega; Order (exchange); Dirichlet boundary condition; Dirichlet distribution; Combinatorics; Physics; Eigenvalues and eigenvectors; Quantum mechanics","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":[0.0008698857,0.000602738,0.0008699902,0.002923713,0.001487024,0.002119427,0.001343574,0.001251796,0.005287008],"category_scores_gemma":[0.009146219,0.0005544284,0.0004483532,0.001054645,0.002077646,0.003439351,0.001972549,0.000779525,0.0006149954],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008139349,"about_ca_system_score_gemma":0.0001858685,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005909061,"about_ca_topic_score_gemma":0.0004128721,"domain_scores_codex":[0.9991836,0.0001889687,0.00005205651,0.0001752344,0.0002280754,0.0001720153],"domain_scores_gemma":[0.9939904,0.002576021,0.001391159,0.0005614564,0.0008412623,0.0006396929],"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":[0.002498423,0.0004949596,0.1278389,0.0007947059,0.0002419551,0.00537332,0.00326947,0.1311911,0.1609219,0.4389891,0.005924953,0.1224612],"study_design_scores_gemma":[0.0001544299,0.0007118397,0.02852004,0.0003339961,0.000152256,0.004147966,0.002758682,0.6060542,0.09125306,0.2540425,0.01168308,0.0001880427],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9420167,0.0002780229,0.050579,0.0001263,0.00003091398,0.00003686338,0.0001142188,0.000104251,0.006713769],"genre_scores_gemma":[0.97072,0.0002754978,0.02511786,0.00003615655,0.00004602925,0.00009634559,0.0003648947,0.00009429684,0.003248825],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005287008,"threshold_uncertainty_score":0.01768684,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02948857959841199,"score_gpt":0.3136458074622928,"score_spread":0.2841572278638808,"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."}}