{"id":"W3028538784","doi":"10.1007/s00023-021-01096-3","title":"The Vanishing of the Fundamental Gap of Convex Domains in $$\\mathbb {H}^n$$","year":2021,"lang":"en","type":"preprint","venue":"Annales Henri Poincaré","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University","funders":"Australian Research Council; Natural Sciences and Engineering Research Council of Canada; Simons Foundation; National Science Foundation","keywords":"Mathematics; Regular polygon; Product (mathematics); Square (algebra); Convex domain; Boundary (topology); Operator (biology); Convex function; Laplace transform; Dirichlet boundary condition; Dirichlet distribution; Mathematical analysis; Pure mathematics; Combinatorics; Boundary value problem; Geometry; Chemistry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001238222,0.0009813799,0.0009811817,0.002843513,0.002344369,0.004027952,0.0017421,0.001743964,0.008927857],"category_scores_gemma":[0.007017555,0.0006156435,0.0006896468,0.0008217886,0.005303155,0.007892291,0.003220633,0.003636157,0.000674887],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001966937,"about_ca_system_score_gemma":0.0009429914,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001539331,"about_ca_topic_score_gemma":0.000853201,"domain_scores_codex":[0.9993569,0.0001826732,0.00002012489,0.0001539927,0.0001294274,0.0001568977],"domain_scores_gemma":[0.9966731,0.001788346,0.0003293118,0.0001655199,0.0003643169,0.0006793955],"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":[0.00003499431,0.00001298779,0.0001104192,0.00002611643,0.00000435305,0.00003547136,0.00009971165,0.000459564,0.0004788018,0.9963069,0.0008985088,0.001532262],"study_design_scores_gemma":[0.00001139947,0.00000861453,0.0002248916,0.00001099863,0.000002829707,0.00006382089,0.00005716396,0.006436865,0.0002679422,0.9921704,0.0007366618,0.000008369692],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"other","genre_scores_codex":[0.6965562,0.001957134,0.1155333,0.00991683,0.001027836,0.00004107024,0.0004608597,0.0002717387,0.1742351],"genre_scores_gemma":[0.9712157,0.0005911703,0.009006756,0.0005527545,0.0005441734,0.00005095523,0.0002238828,0.0001607853,0.01765394],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.008927857,"threshold_uncertainty_score":0.02986664,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08574819194330899,"score_gpt":0.349610777518034,"score_spread":0.2638625855747251,"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."}}