{"id":"W4381378082","doi":"10.21203/rs.3.rs-3069438/v1","title":"A Neumann problem with supercritical and exponential growth in dimension N ≥ 3","year":2023,"lang":"en","type":"preprint","venue":"Research Square","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"Conselho Nacional de Desenvolvimento Científico e Tecnológico; Natural Sciences and Engineering Research Council of Canada; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior","keywords":"Annulus (botany); Monotonic function; Multiplicity (mathematics); Bounded function; Mathematics; Supercritical fluid; Exponential function; Function (biology); Combinatorics; Mathematical analysis; Exponential growth; Pure mathematics; Physics; Thermodynamics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001433558,0.0002718192,0.0004533633,0.001080056,0.0001701566,0.0002171911,0.0002779168,0.0003308788,0.00007188116],"category_scores_gemma":[0.001493722,0.0002305347,0.00007319897,0.0006953289,0.0002890236,0.0000944782,0.001536986,0.001797999,0.00009838385],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001116261,"about_ca_system_score_gemma":0.0002524262,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001142942,"about_ca_topic_score_gemma":0.002765533,"domain_scores_codex":[0.9960144,0.0007317004,0.0004386471,0.0007626645,0.001309928,0.0007426249],"domain_scores_gemma":[0.9974444,0.001258896,0.00002301978,0.0005250346,0.0005162383,0.0002323935],"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":[0.001825332,0.005795999,0.0395167,0.03890896,0.0005900421,0.002347078,0.01490375,0.0002006797,0.01561329,0.8607562,0.01807742,0.001464554],"study_design_scores_gemma":[0.002197256,0.0009109145,0.03012474,0.007456826,0.00009236571,0.00002240595,0.001241194,0.009086125,0.002625527,0.9451759,0.0001106639,0.0009561296],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.992556,0.00007047297,0.001907107,0.002308637,0.0001140498,0.002219926,0.0001137661,0.000212943,0.0004970579],"genre_scores_gemma":[0.99199,0.0001927598,0.006340286,0.000005978445,0.0002389956,0.0005958427,0.0001795875,0.0001254337,0.0003310605],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08441966,"threshold_uncertainty_score":0.9400931,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2067001706195488,"score_gpt":0.4498179553779807,"score_spread":0.2431177847584319,"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."}}