{"id":"W1523487694","doi":"10.1515/ans-2012-0101","title":"Liouville Type Theorems for Stable Solutions of Certain Elliptic Systems","year":2012,"lang":"en","type":"preprint","venue":"Advanced Nonlinear Studies","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Infimum and supremum; Type (biology); Dimension (graph theory); Bounded function; Combinatorics; Lambda; Omega; Mathematics; Hamiltonian (control theory); Discrete mathematics; Physics; Mathematical analysis; 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":[0.002413913,0.0006691904,0.0006479353,0.001776446,0.001227355,0.002013669,0.0009054806,0.001494272,0.003987397],"category_scores_gemma":[0.00657265,0.0003435044,0.001074728,0.0004425847,0.002323507,0.002364465,0.001984851,0.001763638,0.000329104],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001626976,"about_ca_system_score_gemma":0.0008059224,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001114627,"about_ca_topic_score_gemma":0.0006966488,"domain_scores_codex":[0.9994061,0.0001829,0.00003157006,0.00007821807,0.0002098223,0.0000913625],"domain_scores_gemma":[0.9977418,0.0008780645,0.0003916349,0.0001134369,0.0005762199,0.0002988178],"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":[0.00006671779,0.00005593427,0.001672787,0.0001120706,0.00005385192,0.0002986897,0.0004839055,0.02127276,0.0123529,0.957186,0.001152767,0.005291537],"study_design_scores_gemma":[0.00004330015,0.000175237,0.001401094,0.00004860012,0.0000213128,0.0003070735,0.0002254222,0.4333149,0.004744844,0.556799,0.002879674,0.00003961402],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3966657,0.001173029,0.5429532,0.002430064,0.0002480257,0.0002249508,0.0002354402,0.0002673765,0.05580224],"genre_scores_gemma":[0.9646891,0.0004098663,0.02387024,0.0002911872,0.0001674814,0.0001793385,0.0001045827,0.00004757365,0.01024074],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003987397,"threshold_uncertainty_score":0.01333916,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2328633924272905,"score_gpt":0.4220472712747082,"score_spread":0.1891838788474177,"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."}}