{"id":"W2058510008","doi":"10.4153/cmb-2001-035-0","title":"Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group","year":2001,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":5,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Heisenberg group; Mathematics; Exponent; Group (periodic table); Euclidean geometry; Sobolev space; Nonlinear system; Pure mathematics; Mathematical analysis; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.000577192,0.0002018944,0.0002907523,0.0001487718,0.0002039568,0.00004066174,0.0002538709,0.0001275009,0.007429834],"category_scores_gemma":[0.002189752,0.0001519432,0.0001440648,0.0002710806,0.0001639461,0.00002952325,0.00002916871,0.0002273341,0.004524162],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001777018,"about_ca_system_score_gemma":0.0001185508,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009382015,"about_ca_topic_score_gemma":0.003135414,"domain_scores_codex":[0.9982582,0.0001986684,0.0005128114,0.000229807,0.0003783434,0.0004221098],"domain_scores_gemma":[0.9973316,0.00161277,0.0001585603,0.000465124,0.0001440537,0.0002879481],"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":[0.00003171548,0.0003058421,0.00001937834,0.00006195283,0.00005808389,0.00001569894,0.0004037896,0.0000111224,0.0007584252,0.9930601,0.004523257,0.0007506848],"study_design_scores_gemma":[0.0008999384,0.0004842241,0.0004982385,0.0006472357,0.0002715258,0.00005063783,0.0004203885,0.04736987,0.002971382,0.9319901,0.01371666,0.0006797495],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7844826,0.00004224335,0.1231007,0.03937448,0.0002331599,0.002124995,0.0001861104,0.0001419388,0.05031374],"genre_scores_gemma":[0.9900044,0.000006553611,0.007638281,0.0005844127,0.0001924548,0.00006045866,0.00004440745,0.00004947451,0.001419593],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2055218,"threshold_uncertainty_score":0.9962509,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06227482645481203,"score_gpt":0.2810765074286598,"score_spread":0.2188016809738478,"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."}}