{"id":"W4388837764","doi":"10.1515/ans-2023-0084","title":"On singular solutions of Lane-Emden equation on the Heisenberg group","year":2023,"lang":"en","type":"article","venue":"Advanced Nonlinear Studies","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; China Postdoctoral Science Foundation","keywords":"Mathematics; Combinatorics; Heisenberg group; Physics; Mathematical analysis","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":[0.0005676897,0.001041068,0.0008448078,0.001556261,0.001676618,0.001547353,0.001044886,0.001565017,0.006777961],"category_scores_gemma":[0.001935755,0.0003891095,0.001038326,0.0005728083,0.002874158,0.002054715,0.002297655,0.001743221,0.001257491],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009601826,"about_ca_system_score_gemma":0.000605526,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001063452,"about_ca_topic_score_gemma":0.0008277774,"domain_scores_codex":[0.9995309,0.0001429809,0.00002624932,0.00006942304,0.0001366765,0.00009386543],"domain_scores_gemma":[0.9995363,0.00009059495,0.00007515559,0.00005059266,0.00009305654,0.0001543166],"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":[0.00008099257,0.00004759219,0.0003348911,0.00005745962,0.00002110361,0.000443662,0.000386893,0.004546206,0.004741191,0.9828463,0.001247108,0.005246602],"study_design_scores_gemma":[0.00004765251,0.00007835575,0.0002785322,0.0000246087,0.00001284622,0.0003896807,0.0003024817,0.05005524,0.002300649,0.944232,0.002244601,0.00003339157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7427661,0.0006127062,0.187941,0.001362745,0.0004885202,0.00008442751,0.00009431405,0.0005873793,0.0660628],"genre_scores_gemma":[0.9583411,0.0002821794,0.01979447,0.0002639813,0.0001683038,0.00005436072,0.00009288913,0.0001668142,0.02083586],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006777961,"threshold_uncertainty_score":0.02267456,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06683585434921288,"score_gpt":0.3332228112137433,"score_spread":0.2663869568645304,"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."}}