{"id":"W3174963163","doi":"10.4153/s0008439521000436","title":"Nehari–Pohožaev-type ground state solutions of Kirchhoff-type equation with singular potential and critical exponent","year":2021,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Nehari manifold; Type (biology); Exponent; Ground state; Mathematical analysis; Pure mathematics; Quantum mechanics; Nonlinear system; Physics","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":[],"category_scores_codex":[0.0003577679,0.0002283849,0.0004144424,0.0001423847,0.0002450774,0.0001130191,0.0001332882,0.0001282429,0.004829419],"category_scores_gemma":[0.003316567,0.0002176664,0.0000722714,0.000306925,0.0003534468,0.00006657836,0.0000759973,0.0002294026,0.0004633061],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001260128,"about_ca_system_score_gemma":0.0006340657,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007963901,"about_ca_topic_score_gemma":0.002445943,"domain_scores_codex":[0.9979399,0.000187296,0.0005516492,0.0003490002,0.0004142591,0.0005578857],"domain_scores_gemma":[0.9976023,0.0006636592,0.0000999201,0.0004295534,0.0006168101,0.0005877967],"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":[0.00007096078,0.0005049892,0.0000492353,0.0006587052,0.0001642661,0.000230571,0.0007478354,0.00003645511,0.006791843,0.9875022,0.002471798,0.0007711553],"study_design_scores_gemma":[0.001341385,0.0005655817,0.001015225,0.0007028696,0.0006826399,0.0002835083,0.0006469087,0.01058543,0.003612595,0.9746607,0.00499294,0.0009102438],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7682434,0.0003150349,0.2167576,0.01031754,0.0003493623,0.0007692816,0.000121223,0.0001121452,0.003014463],"genre_scores_gemma":[0.9588062,0.00001039144,0.03987332,0.0001608727,0.00008860375,0.00001579124,0.00006278772,0.000058074,0.000923993],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1905628,"threshold_uncertainty_score":0.9960803,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06650583340455703,"score_gpt":0.2931861308213984,"score_spread":0.2266802974168414,"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."}}