{"id":"W4417002358","doi":"10.48550/arxiv.2512.02229","title":"An infinite-dimensional mountain pass theorem with applications to nonlinear elliptic systems","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mountain pass theorem; Mountain pass; Generalization; Nonlinear system; Elliptic curve; Point (geometry)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007139719,0.0006679434,0.0005932014,0.001271654,0.0008887529,0.001208309,0.0007215013,0.000932409,0.00364937],"category_scores_gemma":[0.001867338,0.0002323372,0.0007117942,0.0004075331,0.002000482,0.001788859,0.002120465,0.001508005,0.0003810494],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006076255,"about_ca_system_score_gemma":0.0004470938,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000879029,"about_ca_topic_score_gemma":0.0004556344,"domain_scores_codex":[0.9998115,0.00006223708,0.000008913184,0.00003149822,0.00005637019,0.00002946493],"domain_scores_gemma":[0.9994625,0.0002051793,0.00009037281,0.00003229707,0.0001150041,0.00009458686],"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":[0.00001379362,0.00001101557,0.0001917968,0.00005967971,0.00001649708,0.0002028736,0.0001437749,0.007696688,0.002333459,0.9851795,0.0009109751,0.00324005],"study_design_scores_gemma":[0.00002383077,0.00007807998,0.0004077861,0.00006123532,0.00001772159,0.0003367217,0.0001494641,0.1818123,0.002242388,0.8073727,0.007466545,0.00003119352],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.1786855,0.004053486,0.7448132,0.00265477,0.0003820616,0.0000566886,0.0001077481,0.0002501932,0.06899631],"genre_scores_gemma":[0.9516867,0.001604895,0.03140901,0.0003763796,0.0004757143,0.00008931464,0.00008726439,0.00007210639,0.01419861],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.00364937,"threshold_uncertainty_score":0.0122084,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05778013559742033,"score_gpt":0.3360838021409095,"score_spread":0.2783036665434892,"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."}}