{"id":"W2510550615","doi":"10.1016/j.jfa.2016.08.002","title":"On variational characterization of four-end solutions of the Allen–Cahn equation in the plane","year":2016,"lang":"en","type":"article","venue":"Journal of Functional Analysis","topic":"Nonlinear Partial Differential Equations","field":"Mathematics","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Fundamental Research Funds for the Central Universities; National Science Foundation of Sri Lanka; Natural Sciences and Engineering Research Council of Canada; National Natural Science Foundation of China; Simons Foundation; National Science Foundation","keywords":"Mathematics; Monotone polygon; Bounded function; Allen–Cahn equation; Mathematical analysis; Domain (mathematical analysis); Plane (geometry); Pure mathematics; Applied mathematics; Geometry","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":[0.001152673,0.001079796,0.0009946077,0.002839755,0.001690523,0.002684799,0.001830323,0.001709527,0.004951558],"category_scores_gemma":[0.002360346,0.0004662533,0.00118503,0.0006968972,0.002908604,0.002547082,0.003054568,0.00256856,0.0005221536],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001535599,"about_ca_system_score_gemma":0.001037415,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003584161,"about_ca_topic_score_gemma":0.002556323,"domain_scores_codex":[0.9996643,0.00009868528,0.00001747331,0.00006301983,0.00007566448,0.00008083406],"domain_scores_gemma":[0.9990203,0.0002331115,0.0001712562,0.0000592824,0.0002421126,0.0002738729],"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":[0.00004267806,0.00004699747,0.0007315153,0.00003485768,0.00002746507,0.000153561,0.0002411673,0.008984866,0.00406106,0.9812489,0.0008667698,0.003560184],"study_design_scores_gemma":[0.00002021161,0.0000567039,0.0009426195,0.00004507079,0.0000171097,0.0001771357,0.0003218103,0.1955419,0.001258175,0.7987936,0.002773443,0.00005235303],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5398587,0.001662266,0.3734378,0.002324831,0.0003348959,0.0001412664,0.0004378342,0.000137632,0.08166478],"genre_scores_gemma":[0.9209871,0.0009361212,0.04138134,0.0004672024,0.0002532138,0.0001046206,0.0005080765,0.0001813952,0.035181],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004951558,"threshold_uncertainty_score":0.01656467,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1064699233091454,"score_gpt":0.2828981345069549,"score_spread":0.1764282111978096,"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."}}