{"id":"W4408534475","doi":"10.1088/1361-6544/adbcf0","title":"The 2D Gray–Scott system of equations: constructive proofs of existence of localized stationary patterns","year":2025,"lang":"en","type":"article","venue":"Nonlinearity","topic":"Nonlinear Dynamics and Pattern Formation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Mathematical proof; Mathematics; Gray (unit); Constructive; Calculus (dental); Mathematical analysis; Pure mathematics; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":false,"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":[0.001810034,0.0007635044,0.000661018,0.001411007,0.0006723423,0.001041858,0.0009515071,0.0008915051,0.007462798],"category_scores_gemma":[0.004886027,0.0004405905,0.001113517,0.000390822,0.002207608,0.001656658,0.003318172,0.001851814,0.0006365172],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007700139,"about_ca_system_score_gemma":0.0007298061,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006616325,"about_ca_topic_score_gemma":0.0008055331,"domain_scores_codex":[0.9995171,0.0002180393,0.00002363946,0.00005284386,0.0001446869,0.00004379453],"domain_scores_gemma":[0.9983394,0.00100942,0.000188878,0.0001225278,0.0002206765,0.0001191333],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0000157119,0.00002306218,0.0003192507,0.0001108902,0.00002039501,0.0002385324,0.0002553969,0.0214539,0.002962751,0.9688231,0.0009384898,0.00483859],"study_design_scores_gemma":[0.0000273058,0.00004561157,0.0002500263,0.00005659376,0.0000131682,0.0001456957,0.0001184217,0.3129775,0.002300003,0.6800236,0.004014664,0.00002745992],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05865451,0.0003956176,0.915041,0.001029451,0.0001192285,0.00007344136,0.0001236738,0.0001463325,0.02441676],"genre_scores_gemma":[0.7538415,0.0006448847,0.2306238,0.0004439377,0.0002178127,0.0002732028,0.0001614001,0.000135953,0.01365761],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.007462798,"threshold_uncertainty_score":0.02496552,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01300096067472435,"score_gpt":0.2679291153844766,"score_spread":0.2549281547097523,"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."}}