{"id":"W4392933328","doi":"10.48550/arxiv.2403.10450","title":"Stationary non-radial localized patterns in the planar Swift-Hohenberg PDE: constructive proofs of existence","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Concordia University","keywords":"Swift; Mathematical proof; Constructive; Planar; Mathematics; Pure mathematics; Constructive proof; Calculus (dental); Physics; Geometry; Computer science; Discrete mathematics; Computer graphics (images); Astrophysics; Programming language; Process (computing)","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002363261,0.0002722051,0.0004607135,0.0002126904,0.00006574995,0.00004505461,0.0005509796,0.0002526577,0.00003749291],"category_scores_gemma":[0.0001062932,0.0002275391,0.0001924572,0.0003777035,0.0001964565,0.0001045083,0.0003260746,0.00066086,0.00001561185],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001854234,"about_ca_system_score_gemma":0.0001729318,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006389672,"about_ca_topic_score_gemma":0.0007214256,"domain_scores_codex":[0.9983818,0.000221123,0.0004295131,0.0005671437,0.0001702897,0.0002301607],"domain_scores_gemma":[0.9982941,0.0006178595,0.0003467313,0.000551334,0.0001257531,0.00006427133],"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":[0.00016703,0.0002374431,0.003642775,0.001137186,0.0001691902,0.0002654335,0.002088902,0.0128976,0.00002946888,0.9789029,0.00009569256,0.0003663361],"study_design_scores_gemma":[0.0006925064,0.00005236055,0.001215211,0.0006023342,0.0001520628,0.000005939684,0.001686412,0.1099411,0.00001734347,0.8853239,0.00003678457,0.0002739776],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7478199,0.00003840229,0.2479821,0.00005722779,0.0003526753,0.0008979571,0.0005387058,0.00004704042,0.00226599],"genre_scores_gemma":[0.9983042,0.00003176821,0.001087689,0.00001812887,0.00007044614,0.000008880932,0.0001009456,0.00002383743,0.0003540952],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2504843,"threshold_uncertainty_score":0.9278777,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09235628170996939,"score_gpt":0.24365203125845,"score_spread":0.1512957495484806,"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."}}