{"id":"W2519183108","doi":"10.2140/apde.2018.11.1083","title":"Large sets avoiding patterns","year":2018,"lang":"en","type":"article","venue":"Analysis & PDE","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Countable set; Uncountable set; Hausdorff dimension; Zero (linguistics); Dimension (graph theory); Combinatorics; Euclidean space; Discrete mathematics; Minkowski space; Zero set","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":[0.0005422141,0.0005006634,0.0007363934,0.00108389,0.001001166,0.001442197,0.0009240484,0.0005683592,0.001869932],"category_scores_gemma":[0.003154848,0.0004471645,0.0007262757,0.0005319818,0.001774564,0.001493587,0.00240349,0.001006072,0.0003107124],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006267757,"about_ca_system_score_gemma":0.0003466809,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000324715,"about_ca_topic_score_gemma":0.0003341486,"domain_scores_codex":[0.9993765,0.0001042466,0.0000498152,0.0001716897,0.0001852814,0.000112566],"domain_scores_gemma":[0.9976472,0.0008148508,0.0004089436,0.0005911154,0.0002545653,0.0002832575],"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":[0.0002854567,0.00008208656,0.01040907,0.0001568058,0.00008359263,0.0007611554,0.000662813,0.02406425,0.02489907,0.9170932,0.001409035,0.0200935],"study_design_scores_gemma":[0.00008446008,0.0003839435,0.00858318,0.00008860268,0.00008763793,0.001824481,0.0005986921,0.2037183,0.03575793,0.7383699,0.01041615,0.00008674918],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8488865,0.0002235545,0.1363831,0.0002100791,0.00004415529,0.00003354989,0.0002034375,0.0001729894,0.0138427],"genre_scores_gemma":[0.9676028,0.00008910336,0.02846904,0.00006912948,0.00003583276,0.00009107148,0.0003185575,0.00005382804,0.003270598],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.001869932,"threshold_uncertainty_score":0.006255567,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03738600749356118,"score_gpt":0.3481849090810049,"score_spread":0.3107989015874437,"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."}}