{"id":"W4213332197","doi":"10.1016/j.aim.2022.108252","title":"Fourier dimension and avoidance of linear patterns","year":2022,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Hausdorff dimension; Dimension (graph theory); Pure mathematics; Fourier transform; Invariant (physics); Linear equation; Uncountable set; Mathematical analysis; Discrete mathematics; Countable 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000677106,0.0001553943,0.0004221004,0.00009648383,0.00009821907,0.000007049011,0.0001976554,0.00003680638,0.0002545388],"category_scores_gemma":[0.0004293067,0.0001394779,0.0000554563,0.0001829041,0.00006823755,0.0001357829,0.0002791793,0.000229407,0.000002348153],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003237747,"about_ca_system_score_gemma":0.00001229172,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00000252604,"about_ca_topic_score_gemma":0.000009735355,"domain_scores_codex":[0.9985424,0.00005909994,0.0005969645,0.000199626,0.0003890791,0.0002128703],"domain_scores_gemma":[0.9982805,0.0009563885,0.0003083037,0.0003718813,0.00003543633,0.00004750926],"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":[0.00002111783,0.0009319382,0.002756245,0.002551125,0.00002260663,0.00002495825,0.003740341,0.0003609722,0.0004014688,0.9832433,0.00005075812,0.005895135],"study_design_scores_gemma":[0.000357371,0.0000843465,0.0001113926,0.0001653482,0.00001936253,0.00002581294,0.001080184,0.06861126,0.0001837644,0.928376,0.0008019151,0.0001833182],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9404151,0.00103047,0.05264897,0.0001186032,0.000145028,0.0005115002,0.00006640821,0.00004913922,0.005014724],"genre_scores_gemma":[0.8136258,0.0003636022,0.185414,0.00004523786,0.00002020969,0.00007273345,0.000004211482,0.00004100265,0.0004132711],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.132765,"threshold_uncertainty_score":0.5687743,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01886333133771436,"score_gpt":0.3109450640485268,"score_spread":0.2920817327108125,"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."}}