{"id":"W3127639217","doi":"10.48550/arxiv.1910.10074","title":"Improved bounds on the dimensions of sets that avoid approximate\\n arithmetic progressions","year":2019,"lang":"en","type":"article","venue":"arXiv (Cornell University)","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Hausdorff dimension; Dimension (graph theory); Infimum and supremum; Packing dimension; Effective dimension; Fourier analysis; Upper and lower bounds; Arithmetic; Discrete mathematics; Minkowski–Bouligand dimension; Real line; Combinatorics; Fourier transform; Mathematical analysis; Fractal dimension; Fractal","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":[0.003925275,0.001317927,0.001098239,0.003574702,0.001234137,0.003263293,0.002700469,0.001419803,0.005149109],"category_scores_gemma":[0.02518836,0.0006514067,0.001254881,0.001308482,0.004428918,0.008793087,0.004104961,0.005208684,0.0007141594],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002252151,"about_ca_system_score_gemma":0.0006041903,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008595371,"about_ca_topic_score_gemma":0.001125084,"domain_scores_codex":[0.9981927,0.0004574138,0.00009403982,0.0004423842,0.0005518863,0.0002616326],"domain_scores_gemma":[0.9792921,0.01508398,0.001455003,0.002259346,0.001110858,0.0007986004],"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":[0.0002919447,0.00007952793,0.004129933,0.0003463953,0.00009134111,0.0001015351,0.0005178516,0.04197292,0.007280842,0.909714,0.004898055,0.03057569],"study_design_scores_gemma":[0.00003745025,0.0002218165,0.005130983,0.000165829,0.0001188003,0.0003719022,0.0003149269,0.2801277,0.01212047,0.6892126,0.01205556,0.000121955],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3587023,0.005565777,0.5696387,0.003861403,0.0005219316,0.00007817241,0.0010151,0.0006757144,0.05994096],"genre_scores_gemma":[0.8655771,0.002002389,0.1230723,0.0005843165,0.0006363811,0.0001921259,0.0006497755,0.0002312343,0.007054315],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005149109,"threshold_uncertainty_score":0.02075911,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07348379072963561,"score_gpt":0.2143350532271028,"score_spread":0.1408512624974672,"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."}}