{"id":"W2067467106","doi":"10.1007/pl00001685","title":"An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension","year":2001,"lang":"en","type":"article","venue":"Geometric and Functional Analysis","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":40,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Dimension (graph theory); Minkowski space; Combinatorics; Minkowski–Bouligand dimension; Constant (computer programming); Packing dimension; Arithmetic progression; Hausdorff dimension; Discrete mathematics; Mathematical analysis; Geometry; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008083951,0.0001338618,0.0003121777,0.001147222,0.0002190904,0.00002487218,0.00008956886,0.00009393325,0.0001150323],"category_scores_gemma":[0.000250614,0.00007897513,0.0002081055,0.003152804,0.00009340319,0.00008229926,0.000056192,0.0001046047,6.970426e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002170508,"about_ca_system_score_gemma":0.00001873199,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009409995,"about_ca_topic_score_gemma":0.0001119325,"domain_scores_codex":[0.9989206,0.00004202531,0.0003279948,0.0002684574,0.0002629986,0.0001779501],"domain_scores_gemma":[0.9980763,0.001355323,0.0001159739,0.0002654092,0.0001307607,0.00005619621],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.004666079,0.00284685,0.4643671,0.001049711,0.02130365,0.00004226285,0.005298242,0.007486719,0.01623298,0.2989646,0.01421781,0.163524],"study_design_scores_gemma":[0.001611601,0.0005092841,0.3401233,0.00002783019,0.006452182,0.00002499694,0.0009463039,0.1038924,0.0005350403,0.5432848,0.002122581,0.0004697334],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9742818,0.001757716,0.02314042,0.0002380638,0.0002457223,0.0002054024,0.00002597832,0.00001761911,0.00008724601],"genre_scores_gemma":[0.998288,0.0001709774,0.001033998,0.00008229895,0.00008244936,0.00001900231,0.00003702203,0.00001072928,0.0002755457],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2443202,"threshold_uncertainty_score":0.3220512,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02531179768187286,"score_gpt":0.2783063204869674,"score_spread":0.2529945228050945,"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."}}