{"id":"W3177616869","doi":"10.3390/math9131546","title":"A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals","year":2021,"lang":"en","type":"article","venue":"Mathematics","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Hausdorff dimension; Effective dimension; Mathematics; Dimension function; Hausdorff measure; Packing dimension; Minkowski–Bouligand dimension; Fractal; Outer measure; Pure mathematics; Lebesgue measure; Generalization; Fractal dimension; Lebesgue integration; Measure (data warehouse); Urysohn and completely Hausdorff spaces; Bivariate analysis; Fractal dimension on networks; Discrete mathematics; Mathematical analysis; Fractal analysis; Computer science; Statistics","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":[0.002777341,0.0005371476,0.0008033985,0.001726527,0.001314683,0.002157349,0.0009090015,0.0009820613,0.00240394],"category_scores_gemma":[0.008515574,0.0002716898,0.001221427,0.0008443415,0.003953649,0.006401276,0.002856271,0.002493798,0.0003972953],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001334647,"about_ca_system_score_gemma":0.0005218397,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006329652,"about_ca_topic_score_gemma":0.0003668539,"domain_scores_codex":[0.9988181,0.0002628831,0.00007727546,0.0003901659,0.0003518811,0.00009971342],"domain_scores_gemma":[0.9960973,0.002262185,0.0003775953,0.0006284172,0.0004698719,0.0001647033],"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":[0.000009158091,0.000005030256,0.000344789,0.00007851344,0.00001584693,0.00007687812,0.0001095836,0.001455892,0.0007742177,0.9894487,0.001328833,0.006352521],"study_design_scores_gemma":[0.000009002251,0.00002361548,0.0008457494,0.00003915034,0.00001188615,0.0004130006,0.00006505301,0.01143813,0.0005850962,0.9687254,0.0178215,0.00002240952],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06489507,0.01223927,0.8283769,0.008198765,0.001473741,0.00008823257,0.0005212411,0.0002357932,0.08397104],"genre_scores_gemma":[0.8578512,0.007947702,0.1154516,0.002893978,0.002857727,0.0002323455,0.0003115486,0.00009745128,0.01235628],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002777341,"threshold_uncertainty_score":0.01468813,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04025138681659689,"score_gpt":0.3125498280935314,"score_spread":0.2722984412769345,"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."}}