{"id":"W7116983411","doi":"10.1016/j.aim.2025.110752","title":"Distances in sparse sets of large Hausdorff dimension","year":2025,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Dimension (graph theory); Hausdorff dimension; Hausdorff distance; Hausdorff space; Set (abstract data type)","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":[0.0006897852,0.0001899563,0.0005117323,0.0002600658,0.00005923232,0.000008052169,0.0003021146,0.00009861705,0.00004582969],"category_scores_gemma":[0.0006377219,0.0001530099,0.00007492924,0.0005172116,0.0001324076,0.0001986891,0.0001625969,0.0001948974,0.000001573136],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004424019,"about_ca_system_score_gemma":0.00002227945,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002209757,"about_ca_topic_score_gemma":0.0001791616,"domain_scores_codex":[0.998456,0.00007116653,0.000732774,0.0002206802,0.0002260486,0.0002933523],"domain_scores_gemma":[0.9982482,0.0009711407,0.0002346541,0.000476591,0.00004494449,0.00002449641],"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":[0.00002815677,0.0003205108,0.005421628,0.001150479,0.00001303561,0.00001064453,0.002936046,0.00006781772,0.00008365089,0.9875368,0.00009475297,0.002336517],"study_design_scores_gemma":[0.00067827,0.0000187305,0.0008403811,0.0008763972,0.00001345886,0.000001809871,0.00145706,0.001042962,0.001195301,0.9921086,0.001619829,0.0001471464],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9538662,0.004488932,0.00689171,0.00007243687,0.000534272,0.0005313521,0.00002491648,0.00005339697,0.03353678],"genre_scores_gemma":[0.9567285,0.00069051,0.04213519,0.0000495829,0.00001028165,0.0000223516,0.000002387257,0.00001745214,0.0003437801],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03524349,"threshold_uncertainty_score":0.623956,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01407441497780605,"score_gpt":0.3387595757881969,"score_spread":0.3246851608103909,"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."}}