{"id":"W2313510692","doi":"10.4153/cjm-2012-022-4","title":"Distance Sets of Urysohn Metric Spaces","year":2012,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Injective metric space; Metric space; Convex metric space; Intrinsic metric; Metric differential; Isometry (Riemannian geometry); Metric (unit); Separable space; Urysohn and completely Hausdorff spaces; Subspace topology; Space (punctuation); Combinatorics; Cardinality (data modeling); Discrete mathematics; Pure mathematics; Mathematical analysis; Hausdorff dimension; Computer science","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":[0.0009966958,0.0001331598,0.0004332876,0.0003321034,0.00007809079,0.00001056223,0.0002787381,0.0001016824,0.0002642972],"category_scores_gemma":[0.001761814,0.0001087768,0.0001135349,0.0002546896,0.0002004512,0.0002152449,0.00001125011,0.0002283393,0.00001573466],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008498203,"about_ca_system_score_gemma":0.0002745422,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003996247,"about_ca_topic_score_gemma":0.0008108967,"domain_scores_codex":[0.998766,0.00006451079,0.0005776584,0.00005297932,0.0001793833,0.0003594842],"domain_scores_gemma":[0.9976723,0.0007413313,0.0006870133,0.0002414802,0.0001862473,0.000471591],"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":[0.00001010651,0.0001655992,0.00394865,0.0004280641,0.0001579749,0.00005051369,0.006522605,0.00001527844,0.00007874738,0.982195,0.005386919,0.001040555],"study_design_scores_gemma":[0.0004910878,0.0001220207,0.0007061611,0.0002660328,0.0002285496,0.0007386928,0.005072996,0.00004965608,0.001681273,0.9781124,0.01225461,0.0002764975],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8955966,0.005439082,0.08682936,0.0003406981,0.00105564,0.0001995321,0.00004633827,0.00001523446,0.01047755],"genre_scores_gemma":[0.9271416,0.00002745389,0.07232316,0.00003595149,0.0001065475,8.545572e-7,5.976016e-7,0.00002261536,0.0003412392],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.03154501,"threshold_uncertainty_score":0.443579,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03919585441185798,"score_gpt":0.3061005541878954,"score_spread":0.2669046997760374,"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."}}