{"id":"W745968820","doi":"10.30970/ms.35.2.215-224","title":"Extending pairs of metrics","year":2011,"lang":"en","type":"article","venue":"Matematychni Studii","topic":"Holomorphic and Operator Theory","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Bounded function; Metric space; Hausdorff distance; Uniform continuity; Extension (predicate logic); Metric (unit); Product metric; Intrinsic metric; Operator (biology); Discrete mathematics; Combinatorics; Pure mathematics; Injective metric space; Mathematical analysis; Computer science","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009810848,0.000159383,0.0004197898,0.0001540343,0.00008206027,0.000007643015,0.0002573664,0.00007934047,0.0007362398],"category_scores_gemma":[0.0003336125,0.0001259467,0.00009797839,0.0003668394,0.00009033293,0.00007224368,0.0001274829,0.0001050558,0.0001112888],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002525011,"about_ca_system_score_gemma":0.00001350773,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001272925,"about_ca_topic_score_gemma":0.000002252522,"domain_scores_codex":[0.9987693,0.00009487144,0.0004525579,0.0001871302,0.0002526205,0.0002434547],"domain_scores_gemma":[0.9990345,0.0002088255,0.0001852904,0.0004096506,0.00009768717,0.00006401798],"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":[0.00005933403,0.0007212352,0.009566711,0.001012796,0.0002480294,0.00007598285,0.006268526,2.680013e-7,0.001251597,0.9681958,0.009889938,0.002709787],"study_design_scores_gemma":[0.003076041,0.001009275,0.01906077,0.0009662291,0.0007891945,0.0001426435,0.01709234,0.0001440594,0.1424623,0.8050904,0.008251166,0.00191558],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8299471,0.0006478899,0.007960426,0.00003511877,0.0004929871,0.0008156204,0.00002281964,0.0003427985,0.1597352],"genre_scores_gemma":[0.9840181,0.00003506181,0.01518597,0.00003769064,0.00003171846,0.0000414364,7.648122e-7,0.00003480901,0.0006144431],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1631054,"threshold_uncertainty_score":0.8061309,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.182320854506852,"score_gpt":0.3262496021548087,"score_spread":0.1439287476479567,"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."}}