{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.004363049,0.0007862254,0.0009330729,0.002148726,0.001438819,0.002291515,0.001168416,0.001426315,0.001928047],"category_scores_gemma":[0.01381967,0.0004801647,0.001371003,0.001131333,0.004103353,0.006933029,0.008467121,0.002290784,0.0002727796],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001201377,"about_ca_system_score_gemma":0.0004367697,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004729638,"about_ca_topic_score_gemma":0.0002413455,"domain_scores_codex":[0.9965801,0.0011577,0.000210316,0.001012139,0.0007204399,0.0003194269],"domain_scores_gemma":[0.9946457,0.002217464,0.0007772388,0.0008456809,0.0006598051,0.0008540451],"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":[0.00008870438,0.00003492834,0.002360453,0.0001236754,0.00004351755,0.0006084989,0.001391112,0.005900477,0.003455729,0.9641966,0.0005198243,0.02127647],"study_design_scores_gemma":[0.00001719689,0.0001798366,0.001355647,0.00005820626,0.00003089036,0.0008038522,0.0008084376,0.02266811,0.001821454,0.9636633,0.00855602,0.0000371667],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5390578,0.002182702,0.4328829,0.001226189,0.0002429094,0.0001194283,0.0001799105,0.0001604001,0.02394779],"genre_scores_gemma":[0.9084381,0.00102755,0.08440265,0.0002241826,0.0002041101,0.000128435,0.0002206335,0.00006266814,0.005291608],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004363049,"threshold_uncertainty_score":0.02307427,"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."}}