{"id":"W1936267929","doi":"10.1090/s0002-9939-04-07715-9","title":"Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces","year":2004,"lang":"en","type":"article","venue":"Proceedings of the American Mathematical Society","topic":"Advanced Banach Space Theory","field":"Mathematics","cited_by":16,"is_retracted":false,"has_abstract":true,"ca_institutions":"St. Francis Xavier University","funders":"","keywords":"Lipschitz continuity; Banach space; Separable space; Mathematics; Bounded function; Subspace topology; Quotient; Uniform continuity; Continuous function (set theory); Function (biology); Space (punctuation); Pure mathematics; Combinatorics; Discrete mathematics; Mathematical analysis; 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":[0.0005694596,0.0003304538,0.000895042,0.00005468408,0.0002183471,0.00002466446,0.0006021339,0.00008557626,0.00004290187],"category_scores_gemma":[0.002017654,0.0002136437,0.0006639238,0.0007633838,0.001486605,0.0001466783,0.00024032,0.0004242469,0.0000165768],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001411687,"about_ca_system_score_gemma":0.00006643084,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002156109,"about_ca_topic_score_gemma":0.000001612247,"domain_scores_codex":[0.9979203,0.00001653592,0.0006228868,0.0003374223,0.0006633137,0.0004395086],"domain_scores_gemma":[0.9972364,0.0007410021,0.001090998,0.0004147864,0.0003800029,0.0001368367],"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":[0.0001345552,0.001355998,0.0003539242,0.0007058386,0.0003058139,4.395347e-7,0.005231004,0.00007176847,0.03987861,0.9469322,0.004342454,0.0006874179],"study_design_scores_gemma":[0.0007644882,0.0005128927,0.0007147611,0.000577188,0.0002815624,0.00001749794,0.01956397,0.0002159159,0.01684089,0.9599337,0.0002300786,0.0003470331],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9821132,0.00002801368,0.005465016,0.002656013,0.00005119704,0.0006056063,0.00002306933,0.0001608857,0.008897028],"genre_scores_gemma":[0.9073768,0.00002141122,0.09136093,0.0003107364,0.00005937358,0.00003531846,6.467988e-7,0.00006605157,0.0007687352],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08589592,"threshold_uncertainty_score":0.8712136,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01749435888188461,"score_gpt":0.277268827795853,"score_spread":0.2597744689139684,"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."}}