{"id":"W4389986571","doi":"10.1137/1.9781611977806.ch23","title":"Chapter 23: Lipschitz Continuity and Smoothness","year":2023,"lang":"en","type":"book-chapter","venue":"Society for Industrial and Applied Mathematics eBooks","topic":"Computability, Logic, AI Algorithms","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo; University of British Columbia, Okanagan Campus; University of British Columbia","funders":"","keywords":"Smoothness; Lipschitz continuity; Mathematics; Calculus (dental); Applied mathematics; Computer science; Pure mathematics; Mathematical analysis; Medicine; Orthodontics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008752816,0.001168673,0.0008763244,0.001488871,0.0009419574,0.003564893,0.0009629426,0.001170435,0.02520448],"category_scores_gemma":[0.002642635,0.0005410337,0.001248375,0.001674016,0.002971227,0.003860051,0.001480042,0.003942606,0.009768804],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002722145,"about_ca_system_score_gemma":0.00103249,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003606362,"about_ca_topic_score_gemma":0.002193478,"domain_scores_codex":[0.9992535,0.0001177872,0.00004524147,0.0001888012,0.0003362053,0.00005845637],"domain_scores_gemma":[0.9992825,0.0003237292,0.00003361027,0.0001007876,0.0002155122,0.00004383743],"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":[0.00001685137,0.00001376069,0.0001173622,0.0003095395,0.00002039327,0.00008647911,0.0002440832,0.002102678,0.0008538415,0.8343803,0.1033229,0.05853193],"study_design_scores_gemma":[0.000003606565,0.00001366754,0.0002821146,0.0001903938,0.00001328031,0.0001422213,0.00006316605,0.001602251,0.0005331879,0.5171883,0.4799517,0.00001613107],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.003933264,0.1068567,0.1720967,0.01219283,0.005620195,0.00006742019,0.00132591,0.0007135147,0.6971934],"genre_scores_gemma":[0.1300094,0.1179498,0.1058037,0.006563918,0.01146115,0.0002906155,0.002025274,0.002506413,0.6233897],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.02520448,"threshold_uncertainty_score":0.08431739,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07451822648134829,"score_gpt":0.245163545459863,"score_spread":0.1706453189785147,"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."}}