{"id":"W2042912977","doi":"10.4153/cmb-2013-007-8","title":"How Lipschitz Functions Characterize the Underlying Metric Spaces","year":2013,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Lipschitz continuity; Homeomorphism (graph theory); Bijection; Zero (linguistics); Banach space; Metric map; Metric space; Function space; Pure mathematics; Function (biology); Discrete mathematics; Combinatorics; Convex metric space","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0004031896,0.0002326734,0.0003111006,0.0001857458,0.0005448944,0.0002383263,0.0003658317,0.0001721253,0.02181911],"category_scores_gemma":[0.00282602,0.0001560896,0.0001096761,0.0003517955,0.0003202981,0.00009449855,0.00004639832,0.0004159678,0.01197854],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001040015,"about_ca_system_score_gemma":0.0001112007,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003381169,"about_ca_topic_score_gemma":0.0006651311,"domain_scores_codex":[0.998534,0.0001586632,0.0002607125,0.0002587331,0.0001774831,0.0006104684],"domain_scores_gemma":[0.9970286,0.001760232,0.0001052713,0.0005509213,0.0001065798,0.0004483917],"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":[0.000003744772,0.00004901176,0.00002182523,0.0000869929,0.00007652889,0.00001728329,0.0004798805,8.983238e-7,0.0001272453,0.9447895,0.0509692,0.003377883],"study_design_scores_gemma":[0.0001686105,0.00003112159,0.0003200251,0.00003703822,0.00005403823,0.00007082739,0.002118468,0.00008365915,0.00002747166,0.8244827,0.172357,0.0002490472],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4021803,0.0004754137,0.09961154,0.3665249,0.0008673479,0.00285624,0.00008517983,0.0005445231,0.1268546],"genre_scores_gemma":[0.9375046,0.000008101537,0.005442857,0.001867695,0.0001545281,0.0002159454,0.000009310318,0.00005358838,0.0547433],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5353244,"threshold_uncertainty_score":0.9887908,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05256578678266508,"score_gpt":0.2677134025343054,"score_spread":0.2151476157516403,"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."}}