{"id":"W1834934550","doi":"10.1002/cpa.21685","title":"Approximate Ultrametricity for Random Measures and Applications to Spin Glasses","year":2017,"lang":"en","type":"article","venue":"Communications on Pure and Applied Mathematics","topic":"advanced mathematical theories","field":"Mathematics","cited_by":22,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Ultrametric space; Hilbert space; Spin glass; Sequence (biology); Conjecture; Probability measure; Random field; Unit sphere; Separable space; Law of large numbers","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":[0.003414537,0.0008497422,0.0008777246,0.002729399,0.001619293,0.002324879,0.001193569,0.001570724,0.002681511],"category_scores_gemma":[0.01693891,0.0005815263,0.001359828,0.001316586,0.006342908,0.005391828,0.003992218,0.002942306,0.0002129968],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002312472,"about_ca_system_score_gemma":0.0008851561,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0017597,"about_ca_topic_score_gemma":0.00122048,"domain_scores_codex":[0.9982022,0.0007371902,0.0001002378,0.0003093461,0.0005216033,0.0001295082],"domain_scores_gemma":[0.9919419,0.004846361,0.001048352,0.000671515,0.0007346266,0.0007571536],"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":[0.000006180045,0.000007159357,0.0003054353,0.00002877996,0.000007867585,0.00005364538,0.0001121432,0.002807948,0.0004620785,0.9946257,0.0001628667,0.001420241],"study_design_scores_gemma":[0.000006612092,0.00003454986,0.0004817483,0.00002168873,0.000007009851,0.0001828334,0.000091851,0.07766267,0.0004432471,0.9193497,0.001700108,0.00001803022],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1885905,0.006344531,0.7707382,0.004974224,0.0003753483,0.00008623835,0.0002052307,0.0002606683,0.02842499],"genre_scores_gemma":[0.9169887,0.002306149,0.0744798,0.0005827533,0.0006591213,0.0001293055,0.0001488511,0.00008004288,0.004625191],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.003414537,"threshold_uncertainty_score":0.01805806,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.11805735795029,"score_gpt":0.3911284316245243,"score_spread":0.2730710736742343,"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."}}