{"id":"W2033177258","doi":"10.1007/s00493-007-2241-5","title":"A phase transition for the metric distortion of percolation on the hypercube","year":2007,"lang":"en","type":"article","venue":"COMBINATORICA","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Hypercube; Combinatorics; Distortion (music); Phase transition; Percolation (cognitive psychology); Uniqueness; Bernoulli's principle; Metric (unit); Discrete mathematics; Mathematical analysis; Physics; Condensed matter physics; Thermodynamics","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":[0.001141612,0.00008644695,0.000147848,0.00005986276,0.000146543,0.00001205743,0.0001391911,0.00005493758,0.00004056262],"category_scores_gemma":[0.000821373,0.00004614821,0.0001210538,0.0002852634,0.00003909994,0.00003865587,0.000008897286,0.00009271532,0.000003623613],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006152925,"about_ca_system_score_gemma":0.000009563019,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003213472,"about_ca_topic_score_gemma":0.000001254841,"domain_scores_codex":[0.999213,0.00003055123,0.0002945531,0.00009918087,0.0002308878,0.0001318313],"domain_scores_gemma":[0.9959007,0.003562906,0.0001338133,0.0002674672,0.0001054387,0.00002966577],"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":[0.00006803367,0.001075349,0.00000293674,0.00007950353,0.00002739115,3.74847e-7,0.0006133631,0.000003038098,0.0004772684,0.983877,0.0007632927,0.01301246],"study_design_scores_gemma":[0.00125519,0.0005891952,0.0002713315,0.00003790156,0.0001408165,0.000002355143,0.0003285956,0.03128013,0.00219824,0.9625748,0.00120112,0.0001202903],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3059773,0.0000826901,0.6894639,0.0009597832,0.0001857346,0.000923564,0.00001359095,0.00003026824,0.002363164],"genre_scores_gemma":[0.9992094,0.00001090051,0.000530115,0.0000670091,0.00003094169,0.00004577649,0.000004641816,0.00001397243,0.00008724811],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.6932321,"threshold_uncertainty_score":0.1881869,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06520229943308131,"score_gpt":0.3504754016821607,"score_spread":0.2852731022490794,"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."}}