{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004669585,0.0003410648,0.0006003793,0.001316765,0.001158655,0.002581233,0.0009858429,0.001186238,0.006018028],"category_scores_gemma":[0.004792505,0.0003604802,0.0004793571,0.000605903,0.00220013,0.002053758,0.00116183,0.001234187,0.0003819884],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001603745,"about_ca_system_score_gemma":0.000628315,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001498158,"about_ca_topic_score_gemma":0.0009530979,"domain_scores_codex":[0.9997665,0.00007407106,0.00001052055,0.00003304692,0.00006913222,0.00004679764],"domain_scores_gemma":[0.9986528,0.0006064576,0.0001924028,0.0001148115,0.0001239177,0.0003096171],"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":[0.0001214742,0.00002951709,0.0005802041,0.00007896138,0.00000925938,0.0001248254,0.0001875219,0.009650787,0.003373445,0.9805899,0.002477323,0.002776834],"study_design_scores_gemma":[0.00007820718,0.0000582557,0.00116492,0.00003564382,0.00001043474,0.0003861582,0.0001431943,0.1122647,0.001842434,0.8805507,0.003425839,0.00003943237],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8661962,0.003958819,0.0678061,0.005751299,0.0004777327,0.0001077756,0.0005616358,0.0004306043,0.05470986],"genre_scores_gemma":[0.9887524,0.0005106553,0.006759045,0.0001859596,0.0001322711,0.00004132257,0.0001390643,0.00006762236,0.003411651],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006018028,"threshold_uncertainty_score":0.02013236,"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."}}