{"id":"W3044811636","doi":"10.1214/20-aop1503","title":"The height of Mallows trees","year":2021,"lang":"en","type":"preprint","venue":"The Annals of Probability","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Combinatorics; Permutation (music); Order (exchange); Random permutation; Sigma; Zero (linguistics); Mathematics; Tree (set theory); Infinity; Binary number; Bounded function; Binary tree; Discrete mathematics; Physics; Symmetric group; Mathematical analysis; Arithmetic; Quantum mechanics","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":[0.001307125,0.0002469989,0.0005563967,0.001839271,0.001265756,0.002487626,0.001121313,0.0009896735,0.002857128],"category_scores_gemma":[0.01651825,0.0007686199,0.0005018213,0.001259722,0.002228038,0.003948102,0.00163651,0.001277869,0.0006208038],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002222558,"about_ca_system_score_gemma":0.00109138,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002652488,"about_ca_topic_score_gemma":0.002727744,"domain_scores_codex":[0.9989865,0.000192821,0.00004861252,0.0002132568,0.0002999545,0.0002588003],"domain_scores_gemma":[0.9901932,0.005795415,0.001241318,0.001157727,0.0008502326,0.0007621246],"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":[0.0006763817,0.0001019254,0.01428412,0.0002578016,0.00009144512,0.0003791754,0.001038137,0.1126575,0.02179762,0.762471,0.008626984,0.07761784],"study_design_scores_gemma":[0.00007654924,0.0001909971,0.005834202,0.00006264736,0.0000612123,0.000428188,0.0002181174,0.3963301,0.009281896,0.5781416,0.009310527,0.00006395861],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7495096,0.002468613,0.2284353,0.001456546,0.00007794453,0.00007146237,0.000825181,0.001188914,0.01596653],"genre_scores_gemma":[0.9638582,0.0006347894,0.03000722,0.0002302173,0.00007568872,0.00006884507,0.0006396958,0.0002300461,0.004255258],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002857128,"threshold_uncertainty_score":0.0161258,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2540320288678325,"score_gpt":0.4034076830754604,"score_spread":0.1493756542076278,"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."}}