{"id":"W4297956901","doi":"10.48550/arxiv.1109.4626","title":"Tail bounds for the height and width of a random tree with a given\\n degree sequence","year":2011,"lang":"","type":"preprint","venue":"arXiv (Cornell University)","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"","keywords":"Combinatorics; Exponent; Mathematics; Sequence (biology); Degree (music); Tree (set theory); Order (exchange); Plane (geometry); Discrete mathematics; Geometry; Physics","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006163383,0.0006741302,0.001148391,0.0001479107,0.0004378815,0.00007880369,0.001075188,0.0004189146,0.0001201104],"category_scores_gemma":[0.0008540478,0.0005016878,0.0002726684,0.0004430811,0.0009987521,0.0001560023,0.0006680463,0.0006135837,0.000007145487],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001173151,"about_ca_system_score_gemma":0.0005177419,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001274199,"about_ca_topic_score_gemma":0.0003562369,"domain_scores_codex":[0.9973778,0.000110261,0.0005676806,0.001146142,0.0001879308,0.0006101481],"domain_scores_gemma":[0.993084,0.003847455,0.0009296907,0.001141114,0.000723822,0.0002739355],"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":[0.004861553,0.0002940055,0.0000936249,0.00234411,0.0009706838,0.0001162673,0.001422512,0.0007054689,0.00003331624,0.9844705,0.000066451,0.004621495],"study_design_scores_gemma":[0.005121735,0.0009733878,0.00004365535,0.0007715172,0.002683231,0.00003535131,0.0008030786,0.235755,0.0001679801,0.7528546,0.0001932089,0.0005972239],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01569315,0.0004049551,0.9796776,0.00007717332,0.0002115029,0.001856136,0.0003698191,0.00004015379,0.001669548],"genre_scores_gemma":[0.9778241,0.001033212,0.01960433,0.00003765087,0.00005971138,0.0000170948,0.0000103982,0.00006770161,0.001345833],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.9621309,"threshold_uncertainty_score":0.9997435,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2073288036207169,"score_gpt":0.2261843506371325,"score_spread":0.01885554701641556,"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."}}