{"id":"W4410521533","doi":"10.5802/ahl.231","title":"Critical trees are neither too short nor too fat","year":2025,"lang":"en","type":"article","venue":"Annales Henri Lebesgue","topic":"Stochastic processes and statistical mechanics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McGill University","funders":"Natural Sciences and Engineering Research Council of Canada; McGill University","keywords":"Mathematics; Generality; Domain (mathematical analysis); Upper and lower bounds; Cauchy distribution; Tree (set theory); Distribution (mathematics); Combinatorics; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0001797777,0.0002791489,0.0004505485,0.00009765445,0.0001803736,0.0001056913,0.0003355292,0.0001720619,0.0002191863],"category_scores_gemma":[0.00392381,0.0002399629,0.0001370905,0.000266781,0.0001244664,0.0001258977,0.0001376582,0.0002729424,0.00009970303],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004244848,"about_ca_system_score_gemma":0.00007699672,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001494142,"about_ca_topic_score_gemma":0.0001286027,"domain_scores_codex":[0.9982743,0.00004645041,0.0004301839,0.0004236404,0.0003221838,0.0005031933],"domain_scores_gemma":[0.9973861,0.00169119,0.00004426642,0.0004397317,0.0002813207,0.0001574173],"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":[0.00005174635,0.0002370087,0.000220592,0.000339526,0.00006730831,0.00006244137,0.000152165,0.000002804635,0.000164154,0.9161862,0.07147326,0.01104279],"study_design_scores_gemma":[0.0003840515,0.0001825001,0.0009726573,0.0003900698,0.0001962834,0.00002078037,0.0007259064,0.004731593,0.001215624,0.9536321,0.03704216,0.0005062682],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01366476,0.0009217495,0.9525026,0.005659759,0.0006897901,0.0003749613,0.0001898522,0.0002575578,0.02573897],"genre_scores_gemma":[0.9683524,0.00005148288,0.01967824,0.002875005,0.0002787201,0.00008460868,0.00001299503,0.00005254151,0.008614004],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.9546877,"threshold_uncertainty_score":0.9785405,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05733941254851745,"score_gpt":0.3693569755770033,"score_spread":0.3120175630284859,"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."}}