{"id":"W4404995978","doi":"10.48550/arxiv.2411.18614","title":"Optimal root recovery for uniform attachment trees and $d$-regular growing trees","year":2024,"lang":"en","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":"Natural Sciences and Engineering Research Council of Canada; Canada Research Chairs","keywords":"Root (linguistics); Combinatorics; Tree (set theory); Mathematics; Set (abstract data type); Upper and lower bounds; Preferential attachment; Binary logarithm; Discrete mathematics; Computer science; 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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0002778993,0.0004183534,0.0005511827,0.000192172,0.0001512907,0.000122663,0.000370115,0.0003372266,0.00003469039],"category_scores_gemma":[0.0003049185,0.0004274293,0.0002519897,0.0001842119,0.00008136621,0.0001178383,0.001030694,0.0004434335,0.00001362335],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002040635,"about_ca_system_score_gemma":0.0001378369,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002393918,"about_ca_topic_score_gemma":0.00009734356,"domain_scores_codex":[0.9982435,0.00002858792,0.0002978948,0.0009101954,0.0001125868,0.0004072547],"domain_scores_gemma":[0.9983165,0.0007388795,0.0001642334,0.0004751649,0.0001201024,0.0001850968],"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":[0.0001836416,0.00009030641,0.00001680518,0.001493861,0.0003480715,0.0001492264,0.0001576572,0.01377428,0.00002798891,0.981069,0.0008510082,0.001838107],"study_design_scores_gemma":[0.0004319722,0.0001981873,0.00001504264,0.000427619,0.0006272135,0.000006959443,0.0002712999,0.2563494,0.000096415,0.7408222,0.0003564168,0.0003973185],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1800221,0.0002641373,0.8173301,0.0001308214,0.0005757526,0.0006267992,0.0003168985,0.0001712035,0.0005622199],"genre_scores_gemma":[0.9734544,0.0001181959,0.0231498,0.00003664528,0.0002049414,0.00001173671,0.00004516488,0.00007516403,0.002904019],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.7941803,"threshold_uncertainty_score":0.9998177,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08551445399600212,"score_gpt":0.2473959607276376,"score_spread":0.1618815067316355,"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."}}