{"id":"W3088894617","doi":"","title":"Pascal's Triangle and the Kesten-McKay Law","year":2020,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Random Matrices and Applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Adjacency matrix; Mathematics; Random walk; Adjacency list; Combinatorics; Pascal (unit); Graph; Random graph; Discrete mathematics; Computer science; Statistics","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":[0.002591688,0.0004009482,0.0007379446,0.001256455,0.00103523,0.00209192,0.001286816,0.001467178,0.00691235],"category_scores_gemma":[0.01598362,0.0003419319,0.0008384531,0.00091578,0.005321231,0.004461077,0.001486152,0.002740956,0.001161195],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001795566,"about_ca_system_score_gemma":0.0008160107,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00319591,"about_ca_topic_score_gemma":0.001369326,"domain_scores_codex":[0.9978725,0.0007080689,0.00006796907,0.0003922912,0.0007006825,0.0002585816],"domain_scores_gemma":[0.9940615,0.003615139,0.0004953383,0.000738688,0.0007013335,0.0003879978],"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":[0.00000418922,0.00000292147,0.00007723892,0.000005525944,0.000001432189,0.00002079761,0.00003893815,0.001049739,0.00007127678,0.9970535,0.0004845829,0.001189817],"study_design_scores_gemma":[0.000004710226,0.000005238609,0.0001583701,0.000006483036,0.000001315085,0.00004229652,0.000014159,0.01603958,0.00009956415,0.9810156,0.002604719,0.000007943743],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1381621,0.003357247,0.725694,0.007370139,0.0005643165,0.00009400799,0.0004768155,0.0003530991,0.1239283],"genre_scores_gemma":[0.929866,0.001495543,0.04380217,0.000846384,0.0007706943,0.0001380718,0.0001504827,0.0001548771,0.02277587],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.00691235,"threshold_uncertainty_score":0.0231241,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1417291052834646,"score_gpt":0.216012508010698,"score_spread":0.07428340272723336,"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."}}