{"id":"W3000216555","doi":"10.37236/478","title":"A Classification of Ramanujan Unitary Cayley Graphs","year":2010,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Graph theory and applications","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Queen's University","keywords":"Mathematics; Combinatorics; Cayley graph; Ramanujan's sum; Vertex (graph theory); Multiplicative function; Modulo; Graph; Discrete mathematics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001751057,0.0001032612,0.0002119975,0.0001260826,0.0001255943,0.00001119862,0.0005775284,0.00007535527,0.00002056327],"category_scores_gemma":[0.0002305248,0.00007034695,0.0001512747,0.0004862541,0.0001349565,0.00008692344,0.00002352619,0.0009532086,0.000002813979],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003559921,"about_ca_system_score_gemma":0.0002113077,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002807825,"about_ca_topic_score_gemma":0.00001222411,"domain_scores_codex":[0.9988238,0.0001213048,0.0004651964,0.00006905631,0.0002684073,0.0002522567],"domain_scores_gemma":[0.9980254,0.0005277977,0.0006430916,0.0004173704,0.0003332171,0.0000530809],"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":[0.00002674974,0.000225808,0.0002399084,0.00001234067,0.00006132037,4.652655e-7,0.0002447462,9.073415e-7,0.01533716,0.9832911,0.0003326296,0.0002268513],"study_design_scores_gemma":[0.0003820972,0.0001719397,0.0009611137,0.0000112365,0.0001050686,0.00008374623,0.0002350726,0.00002226765,0.005387457,0.9910066,0.001563898,0.00006954578],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9953898,0.0002330324,0.001941116,0.0007967799,0.0002165477,0.0001338284,0.000001301501,0.00001347925,0.00127416],"genre_scores_gemma":[0.9996009,0.0001230916,0.00007894194,0.00001913704,0.00004027169,0.00000470498,8.665768e-7,0.00001542624,0.0001166359],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009949706,"threshold_uncertainty_score":0.414127,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01874658218390824,"score_gpt":0.2853144750696924,"score_spread":0.2665678928857841,"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."}}