{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003594535,0.0003981685,0.0003438452,0.002111887,0.001349443,0.001764282,0.0007294606,0.0007543162,0.004089295],"category_scores_gemma":[0.001671327,0.0002966382,0.0003932189,0.001544869,0.001422791,0.001586612,0.000800259,0.0008267364,0.0005496534],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007624425,"about_ca_system_score_gemma":0.0005309659,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001494891,"about_ca_topic_score_gemma":0.001737848,"domain_scores_codex":[0.9994559,0.0001044133,0.0000308264,0.0001168482,0.000167915,0.0001241072],"domain_scores_gemma":[0.9989837,0.0003625197,0.0001388425,0.0001486325,0.0002148431,0.0001514962],"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":[0.0000227725,0.00002228277,0.0007768985,0.00003927698,0.000007631964,0.0001198356,0.0002017009,0.001469597,0.002171593,0.9775001,0.002382245,0.01528611],"study_design_scores_gemma":[0.00001794332,0.00003011226,0.001258195,0.00003268574,0.00001531809,0.0005952581,0.0002567534,0.02478536,0.001618271,0.9576268,0.01373454,0.00002881246],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7076442,0.003489129,0.116009,0.001275313,0.0003012844,0.0001516641,0.000601644,0.0005290863,0.1699986],"genre_scores_gemma":[0.9641917,0.001251566,0.0205384,0.0003681739,0.0001916915,0.00009760764,0.0007103196,0.00007179285,0.01257866],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004089295,"threshold_uncertainty_score":0.01368004,"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."}}