{"id":"W4408788915","doi":"10.1007/978-3-031-86602-9_2","title":"Commuting Ramanujan Graphs and the Random Self-reducibility of Isogeny Problems","year":2025,"lang":"en","type":"book-chapter","venue":"Lecture notes in computer science","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"","keywords":"Isogeny; Ramanujan's sum; Computer science; Discrete mathematics; Combinatorics; Mathematics; Abelian group","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":[0.002427055,0.0005792627,0.001254418,0.002158851,0.002797287,0.003723783,0.001509508,0.001559952,0.006642047],"category_scores_gemma":[0.00795108,0.0006442574,0.001220357,0.001846403,0.005634885,0.00560641,0.002309867,0.003628826,0.0006003412],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001501811,"about_ca_system_score_gemma":0.0009773946,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005468802,"about_ca_topic_score_gemma":0.0004689593,"domain_scores_codex":[0.9983621,0.0006637526,0.00006564486,0.0002374745,0.0004643742,0.0002066101],"domain_scores_gemma":[0.9948783,0.003192587,0.0003663767,0.0009018984,0.0002937876,0.0003670811],"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":[0.00000974247,0.0000115997,0.00005572981,0.0000128057,0.000003565951,0.0000154945,0.0000760081,0.0004791481,0.0001117446,0.9973476,0.0004506985,0.001425826],"study_design_scores_gemma":[0.000004995388,0.000002915377,0.00004318819,0.000003255289,0.000001613161,0.0000209468,0.00001945223,0.001084701,0.00007374462,0.9983273,0.0004152,0.000002815077],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6413606,0.00397178,0.1164039,0.005791259,0.0006981629,0.0001351177,0.0003324203,0.000328719,0.2309781],"genre_scores_gemma":[0.9611263,0.001172637,0.01346073,0.0004571531,0.0006282083,0.0001394547,0.000196591,0.0001237981,0.02269503],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006642047,"threshold_uncertainty_score":0.02221984,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02030451864079396,"score_gpt":0.2691006963522291,"score_spread":0.2487961777114351,"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."}}