{"id":"W2051189409","doi":"10.1515/forum.2008.035","title":"Expander graphs and gaps between primes","year":2008,"lang":"en","type":"article","venue":"Forum Mathematicum","topic":"Graph theory and applications","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Ramanujan's sum; Mathematics; Expander graph; Combinatorics; Prime power; Discrete mathematics; Chordal graph; Prime (order theory); Graph","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":[0.0006409789,0.0002773207,0.0003336269,0.001172711,0.0009079851,0.0006722449,0.0005736212,0.0004567837,0.003590954],"category_scores_gemma":[0.003078892,0.0002868852,0.000326172,0.0004087647,0.001855166,0.001455303,0.001217035,0.001079081,0.0002774537],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005945581,"about_ca_system_score_gemma":0.0001897659,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002709985,"about_ca_topic_score_gemma":0.0002518777,"domain_scores_codex":[0.9995747,0.0001324044,0.0000136289,0.00009872698,0.0001140778,0.00006654501],"domain_scores_gemma":[0.9982387,0.000936212,0.0002043184,0.0002847489,0.0001494597,0.0001866158],"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":[0.00006463929,0.00002206965,0.0004438092,0.00003671494,0.000009049128,0.0001668433,0.0002899904,0.004864915,0.005627317,0.9813341,0.0006136459,0.006526893],"study_design_scores_gemma":[0.00001671201,0.00004194033,0.0005642902,0.00001838561,0.00001176241,0.000397245,0.0001604325,0.03074981,0.003346329,0.9608703,0.003807672,0.00001513791],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8373697,0.0005887134,0.1141382,0.0007330026,0.00009436813,0.00002997533,0.0001057523,0.0003503771,0.0465899],"genre_scores_gemma":[0.9854875,0.0001442032,0.011068,0.0001274854,0.00003276549,0.00003458838,0.00006620061,0.00003256878,0.003006722],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003590954,"threshold_uncertainty_score":0.0120129,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05040285597966428,"score_gpt":0.3005628081756454,"score_spread":0.2501599521959811,"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."}}