{"id":"W2012755367","doi":"10.1016/j.laa.2005.12.020","title":"Eigenvalues of graphs and a simple proof of a theorem of Greenberg","year":2006,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":12,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Simple (philosophy); Combinatorics; Pure mathematics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001792085,0.00009604087,0.0002316605,0.00008437954,0.00006907756,0.000003275433,0.0001074324,0.00005673195,0.00001983939],"category_scores_gemma":[0.00003026457,0.00008305418,0.00005787941,0.0003058036,0.000226408,0.00004096927,0.00004165735,0.00005053814,6.090505e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000001528878,"about_ca_system_score_gemma":0.00001412359,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002166942,"about_ca_topic_score_gemma":0.00001446421,"domain_scores_codex":[0.9992364,0.00002643025,0.0003907397,0.000155949,0.00009666138,0.00009383049],"domain_scores_gemma":[0.9990549,0.0002637602,0.0002433397,0.0002761027,0.0001271073,0.00003478296],"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":[0.000007433962,0.0002123048,0.0006092709,0.0002036626,0.00002323596,2.70444e-8,0.0001637869,0.000001934119,0.01475525,0.9828728,0.00007142167,0.001078837],"study_design_scores_gemma":[0.0001815352,0.00003947407,0.001210768,0.0000173802,0.00006747579,0.000002276963,0.0001030365,0.0002295046,0.09531887,0.9021509,0.0006085413,0.00007024403],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9917006,0.0006288154,0.005019643,0.0000930191,0.000002812343,0.0006671973,0.0001469009,0.00002494514,0.001715989],"genre_scores_gemma":[0.9954311,0.00005519388,0.004216823,0.000008813892,0.00001518995,0.0001402737,0.00001965698,0.0000125973,0.0001003871],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.08072194,"threshold_uncertainty_score":0.3386851,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01854813958535024,"score_gpt":0.2788888504103185,"score_spread":0.2603407108249683,"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."}}