{"id":"W2310089532","doi":"","title":"Open Problems on Graph Eigenvalues Studied with AutoGraphiX","year":2012,"lang":"en","type":"article","venue":"Les Cahiers du GERAD","topic":"Graph theory and applications","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Group for Research in Decision Analysis; HEC Montréal","funders":"","keywords":"Adjacency matrix; Graph energy; Mathematics; Combinatorics; Spectral graph theory; Eigenvalues and eigenvectors; Mathematical proof; Graph theory; Discrete mathematics; Line graph; Strength of a graph; Graph; Voltage graph","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005458069,0.0002117725,0.0002509661,0.000129664,0.0005510862,0.0000743376,0.0004662936,0.00009786461,0.00006023355],"category_scores_gemma":[0.00004242817,0.0001550334,0.00008790114,0.000457044,0.0002987794,0.0001892365,0.00006985899,0.0002436906,0.00004272332],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002648959,"about_ca_system_score_gemma":0.00001276935,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002007219,"about_ca_topic_score_gemma":0.00002136594,"domain_scores_codex":[0.9988759,0.0001056224,0.000203345,0.0002486002,0.0001942276,0.0003723727],"domain_scores_gemma":[0.9989339,0.0002479702,0.0001293226,0.0005035661,0.00004615905,0.0001391266],"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":[0.00003644446,0.0004089262,0.004464209,0.00003408372,0.0001355316,0.000001197801,0.00348291,0.000002896535,0.0001546782,0.9878852,0.002635915,0.0007580479],"study_design_scores_gemma":[0.0006752419,0.0001689465,0.004437484,0.00005156773,0.0001089859,0.00001251168,0.001009206,0.000003430229,0.0008495376,0.9757013,0.01665032,0.0003314858],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.969685,0.0001892939,0.002432997,0.000699481,0.00008915319,0.001188471,0.00001692769,0.0002269378,0.02547177],"genre_scores_gemma":[0.9821451,0.00004852639,0.01592436,0.0003081831,0.00009567548,0.0004320054,0.00001021709,0.00004380039,0.0009921661],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0244796,"threshold_uncertainty_score":0.632208,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05481196267456429,"score_gpt":0.3016105306605067,"score_spread":0.2467985679859425,"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."}}