{"id":"W2174316934","doi":"10.37236/5725","title":"Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph","year":2017,"lang":"en","type":"preprint","venue":"The Electronic Journal of Combinatorics","topic":"Graph theory and applications","field":"Mathematics","cited_by":7,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Regina","funders":"","keywords":"Eigenvalues and eigenvectors; Diagonal; Multiplicity (mathematics); Combinatorics; Mathematics; Property (philosophy); Graph; Graph theory; Discrete mathematics; Physics; Mathematical analysis; Quantum mechanics; Geometry","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":[0.002427182,0.000222595,0.0006836304,0.00006160582,0.0003050458,0.00002787975,0.001617588,0.0001322567,0.000009290333],"category_scores_gemma":[0.0005404435,0.000091049,0.0004602425,0.0002051634,0.0009690871,0.00004779806,0.0004186099,0.0009590544,1.860947e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004979403,"about_ca_system_score_gemma":0.0005277137,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000352696,"about_ca_topic_score_gemma":0.00001568366,"domain_scores_codex":[0.9976684,0.0005348938,0.0009354933,0.0001282426,0.0004724805,0.0002604295],"domain_scores_gemma":[0.9941816,0.0006729407,0.00338202,0.001148934,0.0005795268,0.0000349439],"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":[0.00007692674,0.0002270751,0.0009161817,0.00019237,0.0004339179,1.46115e-7,0.0009043875,0.00005319657,0.0001570697,0.996726,0.0002438053,0.00006892564],"study_design_scores_gemma":[0.0008197812,0.00006579345,0.0004948239,0.0002531029,0.0007533405,0.00003790609,0.0001785358,0.0001346758,0.002424698,0.9945486,0.0001904316,0.00009826242],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9882129,0.003073511,0.004518666,0.001316168,0.000283111,0.0008036108,0.00003217667,0.000007028176,0.001752849],"genre_scores_gemma":[0.9981223,0.001279666,0.00005381286,0.000007049335,0.00004678249,0.0000202909,0.000001343059,0.00002565481,0.000443147],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009909374,"threshold_uncertainty_score":0.4166667,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03057293810492978,"score_gpt":0.3075423517524653,"score_spread":0.2769694136475355,"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."}}