{"id":"W2905635537","doi":"10.48550/arxiv.1812.09775","title":"Maximum Modulus of Independence Roots of Graphs and Trees","year":2018,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Guelph; Dalhousie University","funders":"","keywords":"Combinatorics; Independence number; Independence (probability theory); Mathematics; Graph; Upper and lower bounds; Polynomial; Discrete mathematics; Mathematical analysis; Statistics","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":[0.0002461173,0.0001768982,0.0003436497,0.0002082935,0.00005795579,0.000006546857,0.0004516761,0.000247456,0.00005468684],"category_scores_gemma":[0.00005326808,0.0001937334,0.0001424116,0.0002817289,0.0004375647,0.00006357909,0.0004917574,0.0002359187,0.000004441683],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001466121,"about_ca_system_score_gemma":0.00004507004,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00005911113,"about_ca_topic_score_gemma":0.00007606708,"domain_scores_codex":[0.9990936,0.00007169633,0.000217345,0.0004104498,0.00007052117,0.000136424],"domain_scores_gemma":[0.9984867,0.0001453252,0.0003895028,0.0007305068,0.0001795033,0.00006846795],"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":[0.00004546174,0.0001469851,0.004260906,0.0002745057,0.0001048705,0.000006608432,0.000171935,0.0003598674,0.0005530627,0.9938301,0.0001356998,0.0001100386],"study_design_scores_gemma":[0.000240603,0.00004327861,0.004386119,0.0001272868,0.0001626373,0.000001771129,0.0001488707,0.001519512,0.002195333,0.9909931,0.00001832265,0.00016313],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9889812,0.00003604606,0.007123626,0.000009615213,0.00006498856,0.0002421928,0.00006584164,0.00004259334,0.003433903],"genre_scores_gemma":[0.9985483,0.0001013065,0.0008256325,0.000003805648,0.000009100086,9.990637e-7,0.000004926195,0.00001393446,0.0004920478],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009567054,"threshold_uncertainty_score":0.7900217,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08364782340438444,"score_gpt":0.2210497515119239,"score_spread":0.1374019281075395,"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."}}