{"id":"W4406237464","doi":"10.2139/ssrn.5092406","title":"Bounds on Kemeny's Constant of a Graph and the Nordhaus-Gaddum Problem","year":2025,"lang":"en","type":"preprint","venue":"SSRN Electronic Journal","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Manitoba; York University; University of Guelph","funders":"","keywords":"Combinatorics; Graph; Mathematics; Omega; Discrete mathematics; Constant (computer programming); Physics; Quantum mechanics; Computer science","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":["research_integrity"],"consensus_categories":[],"category_scores_codex":[0.003673708,0.0002792663,0.0005098277,0.0002070439,0.0003394979,0.00007344243,0.0005446153,0.0001808936,0.00001712896],"category_scores_gemma":[0.0001204026,0.0001827145,0.000301303,0.0002059215,0.0004507718,0.00002861156,0.0002292596,0.003652941,0.000001798458],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000187022,"about_ca_system_score_gemma":0.001895803,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002731982,"about_ca_topic_score_gemma":0.0002567776,"domain_scores_codex":[0.9975548,0.0002828717,0.0006105271,0.000277802,0.0002741758,0.0009997884],"domain_scores_gemma":[0.9980204,0.0006114593,0.0006432199,0.0005258415,0.0001479361,0.00005115968],"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":[0.0001894077,0.0001201486,0.00003631157,0.0001234576,0.0005747083,4.84289e-7,0.0003805995,0.00001283136,0.00002524074,0.996761,0.0002467349,0.00152913],"study_design_scores_gemma":[0.001169734,0.0001158089,0.00000795705,0.0003074419,0.0003155502,0.00007434694,0.0008218004,0.00002748343,0.00008406549,0.9962549,0.0006590775,0.0001618238],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7212987,0.02302139,0.05998456,0.02139229,0.001070916,0.007590463,0.0004263322,0.0003119865,0.1649033],"genre_scores_gemma":[0.9892167,0.007190229,0.0008000559,0.0001157359,0.00009581479,0.0001364817,0.000006451261,0.00002521779,0.002413313],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.267918,"threshold_uncertainty_score":0.9986457,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01498506784896096,"score_gpt":0.285046998629596,"score_spread":0.270061930780635,"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."}}