{"id":"W4415667466","doi":"10.55016/ojs/cdm.v20i2.76682","title":"A generalization of the Beraha–Kahane–Weiss theorem with graph polynomial applications","year":2025,"lang":"","type":"article","venue":"Contributions to Discrete Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Chromatic polynomial; Tutte polynomial; Factor theorem; Graph property; Graph; Voltage graph; Polynomial; Generalization; Cubic graph","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.00106921,0.0009817868,0.001634246,0.0005353485,0.001188033,0.0002405064,0.001970795,0.0005004293,0.00009815553],"category_scores_gemma":[0.002936974,0.0007174463,0.0006199299,0.004431779,0.0009120079,0.0002585809,0.0009308184,0.000645266,0.00005451969],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006628608,"about_ca_system_score_gemma":0.00094712,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001603644,"about_ca_topic_score_gemma":0.00004810068,"domain_scores_codex":[0.9942021,0.0003596922,0.002501094,0.0008292658,0.001064477,0.001043374],"domain_scores_gemma":[0.9905068,0.001790355,0.00165928,0.003548332,0.002167634,0.0003275629],"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":[0.00008769291,0.00115653,0.00005594774,0.001667416,0.0006067237,0.000001424374,0.002114879,0.001028247,0.001916599,0.9881303,0.00278721,0.0004470471],"study_design_scores_gemma":[0.002600993,0.0002458035,0.00004755349,0.003077634,0.00242486,0.00002604432,0.001687941,0.005156601,0.02625205,0.9494231,0.008108319,0.0009491332],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.009580701,0.0005454444,0.9692646,0.003287747,0.0008244073,0.008157125,0.001555684,0.0001987772,0.006585542],"genre_scores_gemma":[0.8684988,0.0001402598,0.1206232,0.0004028378,0.0004702258,0.002658731,0.0001021825,0.0002760072,0.00682778],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.8589181,"threshold_uncertainty_score":0.9995277,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007507840799624974,"score_gpt":0.2952647826141136,"score_spread":0.2877569418144886,"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."}}