{"id":"W2116052752","doi":"10.37236/728","title":"The Minor Crossing Number of Graphs with an Excluded Minor","year":2008,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":15,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Minor (academic); Combinatorics; Mathematics; Crossing number (knot theory); Graph; Robertson–Seymour theorem; Graph minor; Coxeter graph; Discrete mathematics; 1-planar graph; Line graph; Graph power; Voltage graph","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":[0.001873203,0.0001661,0.0002680676,0.0001021422,0.000932769,0.0001313146,0.002558954,0.00004597227,0.000003309771],"category_scores_gemma":[0.00009100868,0.0000852954,0.0001305525,0.00110788,0.0007524176,0.0006134391,0.0001356812,0.0008272518,0.000002971557],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001387182,"about_ca_system_score_gemma":0.001000207,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007305012,"about_ca_topic_score_gemma":0.000005937176,"domain_scores_codex":[0.9973512,0.0003681305,0.0004396893,0.0001609264,0.0009220397,0.0007580591],"domain_scores_gemma":[0.9973717,0.0005699483,0.0005539308,0.0007634292,0.0006207919,0.0001201745],"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":[0.0002454982,0.0001644689,0.001955771,0.000005511815,0.00008805962,0.00003334324,0.001022985,0.00006140281,0.0005990625,0.9941183,0.00007593323,0.001629717],"study_design_scores_gemma":[0.001129823,0.001368079,0.001163483,0.00002257778,0.0000190299,0.002249829,0.0001275988,0.0004553353,0.007279606,0.9846528,0.001379971,0.0001518607],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9284553,0.00220836,0.06807878,0.0004252068,0.0001974398,0.0001366208,2.963869e-7,0.00001934391,0.0004786854],"genre_scores_gemma":[0.9987409,0.0003442375,0.0004911941,0.00003883922,0.00003395811,0.000002788086,8.921234e-8,0.00001718861,0.0003308439],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0702856,"threshold_uncertainty_score":0.7174199,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01664414367976009,"score_gpt":0.2882565633769669,"score_spread":0.2716124196972068,"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."}}