{"id":"W4403987219","doi":"10.1016/j.laa.2024.10.026","title":"On the Colin de Verdière graph number and penny graphs","year":2024,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Windsor","funders":"","keywords":"Mathematics; Combinatorics; Graph; Discrete mathematics","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":[0.0002092253,0.0001201219,0.0001056012,0.00004652987,0.0003956753,0.00006956075,0.0001212798,0.00007611732,0.0001363629],"category_scores_gemma":[0.00005684743,0.00007562839,0.00005500135,0.0002253128,0.0001097331,0.00004174398,0.00006392798,0.0002039689,0.00002718767],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000588622,"about_ca_system_score_gemma":0.0000146937,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002626164,"about_ca_topic_score_gemma":0.000003129486,"domain_scores_codex":[0.9993615,0.00003818839,0.0001370126,0.0002151306,0.00009695418,0.0001512154],"domain_scores_gemma":[0.9988516,0.0007837119,0.00002503705,0.0002436308,0.00002632828,0.00006970198],"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":[0.000004323068,0.00001683596,0.0000612099,0.00005681053,0.00003825116,9.610394e-7,0.0005503055,3.386652e-7,0.0001061114,0.9944763,0.003398072,0.001290521],"study_design_scores_gemma":[0.00007501725,0.00001486386,0.0003449768,0.00002617181,0.00005153901,0.00002452782,0.0001010116,0.000702747,0.0002935278,0.9753929,0.02287126,0.0001013988],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9820817,0.001482815,0.002404036,0.001918255,0.00009191905,0.0006758564,0.00006930815,0.0001727912,0.01110333],"genre_scores_gemma":[0.997192,0.0004567445,0.0008547094,0.0005053536,0.0001139791,0.0001753757,0.000004976604,0.00002421582,0.0006726591],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01947319,"threshold_uncertainty_score":0.3084036,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01828331707014549,"score_gpt":0.2965910570100491,"score_spread":0.2783077399399036,"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."}}