{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002862376,0.001063478,0.002327611,0.008066519,0.004262153,0.005305716,0.002924249,0.003281434,0.01144176],"category_scores_gemma":[0.01615295,0.001025893,0.00140879,0.00622369,0.01068226,0.01831427,0.004738429,0.00629209,0.001258822],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004170941,"about_ca_system_score_gemma":0.001378035,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00534094,"about_ca_topic_score_gemma":0.00354969,"domain_scores_codex":[0.9979595,0.0008134499,0.00007886967,0.0004395628,0.0004516723,0.0002568777],"domain_scores_gemma":[0.9911823,0.006209638,0.0006558205,0.0004036634,0.0006745118,0.0008740468],"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":[0.000008821564,0.000005705306,0.00006065543,0.00001185734,0.000001570239,0.000008227489,0.00007336718,0.0003091373,0.00003379365,0.9975141,0.0007386638,0.001234206],"study_design_scores_gemma":[0.000003926698,0.000003217449,0.00007953172,0.0000102233,0.000002849512,0.00002188293,0.00003209749,0.002013681,0.00005035069,0.9961085,0.001665441,0.00000837135],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.3060234,0.01078793,0.2490888,0.02827224,0.002439001,0.0001018966,0.0008867584,0.0004544463,0.4019454],"genre_scores_gemma":[0.9057261,0.004862281,0.02873017,0.002383107,0.003330013,0.0002083357,0.0004246208,0.0002892138,0.05404617],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01144176,"threshold_uncertainty_score":0.03827655,"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."}}