{"id":"W4405792749","doi":"10.48550/arxiv.2412.18595","title":"The basis number of 1-planar graphs","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Basis (linear algebra); Planar; Planar graph; Combinatorics; Mathematics; Computer science; Geometry; Graph; Computer graphics (images)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003207973,0.00042611,0.0005342833,0.001750273,0.0007868764,0.001631067,0.000864815,0.0006514094,0.003484715],"category_scores_gemma":[0.002783912,0.0003843807,0.0004125322,0.001130965,0.001356603,0.001776595,0.001176593,0.001097704,0.0005691843],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000901336,"about_ca_system_score_gemma":0.0004535113,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009621471,"about_ca_topic_score_gemma":0.0008417488,"domain_scores_codex":[0.9996831,0.00005847215,0.00001254105,0.00007133668,0.00008944135,0.00008500348],"domain_scores_gemma":[0.9986293,0.000730503,0.0001807641,0.0001044,0.0001549036,0.0002002453],"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":[0.000234605,0.00006385955,0.004724096,0.0002295103,0.00002872236,0.0001484443,0.0003196884,0.03636517,0.01499673,0.8949555,0.006953219,0.04098039],"study_design_scores_gemma":[0.00003754177,0.00007820893,0.004265468,0.00006850992,0.00003236612,0.0005227744,0.0002645648,0.09265883,0.008135085,0.8796397,0.01424733,0.00004957107],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8692099,0.001403318,0.08642359,0.001131112,0.00007086317,0.00005294016,0.001490296,0.0004132914,0.03980473],"genre_scores_gemma":[0.9599685,0.001300642,0.03122867,0.0001232955,0.0000661872,0.0001096533,0.001189516,0.0001230549,0.005890585],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003484715,"threshold_uncertainty_score":0.0116576,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04499730643878502,"score_gpt":0.196937371641014,"score_spread":0.1519400652022289,"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."}}