{"id":"W1992739211","doi":"10.1016/j.jctb.2003.05.001","title":"Arrangements, circular arrangements and the crossing number of C7×C","year":2003,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series B","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":33,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo; University of Prince Edward Island","funders":"","keywords":"Conjecture; Crossing number (knot theory); Cartesian product; Combinatorics; Mathematics; Generalization; Level crossing; Planar; Product (mathematics); Geometry; Mathematical analysis; Computer science; Intersection (aeronautics); Engineering","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":[0.0004349163,0.0004160625,0.0004111167,0.002293947,0.001641027,0.002905438,0.0007860474,0.001031141,0.0126569],"category_scores_gemma":[0.002729565,0.0003339537,0.0003436954,0.00206445,0.002005213,0.001740541,0.001058897,0.001288853,0.0009898536],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001013653,"about_ca_system_score_gemma":0.0005778851,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002386557,"about_ca_topic_score_gemma":0.002693486,"domain_scores_codex":[0.9995452,0.00007154689,0.00003159042,0.0001079933,0.0001250593,0.0001186191],"domain_scores_gemma":[0.9979908,0.0008595689,0.0005052429,0.0001397013,0.00020269,0.0003019355],"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":[0.0002242635,0.00007274544,0.003541562,0.00009512691,0.00001935653,0.0003037855,0.0005000245,0.01202005,0.004565369,0.9349685,0.005422743,0.03826652],"study_design_scores_gemma":[0.00004548682,0.0000886824,0.004367062,0.00005467171,0.00003600816,0.0006457497,0.0005871748,0.03277529,0.004575636,0.9395161,0.01724764,0.00006035698],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.88538,0.0007220593,0.03426417,0.0006475366,0.0002284521,0.00005535653,0.0003876723,0.0002093839,0.0781054],"genre_scores_gemma":[0.9746135,0.0003420383,0.01371913,0.0001402961,0.00007573478,0.00004405193,0.0003914434,0.0000880305,0.01058582],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0126569,"threshold_uncertainty_score":0.04234153,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008694649643631898,"score_gpt":0.2473199663346486,"score_spread":0.2386253166910167,"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."}}