{"id":"W1993463637","doi":"10.1016/j.jcta.2012.03.011","title":"Piercing quasi-rectangles—On a problem of Danzer and Rogers","year":2012,"lang":"en","type":"article","venue":"Journal of Combinatorial Theory Series A","topic":"Computational Geometry and Mesh Generation","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Rectangle; Square (algebra); Unit square; Combinatorics; Mathematics; Center (category theory); Unit (ring theory); Rotation (mathematics); Trajectory; Geometry; Physics; Crystallography","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":[0.001463149,0.00009473512,0.0002112143,0.0001548432,0.00007706736,0.00005124404,0.0002195958,0.0000452789,0.000008744591],"category_scores_gemma":[0.0001216019,0.00007782915,0.00006822048,0.0002662904,0.00004666558,0.0009690243,0.00006660903,0.000127845,0.000001186431],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003020006,"about_ca_system_score_gemma":0.00007240921,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.192689e-7,"about_ca_topic_score_gemma":1.03073e-7,"domain_scores_codex":[0.9989292,0.0001889329,0.0003473076,0.00008097784,0.0003052306,0.000148358],"domain_scores_gemma":[0.9989406,0.0002738249,0.0003579561,0.0001165492,0.0002056212,0.0001054481],"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":[0.0002266159,0.0001655122,0.0002291401,0.00001646065,0.00003675878,0.000002559967,0.001428842,0.000138303,0.002021767,0.9816101,0.0001578448,0.01396616],"study_design_scores_gemma":[0.001870102,0.002728218,0.001470663,0.0001568207,0.00004307545,0.00034504,0.0003704171,0.0003595868,0.03459876,0.9416431,0.01613834,0.0002759154],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8657414,0.001339227,0.1239016,0.0005667694,0.005826347,0.0001702401,0.000001630725,0.00002567718,0.002427149],"genre_scores_gemma":[0.9888681,0.00002780819,0.0105253,0.00005242101,0.0004577881,0.000001296485,3.565972e-7,0.000005435891,0.00006152243],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1231267,"threshold_uncertainty_score":0.3173781,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.00868938134234849,"score_gpt":0.2312529134461897,"score_spread":0.2225635321038412,"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."}}