{"id":"W2047598990","doi":"10.1007/s11856-008-1066-2","title":"The T(4) property of families of unit disks","year":2008,"lang":"en","type":"article","venue":"Israel Journal of Mathematics","topic":"Point processes and geometric inequalities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Calgary","funders":"","keywords":"Mathematics; Property (philosophy); Unit (ring theory); Combinatorics; Algebra over a field; Pure mathematics; Mathematics education","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":[0.001347559,0.0001473338,0.0005869998,0.0001989149,0.0001163612,0.00001305951,0.0005036388,0.00006484664,0.00001638039],"category_scores_gemma":[0.00303991,0.00006780375,0.0002209717,0.0004160579,0.000289696,0.0001141121,0.00007322147,0.0002004585,0.000002452125],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001560478,"about_ca_system_score_gemma":0.000164283,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001753155,"about_ca_topic_score_gemma":0.000008483405,"domain_scores_codex":[0.9975859,0.00006146969,0.001406764,0.00005834318,0.0006945456,0.0001929771],"domain_scores_gemma":[0.9951503,0.001888494,0.001661288,0.0003172085,0.0009280044,0.00005469919],"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":[0.0003686627,0.004568945,0.006674172,0.01314509,0.001804455,0.0001367488,0.06181115,0.0001138012,0.004110217,0.8740337,0.01263407,0.02059903],"study_design_scores_gemma":[0.002602509,0.001713224,0.0008326219,0.00227407,0.0005467014,0.002177928,0.08290689,0.0007853585,0.05824449,0.8343626,0.01293265,0.0006210085],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9847504,0.001169064,0.00801618,0.0002212442,0.0001549448,0.0001496271,0.00001439955,0.00001074019,0.005513427],"genre_scores_gemma":[0.9692419,0.001744023,0.02645735,0.00001853981,0.00009292059,0.000002194875,3.033078e-7,0.00002737437,0.002415415],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05413428,"threshold_uncertainty_score":0.3639276,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1344737302200744,"score_gpt":0.3288914076539466,"score_spread":0.1944176774338723,"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."}}