{"id":"W2083140175","doi":"10.1007/s00026-005-0248-4","title":"Collinear Points in Permutations","year":2005,"lang":"en","type":"article","venue":"Annals of Combinatorics","topic":"Coding theory and cryptography","field":"Computer Science","cited_by":11,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Combinatorics; Mathematics; Conjecture; Transversal (combinatorics); Prime (order theory); Upper and lower bounds; Intersection (aeronautics); Discrete geometry; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003737885,0.00006395338,0.000108872,0.0001874677,0.00004109373,0.00002527751,0.0004463776,0.00003444271,0.00001030844],"category_scores_gemma":[0.00005632179,0.00006765362,0.0000605839,0.0008693828,0.00002963618,0.0002811403,0.00007255696,0.00008873252,0.00002201989],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006321331,"about_ca_system_score_gemma":0.00003507138,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005157368,"about_ca_topic_score_gemma":0.000004208348,"domain_scores_codex":[0.9993182,0.00005355109,0.0001896708,0.0001301916,0.0001558989,0.0001524738],"domain_scores_gemma":[0.9993878,0.0001072406,0.00006090874,0.0002757414,0.0001214677,0.00004681143],"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":[0.00000321821,0.0001770769,0.001454175,0.000004543153,0.000004308793,0.000002233867,0.0005167832,0.00009839878,0.000031847,0.9929337,0.0007451606,0.004028573],"study_design_scores_gemma":[0.0003816481,0.000135105,0.006822098,0.00002333973,0.000001943618,0.000002932486,0.0000298758,0.00906107,0.006639078,0.9568563,0.01989794,0.0001487412],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.901154,0.0006153995,0.07049071,0.01285158,0.0003790148,0.0001737536,0.000004144579,0.0001389778,0.01419236],"genre_scores_gemma":[0.9976654,0.00005727579,0.00172831,0.0004518188,0.00001354241,0.000004068643,7.168175e-7,0.000003488738,0.00007539421],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09651133,"threshold_uncertainty_score":0.2758835,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03988005282922381,"score_gpt":0.3060809598074195,"score_spread":0.2662009069781957,"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."}}