{"id":"W2049622061","doi":"10.1016/j.disc.2007.08.006","title":"Small maximally disjoint union-free families","year":2007,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Disjoint sets; Disjoint union (topology); Combinatorics; 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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.001800516,0.0004062271,0.0005170708,0.0002310979,0.0003436411,0.00007430353,0.0009051026,0.0001957518,0.0001619924],"category_scores_gemma":[0.001234542,0.0003044025,0.0002798412,0.0003108523,0.0002719861,0.0001054859,0.0005896543,0.0003183711,0.00002917723],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005516352,"about_ca_system_score_gemma":0.00002643611,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001144545,"about_ca_topic_score_gemma":0.00009515085,"domain_scores_codex":[0.9976244,0.00006573355,0.0008208081,0.0003450184,0.0004980915,0.0006459235],"domain_scores_gemma":[0.9968708,0.001015816,0.0002996723,0.001501321,0.0001196429,0.000192805],"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":[0.00002066391,0.0001083576,0.0002327565,0.0003847068,0.00008848579,0.00003006009,0.005484945,0.000002297112,0.0001942277,0.9899231,0.001047818,0.002482593],"study_design_scores_gemma":[0.0005423902,0.00007091985,0.000561655,0.0001293264,0.0000967345,0.00004995782,0.003977159,0.0002209886,0.00159118,0.9897961,0.002510584,0.0004530326],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5400336,0.0001680031,0.2521156,0.0003506978,0.000711933,0.0007541628,0.00007556316,0.000576396,0.2052141],"genre_scores_gemma":[0.6017075,0.00008587816,0.395448,0.0002395194,0.0003059481,0.00001979513,0.00001774525,0.0001561897,0.002019402],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2031947,"threshold_uncertainty_score":0.9999408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03713383757873842,"score_gpt":0.2790755487881973,"score_spread":0.2419417112094589,"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."}}