{"id":"W2111430057","doi":"10.1007/s00493-005-0036-0","title":"Proof Of A Conjecture Of Erdős On Triangles In Set-Systems","year":2005,"lang":"en","type":"article","venue":"COMBINATORICA","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":50,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo","funders":"Microsoft Research","keywords":"Conjecture; Combinatorics; Mathematics; Element (criminal law); Set (abstract data type); Discrete mathematics; Law; Computer science","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":[0.003329375,0.001531273,0.001900136,0.002435835,0.002660302,0.003309425,0.002747214,0.002550409,0.0230542],"category_scores_gemma":[0.02059796,0.001097867,0.00245074,0.002902657,0.007717445,0.01308814,0.009108966,0.009691969,0.002113797],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0026294,"about_ca_system_score_gemma":0.001168024,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002807269,"about_ca_topic_score_gemma":0.00202063,"domain_scores_codex":[0.9978698,0.0006262427,0.0001139674,0.0004690431,0.0006603959,0.0002604947],"domain_scores_gemma":[0.9811227,0.01378474,0.0006755914,0.001775031,0.001587799,0.001054165],"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":[0.00009737437,0.00007260955,0.000479549,0.0002191325,0.00003218989,0.0001931946,0.0005609462,0.001648079,0.0007474397,0.9751769,0.01353962,0.007232985],"study_design_scores_gemma":[0.00005073967,0.0000243016,0.0002622909,0.00004092493,0.00002390253,0.0001138478,0.0001132366,0.003862711,0.0003141522,0.9859096,0.009267585,0.00001670667],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.187564,0.005468882,0.3854342,0.1121085,0.006840286,0.0003042507,0.002471302,0.001971391,0.2978372],"genre_scores_gemma":[0.8567197,0.003516896,0.0924035,0.00831488,0.003903299,0.0003963872,0.001514339,0.0005958978,0.03263514],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.0230542,"threshold_uncertainty_score":0.07712394,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03945362164017345,"score_gpt":0.3051523326153394,"score_spread":0.2656987109751659,"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."}}