{"id":"W2950318982","doi":"10.37236/1020","title":"On Directed Triangles in Digraphs","year":2007,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":25,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"Purdue University; American Institute of Mathematics; National Science Foundation","keywords":"Combinatorics; Digraph; Mathematics; Conjecture; Vertex (graph theory); Directed graph; Discrete mathematics; Graph","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":[0.003518399,0.0001429744,0.0002943361,0.0002836087,0.0001274303,0.0000153829,0.0004848714,0.00008447139,0.00001130903],"category_scores_gemma":[0.0007420416,0.000083431,0.0001643344,0.0005857075,0.00006639655,0.00005991996,0.00003198359,0.0009353145,8.967439e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002089086,"about_ca_system_score_gemma":0.00009821714,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001880454,"about_ca_topic_score_gemma":0.00001801125,"domain_scores_codex":[0.9982908,0.0001682304,0.0005383029,0.00008088234,0.0004045538,0.0005172669],"domain_scores_gemma":[0.9973446,0.001876249,0.0003860439,0.0002535536,0.00008512395,0.00005444914],"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":[0.0002999551,0.0001420213,0.000288939,0.000005746329,0.00006015347,0.0000213308,0.0006020244,0.000003900996,0.00003272755,0.997085,0.0004399441,0.001018261],"study_design_scores_gemma":[0.001230168,0.0004787832,0.00108576,0.00003549997,0.00003381324,0.00008131108,0.0001381027,0.000008688366,0.0008055627,0.994861,0.001144073,0.00009724327],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9923702,0.001532659,0.001298462,0.0001821118,0.0005875789,0.0001178223,3.108537e-7,0.00002363973,0.003887249],"genre_scores_gemma":[0.999397,0.0002505922,0.00002544761,0.00007369031,0.00007877083,6.772296e-7,1.373849e-7,0.00001984839,0.0001537775],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007026892,"threshold_uncertainty_score":0.4063528,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01333259802547749,"score_gpt":0.2875840749563781,"score_spread":0.2742514769309006,"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."}}