{"id":"W4388496202","doi":"10.1002/rsa.21196","title":"Counting orientations of random graphs with no directed <i>k</i>‐cycles","year":2023,"lang":"en","type":"article","venue":"Random Structures and Algorithms","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Trinity College","funders":"Conselho Nacional de Desenvolvimento Científico e Tecnológico; Fundação de Amparo à Pesquisa do Estado de São Paulo","keywords":"Combinatorics; Conjecture; Mathematics; Binomial (polynomial); Random graph; Graph; Directed graph; Discrete mathematics; Statistics","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":[0.0003972671,0.0002641362,0.0005788284,0.0002100738,0.0004513481,0.00005091832,0.0001667254,0.0001005728,0.0000682868],"category_scores_gemma":[0.0003002829,0.0001699402,0.0001315306,0.0005580665,0.0003058352,0.0001079009,0.00008244761,0.0001741615,0.000001306571],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000006546919,"about_ca_system_score_gemma":0.00002420545,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000393527,"about_ca_topic_score_gemma":0.00001274903,"domain_scores_codex":[0.9984565,0.0001101399,0.0004195157,0.0003147486,0.0003739601,0.0003251646],"domain_scores_gemma":[0.9980704,0.001128265,0.0002378844,0.0002830173,0.0001906977,0.00008977909],"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":[0.006535155,0.0001340605,0.01997079,0.001577411,0.002051623,0.0001154675,0.01350989,0.0003167667,0.005003652,0.9070895,0.007542238,0.03615349],"study_design_scores_gemma":[0.02172205,0.0001571768,0.01602997,0.0001558857,0.0003219719,0.00007090768,0.0009331286,0.002970134,0.002501982,0.9532993,0.001263808,0.0005736707],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9950456,0.0002990807,0.001338517,0.00004103146,0.0005003815,0.0005343116,0.0001206611,0.0003399823,0.001780458],"genre_scores_gemma":[0.9845671,0.000311311,0.01455563,0.00004591564,0.0001631763,0.00003186515,0.00003841482,0.00004969203,0.0002369022],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.04620985,"threshold_uncertainty_score":0.692996,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01572696611512897,"score_gpt":0.2756589153752371,"score_spread":0.2599319492601081,"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."}}