{"id":"W3013138006","doi":"10.1093/imrn/rnaa251","title":"Asymptotic Bounds on Graphical Partitions and Partition Comparability","year":2020,"lang":"en","type":"preprint","venue":"International Mathematics Research Notices","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Mathematics; Partition (number theory); Combinatorics; Upper and lower bounds; Comparability; Frequency partition of a graph; Discrete mathematics; Joint probability distribution; Graph; Statistics; Line graph; Graph power","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":["metaresearch","metaepi_narrow","research_integrity"],"consensus_categories":[],"category_scores_codex":[0.002436373,0.0005575186,0.0009070773,0.000523924,0.0003694836,0.0007200003,0.001318955,0.0004479612,0.0002371592],"category_scores_gemma":[0.0114239,0.0005255577,0.0002575895,0.0003486034,0.0007864152,0.0002431218,0.001851597,0.002547269,0.0002163093],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003821135,"about_ca_system_score_gemma":0.0002028189,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0000147408,"about_ca_topic_score_gemma":0.00002767732,"domain_scores_codex":[0.993759,0.000497164,0.001257715,0.001021945,0.002802578,0.0006616436],"domain_scores_gemma":[0.9891966,0.007623869,0.0005856323,0.001115718,0.001061611,0.0004165652],"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":[0.00006900498,0.001506248,0.0000938634,0.00210416,0.0003035749,0.00003281456,0.001481812,0.0002507251,0.0001095023,0.9908465,0.003022816,0.0001790457],"study_design_scores_gemma":[0.0004773668,0.000212957,0.0001575935,0.001342668,0.00008607794,0.000008834214,0.0003765146,0.02829495,0.0004048812,0.9673101,0.000896924,0.0004311206],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8942222,0.0002361462,0.02481698,0.02442376,0.004294613,0.004606587,0.0006128842,0.001061062,0.0457258],"genre_scores_gemma":[0.950012,0.0001159768,0.04828023,0.00008710191,0.0006429793,0.0004886214,0.00008085636,0.0001107226,0.0001815411],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05578979,"threshold_uncertainty_score":0.9997539,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.3874518741101598,"score_gpt":0.5102915029724255,"score_spread":0.1228396288622657,"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."}}