{"id":"W4402679330","doi":"10.1007/s11083-024-09685-7","title":"Partition Rank and Partition Lattices","year":2024,"lang":"en","type":"article","venue":"Order","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"","keywords":"Mathematics; Partition (number theory); Combinatorics; Rank (graph theory); Discrete mathematics; Algebra over a field; Pure 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":[],"consensus_categories":[],"category_scores_codex":[0.00007282123,0.00004384777,0.00004082654,0.00002609111,0.00002212632,0.00004952639,0.00001400099,0.00002846923,0.0001870556],"category_scores_gemma":[0.000002777008,0.0000392821,0.00001186401,0.00008821505,0.00001190224,0.0001147889,0.000002875699,0.00004062304,0.0001960615],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000003839829,"about_ca_system_score_gemma":0.000001563133,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001700208,"about_ca_topic_score_gemma":0.000005049666,"domain_scores_codex":[0.9997669,0.00001104656,0.00005611004,0.00006139541,0.00003410528,0.0000704448],"domain_scores_gemma":[0.9999085,0.00001646367,0.000002617834,0.00004656183,0.000005875552,0.00001997789],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0000438381,0.00007489345,0.004851047,0.00485372,0.0005602665,0.0001304605,0.00795175,0.01089151,0.08338305,0.6676922,0.06138786,0.1581794],"study_design_scores_gemma":[0.0004818797,0.0000680061,0.00513793,0.0005226273,0.0001067435,0.00006185789,0.0004373431,0.1598978,0.009297197,0.06142268,0.7619794,0.0005864913],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9681906,0.00503638,0.004167743,0.0001652318,0.0009173622,0.00008673107,0.00000613052,0.0006020023,0.0208278],"genre_scores_gemma":[0.9994648,0.00008284926,0.00003595062,0.00001478018,0.00007931307,0.00001572935,0.000005159717,0.000009724101,0.000291682],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.7005916,"threshold_uncertainty_score":0.2520039,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.006325592644393327,"score_gpt":0.2001727517342348,"score_spread":0.1938471590898414,"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."}}