{"id":"W4416943509","doi":"10.1007/s11083-025-09716-x","title":"Promotion, Tangled Labelings, and Sorting Generating Functions","year":2025,"lang":"en","type":"article","venue":"Order","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada; Combinatorics Foundation; National Security Agency; National Science Foundation","keywords":"Partially ordered set; Conjecture; Operator (biology); Generating function; Generalization; Sorting; Order (exchange); Function (biology)","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0001999824,0.0001035864,0.0001533011,0.00005311637,0.0002164294,0.0000426093,0.00005956881,0.00005779262,0.00005072438],"category_scores_gemma":[0.001898512,0.00009728593,0.00001980005,0.0002848216,0.00002499744,0.00008202888,0.00007051625,0.0001122671,0.00001232114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002834239,"about_ca_system_score_gemma":0.00003751136,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001439558,"about_ca_topic_score_gemma":0.000006271006,"domain_scores_codex":[0.999296,0.00002586627,0.0002644857,0.0001632155,0.00009662,0.000153778],"domain_scores_gemma":[0.9992954,0.0002040842,0.0001001448,0.0001981659,0.0001741247,0.00002812648],"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":[0.000003858245,0.0001855862,0.0006684951,0.0002573399,0.00005958858,0.000002142454,0.0005432638,0.00004279297,0.006254253,0.9804034,0.003029887,0.008549418],"study_design_scores_gemma":[0.0004827412,0.00002495423,0.00001795064,0.0001243724,0.00005617645,0.000004237912,0.000249098,0.005096881,0.001229502,0.990309,0.002263743,0.0001413696],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5190243,0.0002671958,0.4615828,0.001130872,0.00097882,0.0005564624,0.000002499065,0.0004203162,0.01603676],"genre_scores_gemma":[0.5156171,0.00001802886,0.4605166,0.000214211,0.0002729318,0.0001264064,0.000006089711,0.00006395212,0.02316471],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009905598,"threshold_uncertainty_score":0.3967205,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03012760556179584,"score_gpt":0.3230991935536882,"score_spread":0.2929715879918923,"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."}}