{"id":"W4400369766","doi":"10.1017/fms.2025.10068","title":"Schubert polynomial expansions revisited","year":2025,"lang":"en","type":"article","venue":"Forum of Mathematics Sigma","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Canada Research Chairs; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Mathematics; Polynomial; Pure mathematics; Algebra over a field; Mathematical analysis","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004783483,0.0003465645,0.0002868965,0.001635236,0.0006302737,0.001053821,0.0006394269,0.0004628354,0.005713806],"category_scores_gemma":[0.001382063,0.0001968003,0.0003259267,0.0007409758,0.001720594,0.002389727,0.0008858277,0.001449346,0.0007913528],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0006607985,"about_ca_system_score_gemma":0.0003818317,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005683809,"about_ca_topic_score_gemma":0.000833357,"domain_scores_codex":[0.9996025,0.00006638053,0.00001081875,0.0000526887,0.0001940257,0.0000736174],"domain_scores_gemma":[0.99971,0.00008844614,0.0000348084,0.00003524263,0.00009198347,0.00003945068],"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":[0.00001214706,0.000007412555,0.00009579947,0.00001847962,0.00000152475,0.00009108877,0.0001162799,0.0007334445,0.002433025,0.9905319,0.0004490316,0.005509913],"study_design_scores_gemma":[0.00001155877,0.00005231789,0.0006270668,0.00004419887,0.000007523189,0.0004998914,0.0002919107,0.02284672,0.006686783,0.9566517,0.01225452,0.00002576225],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5623578,0.001041871,0.2612004,0.001068956,0.000423392,0.00006965163,0.0001993452,0.000446117,0.1731923],"genre_scores_gemma":[0.9609483,0.0004181607,0.0219923,0.0001900973,0.0001515921,0.00003439074,0.00007374326,0.00009629756,0.01609508],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005713806,"threshold_uncertainty_score":0.01911461,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02213328872049042,"score_gpt":0.3196829180950763,"score_spread":0.2975496293745859,"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."}}