{"id":"W4289599230","doi":"10.48550/arxiv.2207.08573","title":"Geometric vertex decomposition, Gröbner bases, and Frobenius splittings for regular nilpotent Hessenberg varieties","year":2022,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Algebra and Geometry","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Combinatorics; Nilpotent; Vertex (graph theory); Affine variety; Affine transformation; Pure mathematics; Graph","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002587018,0.000489271,0.000436965,0.002003038,0.001179328,0.001457449,0.0006670932,0.000339404,0.003290265],"category_scores_gemma":[0.000447016,0.0002058264,0.0003783217,0.0006293464,0.002163581,0.001778806,0.001121729,0.001174134,0.0003981459],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00108828,"about_ca_system_score_gemma":0.0004167477,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009245569,"about_ca_topic_score_gemma":0.0009018222,"domain_scores_codex":[0.9997974,0.00002823825,0.000006326818,0.00003918385,0.00006707067,0.00006176601],"domain_scores_gemma":[0.999803,0.0000237073,0.0000476863,0.00001578837,0.00002842902,0.00008133581],"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":[0.00002384734,0.00002987956,0.0005859378,0.00001822878,0.000004569411,0.0001012887,0.0002834716,0.003155262,0.002122428,0.9897637,0.0003064924,0.003604951],"study_design_scores_gemma":[0.0000170938,0.00005824673,0.001031193,0.00001363667,0.000006295988,0.0001276297,0.0003231185,0.0128959,0.002485337,0.9807588,0.002260878,0.00002179157],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9324781,0.0004307994,0.03685139,0.000340907,0.00004873788,0.00003160625,0.0001221115,0.00009331575,0.02960313],"genre_scores_gemma":[0.9873351,0.0002064714,0.005916091,0.00003819158,0.00007036576,0.00002202147,0.000131777,0.0000248438,0.006255161],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003290265,"threshold_uncertainty_score":0.01100701,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0751383290933223,"score_gpt":0.2348800216424551,"score_spread":0.1597416925491328,"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."}}