{"id":"W2980664267","doi":"10.1134/s0081543819030192","title":"The Volume Polynomial of Regular Semisimple Hessenberg Varieties and the Gelfand—Zetlin Polytope","year":2019,"lang":"en","type":"article","venue":"Proceedings of the Steklov Institute of Mathematics","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"","keywords":"Mathematics; Monomial; Variety (cybernetics); Flag (linear algebra); Polytope; Intersection homology; Combinatorics; Pure mathematics; Cohomology; Discrete mathematics; Algebra over a field","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":[0.001951846,0.0003806287,0.001073667,0.00007435798,0.0002859685,0.00007060952,0.001550258,0.0001815367,0.00001314692],"category_scores_gemma":[0.002898092,0.0001957963,0.0003242346,0.0004420009,0.001662741,0.0002698704,0.0008329894,0.0003535596,0.000004289963],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004936667,"about_ca_system_score_gemma":0.00008960448,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002263582,"about_ca_topic_score_gemma":0.000005480337,"domain_scores_codex":[0.9969379,0.00003039203,0.001453051,0.0002690722,0.0009251599,0.0003843961],"domain_scores_gemma":[0.9951189,0.00120708,0.002164226,0.0008353082,0.0006102622,0.00006429368],"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":[0.0001548967,0.0001650689,0.0003417619,0.003059389,0.0002414312,1.563803e-7,0.004973867,0.00001218011,0.005586422,0.9837658,0.001448969,0.0002500385],"study_design_scores_gemma":[0.002629435,0.00016529,0.00005311596,0.0008196441,0.0003912862,0.00004113897,0.005890623,0.001618775,0.05367588,0.9291391,0.005262258,0.0003134059],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.987148,0.0004321804,0.0005308328,0.0009786321,0.0008724524,0.001830985,0.00002008712,0.00004665327,0.008140151],"genre_scores_gemma":[0.9672307,0.0001432943,0.02905357,0.00001885806,0.0001171615,0.00004104096,4.89688e-7,0.00007789894,0.003317035],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05462667,"threshold_uncertainty_score":0.7984343,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009989196779778425,"score_gpt":0.2349900450218934,"score_spread":0.225000848242115,"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."}}