{"id":"W2048425798","doi":"10.1007/s00029-007-0037-5","title":"Lattice polytopes, Hecke operators, and the Ehrhart polynomial","year":2007,"lang":"en","type":"article","venue":"Selecta Mathematica","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"Banff International Research Station for Mathematical Innovation and Discovery","keywords":"Polytope; Invertible matrix; Mathematics; Lattice (music); Combinatorics; Pure mathematics; Physics","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001094014,0.0006427382,0.0009006625,0.002411837,0.002417969,0.003718598,0.0008202748,0.00113826,0.01034605],"category_scores_gemma":[0.002494816,0.0004321202,0.0006698074,0.002167824,0.004811675,0.005399971,0.002165378,0.004215355,0.001327523],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001361285,"about_ca_system_score_gemma":0.000736856,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001729024,"about_ca_topic_score_gemma":0.001422237,"domain_scores_codex":[0.9992842,0.0001844145,0.00002658674,0.0001005803,0.0002395565,0.000164734],"domain_scores_gemma":[0.9987909,0.0004927857,0.0002074969,0.0001368598,0.0001205011,0.0002513811],"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":[0.00002132389,0.00001954778,0.00009230491,0.00001424191,0.000003534992,0.00002554678,0.00006571003,0.0005854114,0.0001446826,0.9955996,0.0009586528,0.002469431],"study_design_scores_gemma":[0.00001006168,0.000006689435,0.0001066314,0.000004642194,0.000001926989,0.000026322,0.00005362729,0.001114905,0.00008151646,0.9972113,0.001375488,0.000007039765],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5703278,0.009911679,0.1024802,0.01133251,0.001270395,0.00006358637,0.0007903251,0.0003328064,0.3034908],"genre_scores_gemma":[0.9462231,0.003409542,0.008803771,0.0005721636,0.00108491,0.00004415356,0.0003441728,0.00006426076,0.03945402],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01034605,"threshold_uncertainty_score":0.03461099,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02083208310263222,"score_gpt":0.3023789494058047,"score_spread":0.2815468663031725,"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."}}