{"id":"W2145758416","doi":"10.48550/arxiv.0904.3350","title":"Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory","year":2009,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":53,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Semigroup; Pure mathematics; Intersection theory; Mixed volume; Polytope; Convex geometry; Regular polygon; Convex analysis; Mathematical analysis; Discrete mathematics; Convex optimization; Geometry","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":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0003643114,0.0003187699,0.0003898328,0.0003608763,0.0001072869,0.00009478081,0.000942937,0.0002359448,0.00001177882],"category_scores_gemma":[0.00004325245,0.0003415362,0.0001957475,0.000320995,0.0001713471,0.0004350171,0.001214544,0.0005138655,0.00001012257],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001655359,"about_ca_system_score_gemma":0.0001326449,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002916625,"about_ca_topic_score_gemma":0.00008028698,"domain_scores_codex":[0.9982519,0.0002415161,0.0002804068,0.0008589387,0.00009350367,0.0002737729],"domain_scores_gemma":[0.998648,0.0001477038,0.0003447548,0.0006118648,0.0001083774,0.0001392518],"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":[0.0001083511,0.0001194042,0.0007724421,0.00009087288,0.0001294575,0.00006645096,0.001404981,0.003171167,0.0002109609,0.9763612,0.0005019188,0.01706285],"study_design_scores_gemma":[0.0006221368,0.0001754277,0.005855398,0.0002138965,0.00007226669,0.00001918698,0.0002015957,0.1042905,0.0008772931,0.8870468,0.0001662317,0.0004592718],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5744185,0.0001459672,0.4236923,0.0001813674,0.0005305405,0.0001734101,0.000005536574,0.0001616157,0.0006908152],"genre_scores_gemma":[0.9978172,0.0001370475,0.001247733,0.0001353974,0.00008208701,4.845614e-7,0.00001689716,0.00001090931,0.0005522467],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4233987,"threshold_uncertainty_score":0.9999037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03335046347352386,"score_gpt":0.1772982498522702,"score_spread":0.1439477863787463,"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."}}