{"id":"W2896532202","doi":"10.1007/s11590-018-1338-7","title":"Distance between vertices of lattice polytopes","year":2018,"lang":"en","type":"article","venue":"Optimization Letters","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Agence Nationale de la Recherche","keywords":"Combinatorics; Polytope; Mathematics; Convex hull; Convex polytope; Minkowski addition; Conjecture; Lattice (music); Uniform k 21 polytope; Hexagonal lattice; Birkhoff polytope; Regular polygon; Discrete mathematics; Convex set; Geometry; Physics; Condensed matter physics","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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001229123,0.0001175693,0.0002200138,0.00005583208,0.00007133606,0.00001933325,0.000204268,0.00004555674,0.0003713046],"category_scores_gemma":[0.0006579724,0.0001132709,0.00003998934,0.0002454888,0.0001472278,0.0002150484,0.00004525971,0.00005897527,0.00002005204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003277132,"about_ca_system_score_gemma":0.00001240449,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002119427,"about_ca_topic_score_gemma":9.814561e-7,"domain_scores_codex":[0.9990795,0.00004156891,0.0003344421,0.000155004,0.0002264364,0.0001630726],"domain_scores_gemma":[0.9986882,0.0005434834,0.000271573,0.0003227278,0.0001305826,0.00004341374],"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":[0.0001926862,0.0006544107,0.005625139,0.001424558,0.0005484485,0.00001145981,0.007799269,0.0349788,0.004638738,0.8719852,0.06710029,0.005040993],"study_design_scores_gemma":[0.006235384,0.0009671494,0.0007126995,0.001782278,0.001138549,0.00001127659,0.0009179477,0.1497344,0.08516363,0.69821,0.05194081,0.003185914],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02010863,0.000009122771,0.9756837,0.0007569596,0.0002272529,0.0001741609,0.00002554814,0.0000975579,0.002917054],"genre_scores_gemma":[0.3412986,0.000003711516,0.657823,0.0002811796,0.0003231294,0.00001239176,0.00001646746,0.0000439875,0.0001975474],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.32119,"threshold_uncertainty_score":0.4619055,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03318227745011725,"score_gpt":0.3105982867352557,"score_spread":0.2774160092851384,"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."}}