{"id":"W2984743818","doi":"10.1007/978-3-030-45771-6_26","title":"The Integrality Number of an Integer Program","year":2020,"lang":"en","type":"preprint","venue":"Lecture notes in computer science","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"Einstein Stiftung Berlin","keywords":"Unimodular matrix; Integer (computer science); Combinatorics; Mathematics; Constraint (computer-aided design); Relaxation (psychology); Matrix (chemical analysis); Integer matrix; Discrete mathematics; Computer science; Symmetric matrix; Physics; Nonnegative matrix; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002351919,0.001035891,0.001335354,0.003368707,0.00228279,0.00580155,0.002029282,0.001839177,0.01106391],"category_scores_gemma":[0.01463178,0.0009102377,0.0009809256,0.002857242,0.004791862,0.008937393,0.002647398,0.005266645,0.001061816],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003118245,"about_ca_system_score_gemma":0.001231938,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005292867,"about_ca_topic_score_gemma":0.0004115863,"domain_scores_codex":[0.9980906,0.0004165553,0.00009077634,0.0005205616,0.000466639,0.0004149246],"domain_scores_gemma":[0.9833325,0.01283818,0.001190776,0.0009005842,0.0006580616,0.001079857],"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":[0.0005987139,0.0001140693,0.002123741,0.0002196942,0.00004610644,0.0001412277,0.0003802878,0.01403969,0.005696421,0.955983,0.003862737,0.01679426],"study_design_scores_gemma":[0.00006371707,0.0000687524,0.001004652,0.00004851454,0.00005990701,0.0002502105,0.00009819835,0.04029684,0.004411153,0.949791,0.003878337,0.00002874715],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6950402,0.001073016,0.1447316,0.006820256,0.0003381187,0.00009053185,0.001142369,0.0007568084,0.1500071],"genre_scores_gemma":[0.9589421,0.0006163925,0.02660321,0.00042632,0.0003638039,0.0001551781,0.0008243184,0.000312591,0.01175618],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01106391,"threshold_uncertainty_score":0.03701246,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03321485981109076,"score_gpt":0.3266096243579263,"score_spread":0.2933947645468356,"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."}}