{"id":"W2954735736","doi":"10.1103/physrevlett.123.201602","title":"Vector Space of Feynman Integrals and Multivariate Intersection Numbers","year":2019,"lang":"en","type":"article","venue":"Physical Review Letters","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":156,"is_retracted":false,"has_abstract":true,"ca_institutions":"Perimeter Institute; University of Waterloo","funders":"Horizon 2020 Framework Programme; European Commission; Ontario Ministry of Economic Development and Innovation; Government of Canada; Mainz Institute for Theoretical Physics, Johannes Gutenberg University Mainz; Ministero dello Sviluppo Economico; Institut Périmètre de physique théorique; Innovation, Science and Economic Development Canada","keywords":"Feynman integral; Scalar (mathematics); Feynman diagram; Intersection (aeronautics); Path integral formulation; Volume integral; Slater integrals; Mathematics; Functional integration; Vector space; Order of integration (calculus); Pure mathematics; Algebra over a field; Mathematical physics; Applied mathematics; Integral equation; Mathematical analysis; Physics; Quantum mechanics; Quantum","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":[0.0001078701,0.0001005447,0.0002495808,0.00002935495,0.00001700251,0.00002296152,0.0002013375,0.000005887572,0.000006453103],"category_scores_gemma":[0.00002700428,0.00007996088,0.00008828928,0.0001875948,0.00003000347,0.0002568337,0.0001126166,0.0000900873,0.00006480114],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000234773,"about_ca_system_score_gemma":0.000009219793,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00008348214,"about_ca_topic_score_gemma":0.000001356648,"domain_scores_codex":[0.9993042,0.00006659343,0.0001507667,0.00023216,0.0001250982,0.0001212278],"domain_scores_gemma":[0.9995164,0.0001041607,0.0001104133,0.0001996983,0.00002015572,0.0000491175],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"bench_or_experimental","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.00003782515,0.0003552693,0.00164921,0.003873894,0.0001827654,0.000008570975,0.003936221,0.0002849073,0.3789116,0.3453036,0.006835876,0.2586202],"study_design_scores_gemma":[0.005564979,0.001800746,0.1549705,0.02352982,0.0003894714,0.00009813692,0.0001451183,0.6747409,0.07082448,0.03299962,0.03110949,0.003826794],"study_design_candidate":"simulation_or_modeling","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9834076,0.0004210833,0.009015265,0.006462781,0.0002484079,0.0002276304,7.187451e-7,0.00004169139,0.0001748793],"genre_scores_gemma":[0.9960139,0.000109551,0.001228653,0.002571456,0.00005041183,0.000005901338,0.000001130194,0.000004706559,0.00001431612],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.6744559,"threshold_uncertainty_score":0.326071,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01083601841252309,"score_gpt":0.2698192020306663,"score_spread":0.2589831836181432,"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."}}