{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001084073,0.0005038355,0.0006003575,0.002657227,0.001297587,0.002832924,0.001015029,0.0006782787,0.004205727],"category_scores_gemma":[0.002679135,0.0003071776,0.0005313258,0.001539108,0.002255144,0.004766766,0.001309121,0.001895751,0.0006759746],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00104306,"about_ca_system_score_gemma":0.0007722839,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005255332,"about_ca_topic_score_gemma":0.0004060099,"domain_scores_codex":[0.9994086,0.0001335357,0.00003521884,0.000113058,0.0002099058,0.00009966862],"domain_scores_gemma":[0.9994614,0.0001800348,0.00009414864,0.00007238184,0.0001219806,0.00007005701],"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":[0.000006188647,0.000006611458,0.0001033757,0.000009990023,0.000002700162,0.00002331854,0.00006173312,0.001433696,0.0005833668,0.9923637,0.000182826,0.005222516],"study_design_scores_gemma":[0.000003057399,0.00001171397,0.0002251785,0.00001313808,0.000003832783,0.00007044153,0.00005955124,0.03654303,0.001583872,0.9586073,0.002864726,0.00001420952],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.251058,0.000681078,0.7074019,0.0003039674,0.0001277275,0.00006241447,0.0001754647,0.000356647,0.03983277],"genre_scores_gemma":[0.798181,0.0006637038,0.1874305,0.00008689317,0.0001614298,0.0001519298,0.0002926903,0.0002922775,0.01273955],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004205727,"threshold_uncertainty_score":0.01406956,"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."}}