{"arxiv_id":"hep-th/0411114","incoming":{"papers":8,"sentences":15,"groups":[{"kind":"background","label":"Cites it as background","papers":6,"sentences":7,"quotes":[{"arxiv_id":"0909.4117","title":"A Perspective on Regularization and Curvature","url":"/paper/0909.4117","section":"Introduction","sentence":"Section two of this paper reviews the development of the tools necessary for the construction of the renormalization bundle, following [ref] , [ref] , [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"0909.4122","title":"The geometric $\\beta$-function in curved space-time under operator regularization","url":"/paper/0909.4122","section":"The Hopf algebra","sentence":"The affine group scheme $G$ is developed in detail in [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1212.6905","title":"The Stable Symplectic category and a conjecture of Kontsevich","url":"/paper/1212.6905","section":"Appendix: Grothendieck-Teichmüller groups","sentence":"Remarkably enough, these multizeta values play an important role in Connes, Kreimer, and Marcolli's Galois-theoretic reinterpretation [ref] of the classical BPS renormalization theory of Feynman integrals, in which MZVs appear ubiquitously in explicit computations.","intent_p":0.89,"contests_p":null},{"arxiv_id":"0912.0723","title":"The algebra of integro-differential operators on a polynomial algebra","url":"/paper/0912.0723","section":"Introduction","sentence":"The latter appeared in the work of Baxter [ref] and further explored by Rota [ref] , Cartier [ref] , and Atkinson [ref] , and more recently by many others: Aguiar, Moreira [ref] ; Cassidy, Guo, Keigher, Sit, Ebrahimi-Fard [ref] , [ref] ; Connes, Kreimer, Marcoli [ref] , [ref] , name just a few.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1705.05227","title":"The global dimension of the algebras of polynomial integro-differential operators $\\mathbb{I}_n$ and the Jacobian algebras $\\mathbb{A}_n$","url":"/paper/1705.05227","section":"Introduction","sentence":"The latter appeared in the work of Baxter [ref] and further explored by Rota [ref] , Cartier [ref] , and Atkinson [ref] , and more recently by many others: Aguiar, Moreira [ref] ; Cassidy, Guo, Keigher, Sit, Ebrahimi-Fard [ref] , [ref] ; Connes, Kreimer, Marcoli [ref] , [ref] , Guo, Regensburger, Rosenkranz and Middeke [ref] , name just a few.","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":8},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[{"relation":"same_result","label":"States the same result","papers":[{"arxiv_id":"math/0409306","url":"/paper/math/0409306","title":"Renormalization and motivic Galois theory","main_claim":"We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain `` motivic Galois group'', which is uniquely determined and universal with respect to the set of physical theories.","p":0.8}]}],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-th/0411114"}}