{"arxiv_id":"1007.0213","incoming":{"papers":4,"sentences":4,"groups":[{"kind":"background","label":"Cites it as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1211.5048","title":"Tree-Loop Duality Relation beyond simple poles","url":"/paper/1211.5048","section":"Duality relation at one– and two–loops","sentence":"The extension of the Duality Theorem to two loops has been discussed in detail in [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"1007.3224","title":"Loops and trees","url":"/paper/1007.3224","section":"Summary and outlook","sentence":"Note: While this paper was being completed, works [ref] appeared in which $iϵ$ prescriptions are discussed in the context of cutting open higher-loop graphs.","intent_p":0.88,"contests_p":null}]}],"unlabelled_sentences":2},"outgoing":{"papers":4,"sentences":10,"groups":[{"kind":"extends","label":"Builds on","papers":1,"sentences":2,"quotes":[{"arxiv_id":"0804.3170","title":"From loops to trees by-passing Feynman's theorem","url":"/paper/0804.3170","section":"INTRODUCTION","sentence":"In this talk, the extension of the loop–tree duality theorem derived in Ref. [ref] to higher loop orders is described, with the aim of extending the duality method to the computation of cross sections at NNLO or even higher orders.","intent_p":1.0,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":2,"sentences":2,"quotes":[{"arxiv_id":"0804.3170","title":"From loops to trees by-passing Feynman's theorem","url":"/paper/0804.3170","section":"THE DUAL PROPAGATOR $G_D$","sentence":"The question of the occurrence of real and complex masses in the propagators and their effect on the derivation of the duality theorem, has been discussed in [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"1003.1241","title":"The SM and NLO multileg working group: Summary report","url":"/paper/1003.1241","section":"INTRODUCTION","sentence":"In recent years, important efforts have been devoted to developing efficient methods for the calculation of multi–leg and multi–loop diagrams, realized, e.g., by unitarity–based methods or by traditional Feynman diagram approaches, [ref] .","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":6},"claims":[{"relation":"same_result","label":"States the same result","papers":[{"arxiv_id":"1007.0194","url":"/paper/1007.0194","title":"A Tree-Loop Duality Relation at Two Loops and Beyond","main_claim":"The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops.","p":0.92}]}],"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/1007.0213"}}