{"arxiv_id":"1604.06016","incoming":{"papers":3,"sentences":50,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1712.01125","title":"The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity","url":"/paper/1712.01125","section":"The nonlocal wave equation","sentence":"Following the usual procedure [ref] , presented in [ref] , we obtain the Green function in momentum space, [equation] It should be noticed that the first of these two contributions will eventually give rise to the usual Green function [ref] .","intent_p":0.86,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1607.04123","title":"Degravitation, Orbital Dynamics and the Effective Barycentre","url":"/paper/1607.04123","section":"The effective Newtonian potential:","sentence":"It should be mentioned that in [ref] we reduced the modified retarded 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nonlocally modified Einstein equations:","sentence":"In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"gr-qc/9404061","title":"The basis of nonlocal curvature invariants in quantum gravity theory","url":"/paper/gr-qc/9404061","section":"The nonlocally modified Einstein equations:","sentence":"In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"hep-th/0304229","title":"Nonlocal action for long-distance modifications of gravity theory","url":"/paper/hep-th/0304229","section":"The nonlocally modified Einstein equations:","sentence":"In order to obtain the leading term of $S_NL$, the equation above can be functionally integrated with the aid of the covariant curvature expansion technique presented in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1107.2403","title":"Super-renormalizable Quantum Gravity","url":"/paper/1107.2403","section":"The nonlocally modified Einstein equations:","sentence":"The essence of this technique consists in the possibility to convert noncovariant series in powers of gravitational potentials $h_μν$ into series of spacetime curvature and its derivatives with the covariant nonlocal coefficients [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"0709.4682","title":"Gravitational waves","url":"/paper/0709.4682","section":"The nonlocally modified wave equation:","sentence":"Following the usual procedure [ref] we obtain the Green function in momentum space, [equation] In the remaining part of this article we will retain only the first two leading terms.","intent_p":0.9,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values 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nonlocally modified wave equation:","sentence":"Experimental results [ref] from deviation measurements of the Newtonian law at small length scales ($∼25 μm$) suggest that the dimensionless correction constant needs to be of the order $σ≲10^-4$.","intent_p":0.81,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"gr-qc/0007087","title":"Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations","url":"/paper/gr-qc/0007087","section":"The effective total mass:","sentence":"However they can be discarded as they will cancel out with their wave zone counterparts as was shown in [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"hep-th/0304229","title":"Nonlocal action for long-distance modifications of gravity theory","url":"/paper/hep-th/0304229","section":"Conclusion:","sentence":"Although the nonlocal equations of motion are themselves generally covariant, they cannot (for nontrivial $G_Λ(_g)$) be presented as a metric variational derivative of a diffeomorphism invariant action unless you assume that they are only a first, linear in the curvature, approximation for the complete equations of motion [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"hep-th/0501093","title":"On covariant long-distance modifications of Einstein theory and strong coupling problem","url":"/paper/hep-th/0501093","section":"Conclusion:","sentence":"Although the nonlocal equations of motion are themselves generally covariant, they cannot (for nontrivial $G_Λ(_g)$) be presented as a metric variational derivative of a diffeomorphism invariant action unless you assume that they are only a first, linear in the curvature, approximation for the complete equations of motion [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":35,"sentences":35,"quotes":[{"arxiv_id":"hep-th/0703027","title":"Degravitation of the Cosmological Constant and Graviton Width","url":"/paper/hep-th/0703027","section":"Conclusion:","sentence":"The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-th/0209227","title":"Non-Local Modification of Gravity and the Cosmological Constant Problem","url":"/paper/hep-th/0209227","section":"Conclusion:","sentence":"The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-th/0501093","title":"On covariant long-distance modifications of Einstein theory and strong coupling problem","url":"/paper/hep-th/0501093","section":"Conclusion:","sentence":"The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-th/0304229","title":"Nonlocal action for long-distance modifications of gravity theory","url":"/paper/hep-th/0304229","section":"Conclusion:","sentence":"The general idea of a differential coupling was apparently formulated for the first time in [ref] in order to address the cosmological constant problem [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"1107.2403","title":"Super-renormalizable Quantum Gravity","url":"/paper/1107.2403","section":"The nonlocally modified Einstein equations:","sentence":"The parameter $κ$, although named differently, was encountered in the context of various nonlocal modified theories of gravity which originate from the pursuit of constructing a UV-complete theory of quantum gravity or coming from models of noncommutative geometry [ref] .","intent_p":0.95,"contests_p":null}]}],"unlabelled_sentences":125},"claims":[],"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/1604.06016"}}