{"arxiv_id":"1202.2677","incoming":{"papers":2,"sentences":13,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2001.01460","title":"Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification","url":"/paper/2001.01460","section":"Introduction","sentence":"For completeness, we also generalize the linear model $f(R)=R+2κΛ_6$ previously considered in [ref] to the case of an arbitrary nonlinear background perfect fluid.","intent_p":0.99,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":6,"quotes":[{"arxiv_id":"2001.01460","title":"Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification","url":"/paper/2001.01460","section":"Basic equations","sentence":"We note here that in the linear model with $f”(R_0)= 0$, 1.25 is reduced to its counterpart obtained in papers [ref] .","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":6},"outgoing":{"papers":7,"sentences":8,"groups":[{"kind":"data_used","label":"Uses data or values from","papers":1,"sentences":1,"quotes":[{"arxiv_id":"hep-ph/0611184","title":"Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale","url":"/paper/hep-ph/0611184","section":"Asymptotic black brane","sentence":"If, for example, $|Ω| ∼O(1)$ (and is not equal to -1/2), the upper limit for $λ$ is $λ_ ∼10^-3$cm [ref] .","intent_p":0.82,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":4,"sentences":4,"quotes":[{"arxiv_id":"gr-qc/0103106","title":"Tension Perturbations of Black Brane Spacetimes","url":"/paper/gr-qc/0103106","section":"Introduction","sentence":"For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"hep-th/0107228","title":"The first law of black brane mechanics","url":"/paper/hep-th/0107228","section":"Introduction","sentence":"For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"hep-th/0403103","title":"General Definition of Gravitational Tension","url":"/paper/hep-th/0403103","section":"Introduction","sentence":"For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"hep-th/0607051","title":"Stresses and Strains in the First Law for Kaluza-Klein Black Holes","url":"/paper/hep-th/0607051","section":"Introduction","sentence":"For black strings and black branes, the notion of tension is defined, e.g., in [ref] and it follows from the first law for black hole spacetimes [ref] .","intent_p":0.93,"contests_p":null}]}],"unlabelled_sentences":3},"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/1202.2677"}}