{"arxiv_id":"1006.1901","incoming":{"papers":17,"sentences":25,"groups":[{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1203.3179","title":"Improvement of a provisional solution of the quantum-corrected field equations of d = 11 supergravity on flat R^4 times a compact hyperbolic 7-manifold, and modes that decay along the beam line outside the interaction region at the LHC","url":"/paper/1203.3179","section":"The Kaluza-Klein modes of the metric","sentence":"So from pages 9 to 12 and 16 to 17 of [ref] , it seems likely that in this approximation, the lightest massive modes of $s_μν$ will have intrinsic mass $m̅ = 3$ [ref] , and from pages 42 to 43 of [ref] , their masses as seen on the HW boundary will be $m = 3 A/B$, where $A$ and $B$ are the constants in the metric ansatz ([ref]).","intent_p":0.87,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1506.05598","title":"Hyperbolic extra-dimensions in particle physics and beyond","url":"/paper/1506.05598","section":"Future extensions","sentence":"Compactifications based on hyperbolic orbifolds gather a large number of properties that are useful for these problems, like a Dirac spectrum chiral zero modes, a mass gap with the KK modes, discrete residual symmetries for the stability of dark matter, and interesting cosmological constructions [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1603.02289","title":"Towards Kaluza-Klein Dark Matter on Nilmanifolds","url":"/paper/1603.02289","section":"Introduction","sentence":"The volume grows exponentially with the ratio $l_G/l_c$, allowing a natural solution to the hierarchy problem [ref] . * Typical mass spectra for the Kaluza-Klein (KK) reduction of these spaces feature a mass gap similar to the one present in Randall-Sundrum models [ref] , therefore allowing for a solution to the hierarchy problem that does not require light KK modes [ref] . * When the extra compact space is negatively-curved, rather than flat, the dynamics of the very early universe alleviate standard cosmological problems, allowing to account for the current homogeneity and flatness of the universe [ref] . * Finite volume hyperbolic manifolds of dimension greater than two have the remarkable property of rigidity (Mostow's theorem [ref] ): geometrical quantities as the length of its shortest closed geodesics, the volume, etc. are topological invariants.","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":8,"sentences":8,"quotes":[{"arxiv_id":"2005.00292","title":"Compactified Spacelike Extra Dimension & Brane-Higgs Field","url":"/paper/2005.00292","section":"Introduction","sentence":"A less known approach is the compactification of $q ≥2$ spacelike extra dimension on a compact hyperbolic manifold with a large genus (number of holes) proposed in 2000 in Ref. [ref] (see also Ref. [ref] ).","intent_p":0.9,"contests_p":null},{"arxiv_id":"2303.09872","title":"Three-generation solutions of equations of motion in heterotic supergravity","url":"/paper/2303.09872","section":"Curvatures and gauge field configurations","sentence":"The manifold with $λ_i>0$ is a sphere $S^2$, $λ_i=0$ is a torus $T^2$, and $λ_i<0$ is a compact hyperbolic manifold $H^2/Γ$ [ref] .","intent_p":0.9,"contests_p":null},{"arxiv_id":"2001.07102","title":"Large Star/Rose Extra Dimension with Small Leaves/Petals","url":"/paper/2001.07102","section":"Introduction","sentence":"A less known approach is the compactification of $q ≥2$ spacelike extra dimension on a compact hyperbolic manifold with a large genus (number of holes) proposed in 2000 in Ref. [ref] (see also Ref. [ref] ).","intent_p":0.96,"contests_p":null},{"arxiv_id":"1010.6021","title":"Hyperbolic Inflation","url":"/paper/1010.6021","section":"Introduction","sentence":"Relatively recently in physics there have been works focused on phenomenoloy with a rather low KK scale ($∼$ TeV) [ref] and a compactification scheme in string theory [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2106.03625","title":"Minkowski spacetime and non-Ricci-flat compactification in heterotic supergravity","url":"/paper/2106.03625","section":"Introduction","sentence":"Obtaining four-dimensional theories with non-Ricci-flat manifolds has, of course, a long history [ref] .","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":14},"outgoing":{"papers":4,"sentences":4,"groups":[{"kind":"comparison","label":"Compares with","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0901.0720","title":"Split-UED and Dark Matter","url":"/paper/0901.0720","section":"Implications for the LHC and beyond","sentence":"It is instructive to compare our case with the well known extra dimensional scenarios, e.g., add [ref] , rs [ref] and ued [ref] (see also [ref] ) since some of the features are common while others are quite distinctive.","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0712.1196","title":"Simple de Sitter Solutions","url":"/paper/0712.1196","section":"Introduction","sentence":"In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).","intent_p":0.83,"contests_p":null},{"arxiv_id":"1001.1423","title":"A bulk inflaton from large volume extra dimensions","url":"/paper/1001.1423","section":"Introduction","sentence":"In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).","intent_p":0.83,"contests_p":null},{"arxiv_id":"1001.4008","title":"Compactification on negatively curved manifolds","url":"/paper/1001.4008","section":"Introduction","sentence":"In this paper we consider compact hyperbolic spaces which have been less intensively studied in physics so far [ref] but enjoy several interesting mathematical properties (see [ref] for a mathematical introduction).","intent_p":0.83,"contests_p":null}]}],"unlabelled_sentences":0},"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/1006.1901"}}