{"arxiv_id":"1308.6186","incoming":{"papers":42,"sentences":88,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":7,"sentences":7,"quotes":[{"arxiv_id":"1711.07466","title":"Lensing convergence in galaxy clustering in LambdaCDM and beyond","url":"/paper/1711.07466","section":"Methodology","sentence":"For Gaussian fluctuations the error in the measured power spectra is given by, [ref] [equation] The observed correlation multipoles $C^ij_ℓ, obs$ including shot-noise are [equation] where $N_i = d N_z_i/dΩ$ denotes the number of sources per steradian in the $i$-th bin.","intent_p":0.9,"contests_p":null},{"arxiv_id":"1605.01405","title":"Determining the progenitors of merging black-hole binaries","url":"/paper/1605.01405","section":"Galaxy and GW correlations","sentence":"The errors in the auto- and cross-correlations are given by (see e.g. [ref] ): [equation] and: [equation] where $f_sky$ is the fraction of the sky observed and $n̅_{g, GW}$ is the average number of sources per steradian, i.e. the integral of $dN/dz$ (Equation [ref] in the GW case).","intent_p":0.95,"contests_p":null},{"arxiv_id":"2007.04656","title":"Constraining the growth rate by combining multiple future surveys","url":"/paper/2007.04656","section":"Introduction","sentence":"Here we use the observed galaxy power spectrum in angular harmonic space, $C_ℓ(z,z')$ [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2002.02466","title":"Cross-correlating galaxy catalogs and gravitational waves: a tomographic approach","url":"/paper/2002.02466","section":"Methodology and Formalism","sentence":"A simple analytical procedure to estimate these quantities leads to [ref] (see also [ref] ): [equation] where $Δℓ$ is the width of bin in $ℓ$-space around $ℓ$, and we introduce the fraction of the sky covered by the most restrictive of the two catalogs [equation] and the Poisson noise arising from the discrete number of sources of the catalog, i.e. [equation] with $N_i$ the total number of sources within the catalog $i=a,b$ in the considered field of view.","intent_p":0.8,"contests_p":null},{"arxiv_id":"1505.06179","title":"Cosmological Measurements with General Relativistic Galaxy Correlations","url":"/paper/1505.06179","section":"Summary of results","sentence":"These are given by the inverse of the area of the error ellipses shown in the previous figures, see e.g. [ref] for details.","intent_p":0.82,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":1,"sentences":3,"quotes":[{"arxiv_id":"1307.1459","title":"The CLASSgal code for Relativistic Cosmological Large Scale Structure","url":"/paper/1307.1459","section":"Example","sentence":"Our results cannot be immediately compared to those of [ref] due to a different normalization of the FoM (see [ref] ).","intent_p":1.0,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1603.09073","title":"Curvature constraints from Large Scale Structure","url":"/paper/1603.09073","section":"Error forecasts","sentence":"As shown in [ref] , a larger number of bins is required to extract all the 3-dimensional information from the survey.","intent_p":0.98,"contests_p":null},{"arxiv_id":"2006.13525","title":"The Flat Sky Approximation to Galaxy Number Counts","url":"/paper/2006.13525","section":"Introduction","sentence":"A detailed study of these spectra has shown [ref] that, in nearly all situations, the large scale relativistic terms are very small and can be neglected for percent level accuracy.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1812.02104","title":"A blind method to recover the mask of a deep galaxy survey","url":"/paper/1812.02104","section":"The contribution of lensing","sentence":"This is no surprise, because the contribution of lensing (whose level is appreciable in the right panels) is negligible for auto correlations with respect to clustering and RSD for redshift bins of the width $Δz =0.1$ (see e.g. [ref] ).","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":14,"sentences":17,"quotes":[{"arxiv_id":"2606.17617","title":"Synergy between CSST and future gravitational-wave detectors: Probing primordial black holes by cross-correlating dark sirens with galaxies","url":"/paper/2606.17617","section":"Introduction","sentence":"Rubin Observatory [ref] , and the Chinese Space-station Survey Telescope (CSST) [ref] , will map large galaxy samples over wide areas and broad redshift ranges, providing powerful probes of LSS [ref] .","intent_p":0.83,"contests_p":null},{"arxiv_id":"1510.03436","title":"Relativistic effects in Lyman-alpha forest","url":"/paper/1510.03436","section":"Introduction","sentence":"Recent years have seen a lot of effort put into understanding and possibly measuring the signal of relativistic effects and/or weak gravitational lensing in the 2-point statistics of the galaxy clustering, see e.g. [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1801.02518","title":"General Relativistic corrections in density-shear correlations","url":"/paper/1801.02518","section":"Correlating number counts with shear measurements","sentence":"More details on Eq. ([ref]) are given in [ref] and [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1506.01369","title":"Measuring the lensing potential with tomographic galaxy number counts","url":"/paper/1506.01369","section":"Galaxy number counts","sentence":"which has been thoroughly studied in literature [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"2004.12981","title":"On the importance of lensing for galaxy clustering in photometric and spectroscopic surveys","url":"/paper/2004.12981","section":"The galaxy number counts","sentence":"More details on these terms are given in [ref] .","intent_p":0.93,"contests_p":null}]}],"unlabelled_sentences":58},"outgoing":{"papers":30,"sentences":58,"groups":[{"kind":"contests","label":"Contests","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1207.6487","title":"Recovering 3D clustering information with angular correlations","url":"/paper/1207.6487","section":"Binning strategy","sentence":"In fact, photometric uncertainties cause redshift bins to be correlated, hence the total Fisher matrix is not well approximated by the sum of the Fisher matrices of each bin, as assumed in [ref] and in the present work.","intent_p":0.8,"contests_p":0.8}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":2,"sentences":6,"quotes":[{"arxiv_id":"1307.1459","title":"The CLASSgal code for Relativistic Cosmological Large Scale Structure","url":"/paper/1307.1459","section":"Conclusions","sentence":"We have shown how the new code gal [ref] can be used to analyze galaxy surveys in an optimal way.","intent_p":0.99,"contests_p":null},{"arxiv_id":"1207.6487","title":"Recovering 3D clustering information with angular correlations","url":"/paper/1207.6487","section":"Fisher matrix forecasts","sentence":"Assuming that the fluctuations are statistically homogeneous, isotropic and Gaussian distributed, the covariance matrix between different power spectra can be approximated as in Ref. [ref] , Cov_[ℓ,ℓ'] [(ij), (pq)]=_ℓ,ℓ'C_ℓ^obs,i p C_ℓ^obs,jq + C_ℓ^obs,i q C_ℓ^obs,jp/f_sky ( 2 ℓ+ 1 ) , where $f_sky$ is the sky fraction covered by the survey.","intent_p":0.94,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":1,"sentences":2,"quotes":[{"arxiv_id":"1110.3193","title":"Euclid Definition Study Report","url":"/paper/1110.3193","section":"Measuring the lensing potential","sentence":"We consider a tophat window for the narrowest case, $z=0.01$ and Gaussian window functions with standard deviations $z≳0.05(1+z)$, which corresponds to Euclid photometric errors [ref] for the panels on the second line.","intent_p":0.86,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":2,"sentences":6,"quotes":[{"arxiv_id":"1207.6487","title":"Recovering 3D clustering information with angular correlations","url":"/paper/1207.6487","section":"2D and 3D performances","sentence":"The definition of Ref. [ref] is sufficient for a narrow band survey, but not for a Euclid-like survey.","intent_p":0.88,"contests_p":null},{"arxiv_id":"1305.0934","title":"Redshift-space distortions from the cross-correlation of photometric populations","url":"/paper/1305.0934","section":"A DES-like catalog","sentence":"The novelties of the present analysis is that we marginalize over cosmological parameters which have been fixed in Refs. [ref] and we use a more sophisticated definition of the nonlinearity scale.","intent_p":0.83,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1307.1459","title":"The CLASSgal code for Relativistic Cosmological Large Scale Structure","url":"/paper/1307.1459","section":"2D and 3D performances","sentence":"However, since for slimmer redshift bins not only the shot noise but also the signal increases, see [ref] for details, the optimal number of bins is larger than a naive estimate.","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":10,"sentences":10,"quotes":[{"arxiv_id":"1205.5221","title":"Beyond the plane-parallel and Newtonian approach: Wide-angle redshift distortions and convergence in general relativity","url":"/paper/1205.5221","section":"Introduction","sentence":"The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1305.1299","title":"Cosmic Clocks","url":"/paper/1305.1299","section":"Introduction","sentence":"The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1009.3021","title":"General Relativistic Description of the Observed Galaxy Power Spectrum: Do We Understand What We Measure?","url":"/paper/1009.3021","section":"Introduction","sentence":"The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1107.5427","title":"Large-scale clustering of galaxies in general relativity","url":"/paper/1107.5427","section":"Introduction","sentence":"The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"0907.0707","title":"New Perspective on Galaxy Clustering as a Cosmological Probe: General Relativistic Effects","url":"/paper/0907.0707","section":"Introduction","sentence":"The problem how the galaxy distribution, number counts and distance measurements are affected by the propagation of light in a perturbed geometry has also been investigated in other works; see, e.g. [ref] .","intent_p":0.99,"contests_p":null}]}],"unlabelled_sentences":32},"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":{"arxiv_id":"1308.6186","kind":"model","paper_version":3,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T23:40:34+00:00","loaded_at":"2026-10-28T01:04:39.992660+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2016,"title":"The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Angular clustering tomography and its cosmological implications","arxiv_id":"1607.03144"}],"verified":true,"paraphrase":"Based its optimisation of the number and width of redshift shells on this paper's binning strategy, which sets each shell's width so all have the same number of galaxies."},{"p":0.91,"quote":null,"citing":[{"self":false,"year":2026,"title":"PowerFull: fast and accurate computation of the relativistic angular galaxy power spectrum including local primordial non-Gaussianity","arxiv_id":"2608.18334"}],"verified":true,"paraphrase":"Took its expression for the maximum of zero and the redshift-interval differences as following from this paper."}],"papers_all":11,"self_papers":1,"self_entries":[{"p":0.9,"quote":null,"citing":[{"self":true,"year":2017,"title":"Lensing convergence in galaxy clustering in LambdaCDM and beyond","arxiv_id":"1711.07466"}],"verified":true,"paraphrase":"Used this paper's expression for the error in the measured power spectra for Gaussian fluctuations."}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"entries":[],"papers_all":4,"self_papers":1,"self_entries":[{"p":0.96,"quote":null,"citing":[{"self":true,"year":2018,"title":"A blind method to recover the mask of a deep galaxy survey","arxiv_id":"1812.02104"}],"verified":true,"paraphrase":"Cited this paper as support for the statement that lensing is negligible for auto correlations relative to clustering and RSD for redshift bins of width 0.1."}]}],"counts":{"by_kind":{"comparison":1,"method_or_tool":11,"supports_this_paper":4},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":13,"self_papers":26,"citing_papers":48,"sentences_read":16,"citing_sentences":96,"unambiguous_read":16,"typed_independent":7,"independent_papers":22,"by_kind_independent":{"method_or_tool":7}},"input_sha256":"3966c50ef2296f35a87de31e34cd835153f3923dc9bdcd2a4646dc92f814e220","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"2 later papers by other authors are listed below: 2 used its method or tool. 2 more papers by the same authors are listed: 1 used its method or tool and 1 cited it as support."},"_links":{"html":"https://pith.science/paper/1308.6186"}}