{"arxiv_id":"gr-qc/0508107","incoming":{"papers":83,"sentences":123,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":3,"quotes":[{"arxiv_id":"2106.02595","title":"Tidal deformation of dynamical horizons in binary black hole mergers","url":"/paper/2106.02595","section":"Preliminaries","sentence":"Our calculation of the tidal deformations of black holes is based on the formalism of quasi-local horizons [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2605.10874","title":"Cusp Formation in Merging Black Hole Horizons","url":"/paper/2605.10874","section":"Introduction","sentence":"As is conventional and practically useful in numerical relativity, we shall use the notion of quasi-local horizons (QLHs), which are 3-surfaces obtained by the time evolution of “apparent horizons” or more correctly marginally outer trapped surfaces (MOTSs) [ref] .","intent_p":0.82,"contests_p":null},{"arxiv_id":"1011.0623","title":"Dynamics of Diffeomorphism Degrees of Freedom at a Horizon","url":"/paper/1011.0623","section":"Isolated Horizons","sentence":"We largely follow the approach of [ref] and [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":45,"sentences":58,"quotes":[{"arxiv_id":"2103.05305","title":"An invariant characterization of the quasi-spherical Szekeres dust models","url":"/paper/2103.05305","section":"Introduction","sentence":"The apparent horizon is defined as the locus of the vanishing expansion, $θ_(ℓ)$ of a null geodesic congruence, $ℓ_a$ emanating from trapped surfaces with spherical topology [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"2402.17977","title":"Null Infinity as a Weakly Isolated Horizon","url":"/paper/2402.17977","section":"General Framework","sentence":"In the terminology used in the literature [ref] an NEH $$, equipped with an equivalence class $[k̅^a]$ of null normals satisfying $_ḵ ω̱_a 0$ is said to be a Weakly Isolated Horizon.","intent_p":0.93,"contests_p":null},{"arxiv_id":"2604.00170","title":"Thermodynamics of dynamical black holes beyond perturbation theory","url":"/paper/2604.00170","section":"Quasi-local horizons: A brief overview","sentence":"In contrast to EHs, Quasi-local horizons (QLHs) [ref] ) do not refer to $$.","intent_p":0.9,"contests_p":null},{"arxiv_id":"2512.11659","title":"Thermodynamics of Black Holes, far from Equilibrium","url":"/paper/2512.11659","section":"Introduction","sentence":"An answer is provided by quasi-local horizons (QLHs), introduced over two decades ago (see, in particular, [ref] .) Since they are free of teleology, they are routinely used in numerical simulations of BH mergers.","intent_p":0.81,"contests_p":null},{"arxiv_id":"1010.6301","title":"Black Brane Entropy and Hydrodynamics","url":"/paper/1010.6301","section":"Introduction","sentence":"For example, in the gravity literature much attention has been devoted to the study of so-called quasilocal horizons, since in contrast to the event horizon they may be defined without determining the full causal structure of spacetime (see [ref] for reviews).","intent_p":0.98,"contests_p":null}]}],"unlabelled_sentences":62},"outgoing":{"papers":0,"sentences":0,"groups":[],"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":{"arxiv_id":"gr-qc/0508107","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T17:58:45+00:00","loaded_at":"2026-10-28T01:03:02.644572+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"entries":[{"p":0.98,"quote":null,"citing":[{"self":false,"year":2010,"title":"Dynamics of Diffeomorphism Degrees of Freedom at a Horizon","arxiv_id":"1011.0623"}],"verified":true,"paraphrase":"Largely followed the approach of this paper and another work."}],"papers_all":5,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"method_or_tool":5,"supports_this_paper":1},"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":9,"self_papers":7,"citing_papers":93,"sentences_read":11,"citing_sentences":135,"unambiguous_read":11,"typed_independent":6,"independent_papers":86,"by_kind_independent":{"method_or_tool":5,"supports_this_paper":1}},"input_sha256":"0ac033f33ae906c6b81cd1e4408bcddaea309da33c7f4db1aa69f91a513ee84b","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":"1 later paper by other authors is listed below: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/gr-qc/0508107"}}