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A numerical study of the correspondence between paths in a causal set and geodesics in the continuum

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Raluca Ilie, Gregory B. Thompson, David D. Reid

General Relativity and Quantum Cosmology · Submitted 13 Dec 2005

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.

how it is stated · asserted 0.66 read the record →

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arXiv IDgr-qc/0512073 (version 1)
Pith IDA7NFRSTX, Pith's permanent record of this paper and its review
CitationDavid D. Reid, Gregory B. Thompson, Raluca Ilie. "A numerical study of the correspondence between paths in a causal set and geodesics in the continuum." arXiv:gr-qc/0512073 (2005). https://pith.science/paper/A7NFRSTX
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,302 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.29 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. contribution 0.99 0.85 0.05 asserted 0.68
s1 For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit. result 1.00 0.94 0.91 asserted 0.66

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

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  • references and citing sentences
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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

This paper presents the results of a computational study related to the path-geodesic correspondence in causal sets. For intervals in flat spacetimes, and in selected curved spacetimes, we present evidence that the longest maximal chains (the longest paths) in the corresponding causal set intervals statistically approach the geodesic for that interval in the appropriate continuum limit.

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References
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2 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as support 1 paper
  • Numerical studies (see Refs [ref] and [ref] ) confirmed that in the case of a Poisson distribution of points on a Lorentzian manifold there is, in fact, a close correlation between the Lorentzian distance defined in the usual way and the one defined in terms of chains of points as above.

    Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets · Volumes and Distances on a Causal Set · 0.98

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