Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-01T04:42:49.188754Z
Paper Citation Record · LEDGER
Distinguishability threshold for random geometric graphs
As of 14 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2607.22480.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
44 of 44 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved44
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 54c28782-4d07-4202-a3f2-6627567bca2a · outbound
This paper cites Abdalla, A.
Distinguishability threshold for random geometric graphs Abdalla, A
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:44.808190Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 95f42abc-f70c-4e1b-a378-400320d37ca1 · outbound
This paper cites Balogh, B.
Distinguishability threshold for random geometric graphs Balogh, B
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:44.946597Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f0e8d634-82bd-482e-a8b2-7d4ec13eda5f · outbound
This paper cites Bangachev and G.
Distinguishability threshold for random geometric graphs Bangachev and G
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.107013Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8b2c844b-8545-4e8d-9e1c-24c62e69fc07 · outbound
This paper cites On The Fourier Coefficients of High-Dimensional Random Geometric Graphs.
Distinguishability threshold for random geometric graphs On The Fourier Coefficients of High-Dimensional Random Geometric Graphs
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.262989Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6c9ece48-7eb2-43f4-ae7a-80af2cc4aaf1 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.379219Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c423341f-cf20-47ba-9c8d-53d23eca0ad8 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.495364Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f855beb2-3a9b-4965-9bbd-8e6b36d70915 · outbound
This paper cites Brennan, G.
Distinguishability threshold for random geometric graphs Brennan, G
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.634988Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a439771f-8973-410e-a756-23274c52f3ae · outbound
This paper cites Brennan, G.
Distinguishability threshold for random geometric graphs Brennan, G
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.771109Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 532343cc-034d-4dc0-b74b-909a4f6fc5de · outbound
This paper cites Bubeck, J.
Distinguishability threshold for random geometric graphs Bubeck, J
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:45.926915Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4cf66274-a3ee-4673-8038-a841c8f1894b · outbound
This paper cites Chatterjee.A generalization of the Lindeberg principle.Ann.
Distinguishability threshold for random geometric graphs Chatterjee.A generalization of the Lindeberg principle.Ann
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.096070Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f7037ddc-6c79-48fe-981a-829fe3d8b837 · outbound
This paper cites Spectra of high-dimensional sparse random geometric graphs.
Distinguishability threshold for random geometric graphs Spectra of high-dimensional sparse random geometric graphs
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.228099Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0e9c881f-444c-489b-bb6e-51f2e9131ee5 · outbound
This paper cites Random Geometric Graph: Some recent developments and perspectives.
Distinguishability threshold for random geometric graphs Random Geometric Graph: Some recent developments and perspectives
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.346956Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 59170e57-33bf-4307-a783-9fbc6d332d90 · outbound
This paper cites Devroye, A.
Distinguishability threshold for random geometric graphs Devroye, A
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.465003Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 97b33292-bcec-4590-a0b2-a30e35e847ae · outbound
This paper cites Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime.
Distinguishability threshold for random geometric graphs Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the $d>n$ Regime
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.615336Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 58a98fea-7519-4a77-a855-87915cf6b6a0 · outbound
This paper cites Eldan and D.
Distinguishability threshold for random geometric graphs Eldan and D
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.789387Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c4347e83-9802-43ae-b465-c20f26468993 · outbound
This paper cites Erd˝ os and A.
Distinguishability threshold for random geometric graphs Erd˝ os and A
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:46.927741Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4f20943d-5383-4de8-828b-5d7fc868e74d · outbound
This paper cites Erd˝ os.Some remarks on the theory of graphs.Bull.
Distinguishability threshold for random geometric graphs Erd˝ os.Some remarks on the theory of graphs.Bull
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.038926Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e7fd614e-c2a1-410f-953e-514974b6b1f0 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.154703Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 405c3c67-01e2-414a-b394-f839f4deeac6 · outbound
This paper cites Gaussian random graphs and Ramsey numbers.
Distinguishability threshold for random geometric graphs Gaussian random graphs and Ramsey numbers
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.273732Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4ac30225-5ccd-478b-988b-c4d6c3fd1578 · outbound
This paper cites Janson, T.
Distinguishability threshold for random geometric graphs Janson, T
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.381245Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation eebaef8c-9dcd-46b6-8266-5c35397fbe4c · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.515842Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e347df5-8b2c-4f95-a5cc-eff1d99c9ad1 · outbound
This paper cites Laurent and P.
Distinguishability threshold for random geometric graphs Laurent and P
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.568059Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fd5f434b-e676-4d76-9d10-1db23d6b71ba · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 23
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.626173Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8de9584e-9126-4d24-8578-5304c1bcbc4c · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.699324Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 55f6f2fc-5b1c-48c7-b358-c1cb751b9a12 · outbound
This paper cites Phase transition in noisy high-dimensional random geometric graphs.
Distinguishability threshold for random geometric graphs Phase transition in noisy high-dimensional random geometric graphs
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.755401Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 78a9751f-1297-4f69-89a1-cbcaac622033 · outbound
This paper cites Liu and M.
Distinguishability threshold for random geometric graphs Liu and M
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.835592Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2f733742-a589-463e-8eb2-887edba550ae · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.856230Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 532935be-4923-4d53-8f20-9edd56865190 · outbound
This paper cites McDiarmid and T.
Distinguishability threshold for random geometric graphs McDiarmid and T
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.927930Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 082f1bbb-789b-4abe-b353-e9b86568f9d3 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:47.982121Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39fefe1b-75e1-4692-953e-12bba5fd6de9 · outbound
This paper cites M¨ uller.Two-point concentration in random geometric graphs.Combinatorica 28(5) (2008), 529–545.
Distinguishability threshold for random geometric graphs M¨ uller.Two-point concentration in random geometric graphs.Combinatorica 28(5) (2008), 529–545
Reference 30
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.072011Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b730fae5-df54-4cf9-a6d7-3d550617e53b · outbound
This paper cites Random geometric graphs and the spherical Wishart matrix.
Distinguishability threshold for random geometric graphs Random geometric graphs and the spherical Wishart matrix
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.162819Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation df918360-a454-498e-b790-0faafffcff78 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.255276Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39c91793-7e02-4b99-a00a-a3ca3da5553c · outbound
This paper cites Penrose.Random geometric graphs.Oxford Studies in Probability 5, Oxford University Press, Oxford, 2003.
Distinguishability threshold for random geometric graphs Penrose.Random geometric graphs.Oxford Studies in Probability 5, Oxford University Press, Oxford, 2003
Reference 33
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.339584Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d5389941-5fd4-4e98-bef5-62e15783d4f0 · outbound
This paper cites Rudelson and R.
Distinguishability threshold for random geometric graphs Rudelson and R
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.427712Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a99449a-7743-46af-9d4a-2df911c44be8 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.514235Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ab39b731-fa18-4f03-a590-7e58617f52b8 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.598728Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 36c4ca87-28dd-40e9-9bdd-f585d125dce5 · outbound
This paper cites Vershynin.High-dimensional probability.
Distinguishability threshold for random geometric graphs Vershynin.High-dimensional probability
Reference 37
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.686773Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a73d7747-7802-4d2f-bf0e-44c630b442b2 · outbound
This paper cites ν(x)” to denote what is−λ(x) in our notation, and “λ(x) =ν ′(x).
Distinguishability threshold for random geometric graphs ν(x)” to denote what is−λ(x) in our notation, and “λ(x) =ν ′(x)
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.746301Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 908b6361-d41e-4ee4-86de-8ddfc03b80c7 · outbound
This paper cites Here, we give its simplified statement, in the regime wheremandℓare constant, and p≥n −1/2.
Distinguishability threshold for random geometric graphs Here, we give its simplified statement, in the regime wheremandℓare constant, and p≥n −1/2
Reference 39
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.834228Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 28feaef1-4dc5-41c6-a453-2553d2e78177 · outbound
This paper cites Hence, the standard Gaussian tail estimate gives P |⟨πs(gi), πs(gj)⟩| ≥3 p 2nlogn gi ≤2 exp(−9(logn)/2)≤n −4.
Distinguishability threshold for random geometric graphs Hence, the standard Gaussian tail estimate gives P |⟨πs(gi), πs(gj)⟩| ≥3 p 2nlogn gi ≤2 exp(−9(logn)/2)≤n −4
Reference 40
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.894947Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3cebe48f-7a45-49a1-bd7c-a068dd8e763b · outbound
This paper cites Namely, they have shown that ifδ >0 is chosen such thatP[G(n, d, p) =△] =p 3(1 +δ), then Var[N △(G)]≤O(n 3p3(1 + δ) +p 5δ2n4 +p 6δn4).
Distinguishability threshold for random geometric graphs Namely, they have shown that ifδ >0 is chosen such thatP[G(n, d, p) =△] =p 3(1 +δ), then Var[N △(G)]≤O(n 3p3(1 + δ) +p 5δ2n4 +p 6δn4)
Reference 41
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:48.953360Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b278af74-3f8c-4ee6-9230-3da115ee3228 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:49.004583Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation abb5c2e2-dc66-4514-8bd4-66551b9667b5 · outbound
This paper cites an unresolved cited work.
Distinguishability threshold for random geometric graphs Unresolved cited work
Reference 43
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:49.090838Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9d456a31-d176-43cc-920c-d9cf051ca0cc · outbound
This paper cites On the other hand, using the Taylor series of the functionA7→log detA, we find that when∥M ′∥op is sufficiently small, then we have log det(I−2M ′) =− P∞ k=1 tr((2M ′)k)/k.
Distinguishability threshold for random geometric graphs On the other hand, using the Taylor series of the functionA7→log detA, we find that when∥M ′∥op is sufficiently small, then we have log det(I−2M ′) =− P∞ k=1 tr((2M ′)k)/k
Reference 44
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T04:42:49.188754Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.