Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-10T17:23:44.280830Z
Paper Citation Record · LEDGER
Sharp threshold for reconstructing points on the line
As of 14 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2604.09176.
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
20 of 20 outbound references displayed
- verified exact3
- verified fuzzy14
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation fdecffc5-18cd-4833-af98-d09a544ef514 · outbound
This paper cites Alon and J.H.
Sharp threshold for reconstructing points on the line Alon and J.H
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.269543Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 16680de9-7391-4ee6-9503-2bea97eb9ba3 · outbound
This paper cites Benjamini, K.
Sharp threshold for reconstructing points on the line Benjamini, K
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.250108Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2c6cc174-2c97-42fb-8a89-1a7ceadca9ed · outbound
This paper cites Determining a Points Configuration from a Subset of the Pairwise Distances.
Sharp threshold for reconstructing points on the line Determining a Points Configuration from a Subset of the Pairwise Distances
Reference 3
- Resolution
- verified exact
- arxiv_id, observed 2026-06-02T02:04:03.486361Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f43457f2-c254-4c9d-9de4-fd0ef77552f4 · outbound
This paper cites Bollob´ as,The art of mathematics: Coffee time in Memphis, Cambridge University Press (2006).
Sharp threshold for reconstructing points on the line Bollob´ as,The art of mathematics: Coffee time in Memphis, Cambridge University Press (2006)
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.260211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 167cb094-cd50-49c4-81bc-cae3b5ce5922 · outbound
This paper cites Bollob´ as,The isoperimetric number of random regular graphs.European Journal of Com- binatorics9:3 (1988), 241–244.
Sharp threshold for reconstructing points on the line Bollob´ as,The isoperimetric number of random regular graphs.European Journal of Com- binatorics9:3 (1988), 241–244
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.266682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e4a223f2-42e2-4230-8c60-fab97eeb5309 · outbound
This paper cites an unresolved cited work.
Sharp threshold for reconstructing points on the line Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-05-17T10:41:44.239604Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation ee532058-e2a9-43d9-8040-e2186989f1cb · outbound
This paper cites Ding, J.H.
Sharp threshold for reconstructing points on the line Ding, J.H
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.224530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 62c9f7b7-7860-4cc4-866f-9091ecb6dd42 · outbound
This paper cites an unresolved cited work.
Sharp threshold for reconstructing points on the line Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-05-17T10:41:44.278673Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 33f51ba0-0a71-4494-89eb-c53d4b14aef8 · outbound
This paper cites Friedman,A proof of Alon’s second eigenvalue conjecture and related problems, American Mathematical Society, (2008).
Sharp threshold for reconstructing points on the line Friedman,A proof of Alon’s second eigenvalue conjecture and related problems, American Mathematical Society, (2008)
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.251133Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 45fac6b9-1430-47a6-916b-17d7dc19b428 · outbound
This paper cites Frieze, M.
Sharp threshold for reconstructing points on the line Frieze, M
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.263080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation de2206f1-2103-4f7f-9a76-31911e8125cd · outbound
This paper cites an unresolved cited work.
Sharp threshold for reconstructing points on the line Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-05-17T10:41:44.253363Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3e84d33f-1195-4620-bf73-cdef96b96e84 · outbound
This paper cites Garamv¨ olgyi,Global rigidity of (quasi-)injective frameworks on the line, Discrete Mathe- matics,345:2, (2022).
Sharp threshold for reconstructing points on the line Garamv¨ olgyi,Global rigidity of (quasi-)injective frameworks on the line, Discrete Mathe- matics,345:2, (2022)
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.242488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4c669e14-109d-4235-8221-3f576af8b6cf · outbound
This paper cites Gir˜ ao, F.
Sharp threshold for reconstructing points on the line Gir˜ ao, F
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.256660Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation dd5805b2-d5b4-4a31-af8a-1116a8920a08 · outbound
This paper cites Graver, B.
Sharp threshold for reconstructing points on the line Graver, B
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.272655Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7985f821-95a7-474d-a7fc-174993ffd169 · outbound
This paper cites Greenhill and B.
Sharp threshold for reconstructing points on the line Greenhill and B
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.275542Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4488c6ee-5d11-44ca-83e6-6ea984c9fa7d · outbound
This paper cites Global rigidity of random graphs in $\mathbb{R}$.
Sharp threshold for reconstructing points on the line Global rigidity of random graphs in $\mathbb{R}$
Reference 16
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T06:55:59.122971Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4ede560a-475f-420f-a6b6-bba523bdf004 · outbound
This paper cites Pittel, J.
Sharp threshold for reconstructing points on the line Pittel, J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.235685Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 5161cd57-3ffd-412a-8171-26f1c171675b · outbound
This paper cites Portier,Reconstructing a Giant Component of a Point Set inR, arXiv preprint, arXiv:2602.23122, (2026).
Sharp threshold for reconstructing points on the line Portier,Reconstructing a Giant Component of a Point Set inR, arXiv preprint, arXiv:2602.23122, (2026)
Reference 18
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T06:55:59.140278Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 36cd096c-ee52-4749-be56-76c5a9a862f6 · outbound
This paper cites Portier,Topics in Probabilistic Combinatorics, Doctoral Dissertation (2025).
Sharp threshold for reconstructing points on the line Portier,Topics in Probabilistic Combinatorics, Doctoral Dissertation (2025)
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.285757Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 948183fd-bfdc-47fa-8eb3-ffd9a5ef2ebe · outbound
This paper cites Janson and M.J.
Sharp threshold for reconstructing points on the line Janson and M.J
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-17T10:41:44.282816Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.