Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T15:49:10.617331Z
Paper Citation Record · LEDGER
Erd\H{o}s's unit distance problem and rigidity
As of 24 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2507.15679.
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 2026-08-23T06:30:58.430688+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
30 of 30 outbound references displayed
- verified exact0
- verified fuzzy22
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 3a77eccb-a7a6-416d-89c7-fcd8cecb973d · outbound
This paper cites The rigidity of graphs.
Erd\H{o}s's unit distance problem and rigidity The rigidity of graphs
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:17.998911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8174654d-4014-4e19-b840-e30fcda046e4 · outbound
This paper cites The rigidity of graphs II.
Erd\H{o}s's unit distance problem and rigidity The rigidity of graphs II
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:17.737848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 58634682-30da-4951-966c-b391c6949a3b · outbound
This paper cites Borcea and I.
Erd\H{o}s's unit distance problem and rigidity Borcea and I
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T15:49:07.026673Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3f7bd007-1ff3-44e3-855d-3fd25bf5fd84 · outbound
This paper cites Moser, and J´ anos Pach.
Erd\H{o}s's unit distance problem and rigidity Moser, and J´ anos Pach
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:17.472535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 33ef5e49-7d12-45b6-b8d9-550b7a5637d4 · outbound
This paper cites Generic global rigidity.
Erd\H{o}s's unit distance problem and rigidity Generic global rigidity
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:17.152283Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5571fb8c-a7ba-4f92-80cf-b3f2388ab412 · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:16.937218Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e9cff628-870f-4c23-b924-8fed57d13342 · outbound
This paper cites Clarkson, Herbert Edelsbrunner, Leonidas J.
Erd\H{o}s's unit distance problem and rigidity Clarkson, Herbert Edelsbrunner, Leonidas J
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:16.698525Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation da0044ca-c6cf-4716-aebf-546bca93caf1 · outbound
This paper cites On sets of distances of n points.
Erd\H{o}s's unit distance problem and rigidity On sets of distances of n points
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:16.319211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f1532bd6-1102-485a-bdeb-08f70397a7b4 · outbound
This paper cites On sets of distances of n points in Euclidean space.
Erd\H{o}s's unit distance problem and rigidity On sets of distances of n points in Euclidean space
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:15.989120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1b6e8f85-869e-449a-938b-4004c18d4134 · outbound
This paper cites The Erdos Distance Problem.
Erd\H{o}s's unit distance problem and rigidity The Erdos Distance Problem
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:15.665768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3b355de9-f6b3-40f6-805d-0e69d1e88d52 · outbound
This paper cites Polynomial partitioning for a set of varieties.
Erd\H{o}s's unit distance problem and rigidity Polynomial partitioning for a set of varieties
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:15.323966Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7a08219f-bb94-4354-bbe7-aa0a4a823f88 · outbound
This paper cites Polynomial Methods in Combinatorics.
Erd\H{o}s's unit distance problem and rigidity Polynomial Methods in Combinatorics
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:15.027944Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 410fcf6c-f2a0-443b-a2c9-b6fe72a81f9b · outbound
This paper cites On the Erd˝ os distinct distances problem in the plane.
Erd\H{o}s's unit distance problem and rigidity On the Erd˝ os distinct distances problem in the plane
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:14.763550Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 842a5739-52d0-4a91-a10c-8e372c51cc5a · outbound
This paper cites A new entropy inequality for the Erd˝ os distance problem.
Erd\H{o}s's unit distance problem and rigidity A new entropy inequality for the Erd˝ os distance problem
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:14.495271Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3460a3c5-8959-4183-9c2b-a5edc92d11aa · outbound
This paper cites Springer Science & Business Media, 2013.
Erd\H{o}s's unit distance problem and rigidity Springer Science & Business Media, 2013
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:14.283992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6546b114-4ca0-460f-95c0-9bc3c8604070 · outbound
This paper cites Milnor, On the Betti numbers of real varieties, Proc.
Erd\H{o}s's unit distance problem and rigidity Milnor, On the Betti numbers of real varieties, Proc
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:13.972521Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4c24844c-4252-4225-8fd4-c0c2cbeb9b7d · outbound
This paper cites On the different distances determined by n points.
Erd\H{o}s's unit distance problem and rigidity On the different distances determined by n points
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:13.731622Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9e35ab8c-0132-4113-b040-0a473e17d9ea · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:13.470337Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9a3559b5-851b-41c9-b9f4-278b91db75b1 · outbound
This paper cites Forbidden paths and cycles in ordered graphs and matrices.
Erd\H{o}s's unit distance problem and rigidity Forbidden paths and cycles in ordered graphs and matrices
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:13.219614Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 43870ff4-9ae1-4bac-a81e-d310440eb2eb · outbound
This paper cites Raz and J´ ozsef Solymosi.
Erd\H{o}s's unit distance problem and rigidity Raz and J´ ozsef Solymosi
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:13.061296Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bba84abe-fbf9-4999-81ba-b548779dee4e · outbound
This paper cites Rational distances with rational angles.
Erd\H{o}s's unit distance problem and rigidity Rational distances with rational angles
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:12.872812Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b9569365-cda0-4fd9-a968-cb2e34fe1a92 · outbound
This paper cites Using the subspace theorem to bound unit distances, Mosc.
Erd\H{o}s's unit distance problem and rigidity Using the subspace theorem to bound unit distances, Mosc
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:12.673646Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 325d0713-4d6e-4b7b-9431-8a37826579f4 · outbound
This paper cites Classification of maps sending lines into translates of a curve, Linear Algebra and its Applications , Volume 668, 2023, 161-172,.
Erd\H{o}s's unit distance problem and rigidity Classification of maps sending lines into translates of a curve, Linear Algebra and its Applications , Volume 668, 2023, 161-172,
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:12.426324Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8058e8df-bac7-47d6-8a04-b18c164ea19b · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:12.228447Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d6c7f02a-3312-4701-a920-f9db214d3fd2 · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:12.091348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c2f5bef5-d145-4ae6-a401-7407978fa6bf · outbound
This paper cites Crossing numbers and hard Erd˝ os problems in discrete geometry.Com- binatorics, Probability and Computing 6, no.
Erd\H{o}s's unit distance problem and rigidity Crossing numbers and hard Erd˝ os problems in discrete geometry.Com- binatorics, Probability and Computing 6, no
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:11.837531Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 48f2ccfb-bcda-4a48-9b9f-ff9bdb6b4d8c · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:11.601446Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c8c03afb-353e-45bf-8b95-e21b5c2d4664 · outbound
This paper cites Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory.
Erd\H{o}s's unit distance problem and rigidity Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:49:11.368281Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation da8a4815-0db0-4a57-acb4-fade70029842 · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:11.096822Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7777ef97-5925-4655-9060-6fc399b48706 · outbound
This paper cites an unresolved cited work.
Erd\H{o}s's unit distance problem and rigidity Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:49:10.873919Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.