Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T14:14:17.278587Z
Paper Citation Record · LEDGER
Link Crossing Number is NP-hard
As of 16 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:1908.04073.
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 2026-08-16T06:30:59.297886+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
10 of 10 outbound references displayed
- verified exact1
- verified fuzzy8
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 2e88c427-a349-4a36-baec-1552c08ecbf6 · outbound
This paper cites An upper bound on Reidemeis- ter moves.
Link Crossing Number is NP-hard An upper bound on Reidemeis- ter moves
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.422893Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 88404502-f911-4a83-a6d3-e231aaeedd1a · outbound
This paper cites Fox and John W.
Link Crossing Number is NP-hard Fox and John W
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.410062Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 64a7b9d5-e7b2-4a57-8751-5bab4e0eb9ba · outbound
This paper cites Lagarias, and Nicholas Pippenger.
Link Crossing Number is NP-hard Lagarias, and Nicholas Pippenger
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.397093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d8cab7ca-4f04-4949-b2e5-fc71f4d5ea1d · outbound
This paper cites The efficient certification of knottedness and Thurston norm.
Link Crossing Number is NP-hard The efficient certification of knottedness and Thurston norm
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T14:14:17.313834Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6cdac4de-d223-4c5a-a6d8-ef3c58c55151 · outbound
This paper cites Elementary knot theory.
Link Crossing Number is NP-hard Elementary knot theory
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.385186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation acfaba9f-b120-4d03-90d9-a0222c44243e · outbound
This paper cites Link groups.
Link Crossing Number is NP-hard Link groups
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.372929Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6f62f01f-6768-4ddb-b708-7637e72ec55e · outbound
This paper cites One sided crossing minimization is NP-hard for sparse graphs.
Link Crossing Number is NP-hard One sided crossing minimization is NP-hard for sparse graphs
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.361586Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 54ff8cfb-113e-4155-8c21-10dd15358491 · outbound
This paper cites The graph crossing number and its variants: A survey.
Link Crossing Number is NP-hard The graph crossing number and its variants: A survey
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.349325Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 91421fdf-ce59-4111-82aa-403a4339c3d8 · outbound
This paper cites A low and a high hierarchy within NP.
Link Crossing Number is NP-hard A low and a high hierarchy within NP
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T14:14:17.338197Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2f0db8a6-74bb-47c4-a7ab-0c00d82b4b25 · outbound
This paper cites an unresolved cited work.
Link Crossing Number is NP-hard Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T14:14:17.328186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.