Paper Citation Record · LEDGER

Tangent Spheres and Integer Distances

As of 18 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2606.18569.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.18569 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T18:59:58.177328Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

13 of 13 outbound references displayed

verified exact9
verified fuzzy0
unresolved3
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation caebdddd-d8ab-43f5-aa20-78539b98573d · outbound

This paper cites Abel and James W.

Tangent Spheres and Integer Distances Abel and James W

Reference 1

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.564817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f13bbaaf-ddfd-4daa-8938-7725268f489d · outbound

This paper cites Anning and Paul Erdős.

Tangent Spheres and Integer Distances Anning and Paul Erdős

Reference 2

Resolution: malformed identifier; no resolver link, observed 2026-06-26T18:59:58.177328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bf645e1-6402-4484-a6c6-dfdb456beb7e · outbound

This paper cites an unresolved cited work.

Tangent Spheres and Integer Distances Unresolved cited work

Reference 3

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.569660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c24dd096-6ebb-47a2-8ace-ca727048efb2 · outbound

This paper cites Chandru, D.

Tangent Spheres and Integer Distances Chandru, D

Reference 4

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.570352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 05645671-6723-4b53-8415-30ce1fff367a · outbound

This paper cites an unresolved cited work.

Tangent Spheres and Integer Distances Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T18:59:58.177328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1851bed2-8cd8-4b4a-97fc-170ea6fabbbd · outbound

This paper cites A Möbius-invariant power dia- gram and its applications to soap bubbles and planar Lombardi drawing.Discrete & Compu- tational Geometry, 52(3):515–550, 2014.doi:10.

Tangent Spheres and Integer Distances A Möbius-invariant power dia- gram and its applications to soap bubbles and planar Lombardi drawing.Discrete & Compu- tational Geometry, 52(3):515–550, 2014.doi:10

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T18:59:58.177328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b9a378b-0ac5-4df3-9876-82e840c53c04 · outbound

This paper cites Bipartite and series-parallel graphs without planar Lombardi drawings.J.

Tangent Spheres and Integer Distances Bipartite and series-parallel graphs without planar Lombardi drawings.J

Reference 7

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.565756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 68f6f431-e0b7-45bd-b314-e31ba42ea8d8 · outbound

This paper cites Non-Euclidean Erdős–Anning the- orems.J.

Tangent Spheres and Integer Distances Non-Euclidean Erdős–Anning the- orems.J

Reference 8

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.571899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 49bf991d-d635-495a-a93f-384e5bb9f23c · outbound

This paper cites Integral distances.Bulletin of the American Mathematical Society, 51:996.

Tangent Spheres and Integer Distances Integral distances.Bulletin of the American Mathematical Society, 51:996

Reference 9

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.571415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bd76d3d0-e118-4ede-86cc-1ffe3406f49d · outbound

This paper cites On integer distance sets.

Tangent Spheres and Integer Distances On integer distance sets

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-07-04T02:49:25.112435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c7108fc8-0310-479b-8099-aec7eef6fa1b · outbound

This paper cites Chelsea Publishing, 1952.

Tangent Spheres and Integer Distances Chelsea Publishing, 1952

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T18:59:58.177328Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34240f5d-2a01-439e-b7b9-5b26bcbf31ed · outbound

This paper cites Convex distance functions in 3-space are different.Fundamenta Informaticae, 22(4):331–352, 1995.doi:10.3233/FI-1995-2242.

Tangent Spheres and Integer Distances Convex distance functions in 3-space are different.Fundamenta Informaticae, 22(4):331–352, 1995.doi:10.3233/FI-1995-2242

Reference 12

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.566841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 783ba9a7-5c34-4e20-85cf-04348f55b367 · outbound

This paper cites Noteonintegraldistances.Discrete & Computational Geometry, 30(2):337–342, 2003.

Tangent Spheres and Integer Distances Noteonintegraldistances.Discrete & Computational Geometry, 30(2):337–342, 2003

Reference 13

Resolution: verified exact; doi, observed 2026-06-26T19:19:48.568750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.