Paper Citation Record · LEDGER

On Nathanson's Triangular Number Phenomenon

As of 12 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 5 inbound Pith citation observations for arXiv:2506.20836.

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

pith.paper-citation-record.v1
2506.20836 v2

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:50:27.147037Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:24:51.874790Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T16:06:46.078137Z

Reference resolution

11 of 11 outbound references displayed

verified exact3
verified fuzzy4
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d3326b50-cba0-45d4-b5d5-4971e64a2750 · outbound

This paper cites Nathanson.

On Nathanson's Triangular Number Phenomenon Nathanson

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T22:50:27.183221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 31777aae-1548-441d-b602-a3484df8bae0 · outbound

This paper cites Nathanson.

On Nathanson's Triangular Number Phenomenon Nathanson

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:50:27.319256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ea056733-6e95-4ac9-9727-b9a13fddb665 · outbound

This paper cites Nathanson.

On Nathanson's Triangular Number Phenomenon Nathanson

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:50:27.311407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d94c2698-fb41-402f-98bd-9e15311b86c0 · outbound

This paper cites Nathanson.

On Nathanson's Triangular Number Phenomenon Nathanson

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:50:27.303492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ca2d5053-9be3-4f38-9cdf-bb58b5e71552 · outbound

This paper cites Explicit sumset sizes in additive number theory.

On Nathanson's Triangular Number Phenomenon Explicit sumset sizes in additive number theory

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T22:50:27.132933Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df067b39-780f-449d-96d7-b1f092fd7105 · outbound

This paper cites Inverse problems for sumset sizes of finite sets of integers.

On Nathanson's Triangular Number Phenomenon Inverse problems for sumset sizes of finite sets of integers

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:50:27.270025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 44c38db0-1019-4df3-83f7-b9bcf742a25c · outbound

This paper cites Nathanson.

On Nathanson's Triangular Number Phenomenon Nathanson

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T22:50:27.138628Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c00a8def-3676-467c-b0e7-3cb31852b067 · outbound

This paper cites Triangular and tetrahedral number differences of sumset sizes in additive number theory.

On Nathanson's Triangular Number Phenomenon Triangular and tetrahedral number differences of sumset sizes in additive number theory

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T22:50:27.141336Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b9a2ead-81af-4a35-a8ae-9e83053fc260 · outbound

This paper cites Nathanson, Kevin O’Bryant, Brooke Orosz, Imre Ruzsa, and Manuel Silva.

On Nathanson's Triangular Number Phenomenon Nathanson, Kevin O’Bryant, Brooke Orosz, Imre Ruzsa, and Manuel Silva

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T22:50:27.174528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cae6259d-5b67-4c1d-a9c0-27591d49b02c · outbound

This paper cites Visualizing the sum-product conjecture, 2025.

On Nathanson's Triangular Number Phenomenon Visualizing the sum-product conjecture, 2025

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:50:27.295693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9f2e8ab6-cc81-4b21-b2a4-59eed8a919ed · outbound

This paper cites Compression and complexity for sumset sizes in additive number theory.

On Nathanson's Triangular Number Phenomenon Compression and complexity for sumset sizes in additive number theory

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-06T22:50:27.129701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 77065bc9-19d1-4279-bb34-01ebf30710dd · inbound

Explicit sumset sizes in additive number theory cites this paper.

Explicit sumset sizes in additive number theory On Nathanson's Triangular Number Phenomenon

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-22T16:06:46.081490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0e30685d-df5e-4aaf-8c3f-3a7bb4539f04 · inbound

Additive sumset sizes with tetrahedral differences cites this paper.

Additive sumset sizes with tetrahedral differences On Nathanson's Triangular Number Phenomenon

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T18:24:51.874790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e31ec5c-9fb3-4611-b668-32132d06b823 · inbound

Possible Sizes of Sumsets cites this paper.

Possible Sizes of Sumsets On Nathanson's Triangular Number Phenomenon

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T08:08:31.759393Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba500a58-08be-44b2-b2b3-aca5385e3b4d · inbound

Intersections of sumsets in additive number theory cites this paper.

Intersections of sumsets in additive number theory On Nathanson's Triangular Number Phenomenon

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-16T19:18:19.399535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2611ebb9-e44d-4f24-8602-d05b1944c085 · inbound

On the size of $h$-fold sumsets cites this paper.

On the size of $h$-fold sumsets On Nathanson's Triangular Number Phenomenon

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T05:13:31.232816Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.