Paper Citation Record · LEDGER

Triangular and tetrahedral number differences of sumset sizes in additive number theory

As of 15 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 5 inbound Pith citation observations for arXiv:2506.15015.

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

pith.paper-citation-record.v1
2506.15015 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T00:14:39.757173Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:50:27.141336Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-16T19:18:19.383081Z

Reference resolution

16 of 16 outbound references displayed

verified exact1
verified fuzzy2
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ecd6c652-cb37-444f-8df0-97ada35eac48 · outbound

This paper cites Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Hilbert's sixth problem: derivation of fluid equations via Boltzmann's kinetic theory

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:37.844606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba1a2435-d06c-41aa-898a-ac7ae7e2e4ae · outbound

This paper cites an unresolved cited work.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:14:41.057286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6b0bb302-9a39-4d73-8d5c-e54a27a40201 · outbound

This paper cites Kravitz, Relative sizes of iterated sumsets, J.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Kravitz, Relative sizes of iterated sumsets, J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.009667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed7a4116-f1fc-4a53-b312-5eb8f0c1fca1 · outbound

This paper cites an unresolved cited work.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:14:40.877977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5229b3d1-8b5c-4fa5-8629-7901dc6e62c1 · outbound

This paper cites an unresolved cited work.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T00:14:40.626630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation de09167a-bc22-4491-8a8e-ced22b6b88fa · outbound

This paper cites $B_h$-sets of real and complex numbers.

Triangular and tetrahedral number differences of sumset sizes in additive number theory $B_h$-sets of real and complex numbers

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.304917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45f9fde2-3259-40fe-8ab2-d5fce980d24d · outbound

This paper cites an unresolved cited work.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.401535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34a6ebc1-af8c-456b-b9f5-9482d07e1415 · outbound

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

Triangular and tetrahedral number differences of sumset sizes in additive number theory Inverse problems for sumset sizes of finite sets of integers

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.484034Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8ec9b2da-141b-4f16-8145-b7b2ad70ec1c · outbound

This paper cites ${\mathbf Q}$-independence and the construction of $B_h$-sets of integers and lattice points.

Triangular and tetrahedral number differences of sumset sizes in additive number theory ${\mathbf Q}$-independence and the construction of $B_h$-sets of integers and lattice points

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:14:40.119419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6c5c83b8-0b1e-473b-a18b-4e3912c93f93 · outbound

This paper cites Explicit sumset sizes in additive number theory.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Explicit sumset sizes in additive number theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.844472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33859a3e-35aa-4a43-aacf-b5943534c416 · outbound

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

Triangular and tetrahedral number differences of sumset sizes in additive number theory Compression and complexity for sumset sizes in additive number theory

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:38.999679Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1dbfa50-7c87-4f0f-a925-87f222ae3b80 · outbound

This paper cites O’Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron.

Triangular and tetrahedral number differences of sumset sizes in additive number theory O’Bryant, A complete annotated bibliography of work related to Sidon sequences, Electron

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:39.195785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cd32bb0-7737-442d-8038-a3e7d994782c · outbound

This paper cites A note on iterated sumsets races.

Triangular and tetrahedral number differences of sumset sizes in additive number theory A note on iterated sumsets races

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:39.352715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0abfde49-39a5-4734-a5d3-f0eb0fc7647f · outbound

This paper cites On the Sumset of Sets of Size $k$.

Triangular and tetrahedral number differences of sumset sizes in additive number theory On the Sumset of Sets of Size $k$

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T00:14:39.482142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81b6837d-326c-4e17-bc63-4ed52da9affd · outbound

This paper cites Sloman, Epic effort to ground physics in math opens up the secrets of time, Quanta Magazine, June 11, 2025.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Sloman, Epic effort to ground physics in math opens up the secrets of time, Quanta Magazine, June 11, 2025

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:14:40.464935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 3bc84dd4-9fce-4602-ae9b-9b3aef04494a · outbound

This paper cites Tao and V.

Triangular and tetrahedral number differences of sumset sizes in additive number theory Tao and V

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T00:14:40.307872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

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

On Nathanson's Triangular Number Phenomenon cites this paper.

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 340c6ff3-6d10-4ad9-ae80-65b830fbc412 · inbound

Additive sumset sizes with tetrahedral differences cites this paper.

Additive sumset sizes with tetrahedral differences Triangular and tetrahedral number differences of sumset sizes in additive number theory

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T18:24:51.766188Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82476f35-391d-4ab6-a658-e604d77a9151 · inbound

Possible Sizes of Sumsets cites this paper.

Possible Sizes of Sumsets Triangular and tetrahedral number differences of sumset sizes in additive number theory

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T08:08:31.488632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a6b0b01-59d3-4125-a96d-b33b364a7b6f · inbound

Intersections of sumsets in additive number theory cites this paper.

Intersections of sumsets in additive number theory Triangular and tetrahedral number differences of sumset sizes in additive number theory

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-16T19:18:19.384692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 48fa7952-524b-4f9f-b041-04c9fba2f48c · inbound

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

On the size of $h$-fold sumsets Triangular and tetrahedral number differences of sumset sizes in additive number theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T05:13:31.017169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.