Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-16T11:35:30.434600Z
Paper Citation Record · LEDGER
On commuting integer matrices
As of 21 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 2 inbound Pith citation observations for arXiv:2504.15839.
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 2026-08-21T06:32:19.484+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-21T22:58:45.700030Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T23:00:43.625062Z
Reference resolution
20 of 20 outbound references displayed
- verified exact0
- verified fuzzy5
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 7a1ae14a-0ce1-4f09-9aa7-54573edffb33 · outbound
This paper cites A uniform formula on the number of integer matrices with given determinant and height.
On commuting integer matrices A uniform formula on the number of integer matrices with given determinant and height
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.359479Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c9dec34e-0503-4f82-8eea-9d37ebb4ccc5 · outbound
This paper cites Apostol, Introduction to analytic number theory , Undergraduate Texts in Mathematics, Springer- Verlag, New York-Heidelberg, 1976.
On commuting integer matrices Apostol, Introduction to analytic number theory , Undergraduate Texts in Mathematics, Springer- Verlag, New York-Heidelberg, 1976
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:35:30.727761Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 9053a4ba-8183-46cf-b050-39f7d718b443 · outbound
This paper cites Basili, On the irreducibility of varieties of commuting matrices , J.
On commuting integer matrices Basili, On the irreducibility of varieties of commuting matrices , J
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:35:30.714177Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 9003c9fa-58f1-44ca-aaed-219c5c7d694c · outbound
This paper cites Browning, W.
On commuting integer matrices Browning, W
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.372332Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d49cd57e-39c9-4186-a117-cc2b45f2e2b3 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.698702Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 83df5b78-d22a-41fa-9e69-4fd21faacbf6 · outbound
This paper cites Erd˝ os, P.
On commuting integer matrices Erd˝ os, P
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.380066Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation caa631b0-5138-47e7-9e45-ab23f2c94cbb · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.383853Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2c46e059-2693-45d3-a17b-80c12d4732cc · outbound
This paper cites Lattice points on determinant surfaces and the spectrum of the automorphic Laplacian.
On commuting integer matrices Lattice points on determinant surfaces and the spectrum of the automorphic Laplacian
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.387441Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 989efd7f-2d5e-4635-93f4-affe7bd589c6 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.391588Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fe834ad2-25c7-412f-a969-978f5dddedb0 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.663669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6440bffa-e088-4e0d-a533-b1a2dd952631 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.649482Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 93be9471-2f94-4d68-858b-0ca844cdfd00 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.636869Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0f560f6d-282b-4d99-842a-0ba9781e7678 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.623569Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 7af3c605-2304-4fb2-b53d-a4d887338158 · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.611102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 40053dc6-167b-46fd-96b1-3507226feeab · outbound
This paper cites Motohashi, The binary additive divisor problem , Ann.
On commuting integer matrices Motohashi, The binary additive divisor problem , Ann
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:35:30.597347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 1a730b4e-b3a9-4a1d-9d91-ef5bce6acd4e · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-16T11:35:30.585623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation aee3de6a-9f22-4b40-86f1-c67f8ebc32cb · outbound
This paper cites On commuting pairs in arbitrary sets of 2x2 matrices.
On commuting integer matrices On commuting pairs in arbitrary sets of 2x2 matrices
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.422184Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cb35ad7c-e924-445e-86ac-a43706fb498a · outbound
This paper cites an unresolved cited work.
On commuting integer matrices Unresolved cited work
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-16T11:35:30.426284Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a377594-1bd1-4860-a671-b8fefbe2f043 · outbound
This paper cites Salberger, Counting rational points on projective varieties , Proc.
On commuting integer matrices Salberger, Counting rational points on projective varieties , Proc
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:35:30.567567Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 5e2f03ba-6a78-43d0-94d8-1fe8c64a1bc3 · outbound
This paper cites Solymosi, Bounding multiplicative energy by the sumset , Adv.
On commuting integer matrices Solymosi, Bounding multiplicative energy by the sumset , Adv
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-16T11:35:30.555899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Pith citing papers
Observation 4aea16b8-2aae-476c-9664-1833ad4be115 · inbound
Counting $2 \times 2$ integer matrices with a given determinant cites this paper.
Counting $2 \times 2$ integer matrices with a given determinant On commuting integer matrices
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-05-21T23:00:43.628134Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 79203461-69f9-42e3-b7ed-77d1fc7aa76c · inbound
Counting solutions to the quadratic determinant equation cites this paper.
Counting solutions to the quadratic determinant equation On commuting integer matrices
Reference 3
- Resolution
- verified exact
- arxiv_id, observed 2026-05-19T14:57:36.526846Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.