Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T15:30:15.106766Z
Paper Citation Record · LEDGER
New results similar to Lagrange's four-square theorem
As of 21 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2411.14308.
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 2026-08-06T16:28:10.867099Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T16:28:11.189108Z
Reference resolution
12 of 12 outbound references displayed
- verified exact1
- verified fuzzy8
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation aebac38f-95dd-4acc-aafd-3f755e3ab7ff · outbound
This paper cites an unresolved cited work.
New results similar to Lagrange's four-square theorem Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T15:30:15.317835Z
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 af1d2aad-1fe7-44f9-9a91-881cc51cdb56 · outbound
This paper cites Krachun and Z.-W.
New results similar to Lagrange's four-square theorem Krachun and Z.-W
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.302195Z
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 2f895f7f-4d1d-4ec4-9f6d-eab77e56c534 · outbound
This paper cites Sums of four polygonal numbers: precise formulas.
New results similar to Lagrange's four-square theorem Sums of four polygonal numbers: precise formulas
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T15:30:15.149404Z
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 64dbbf44-2f77-43c6-a3df-483cae95f676 · outbound
This paper cites Meng and Z.-W.
New results similar to Lagrange's four-square theorem Meng and Z.-W
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.286853Z
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 232d600a-cf56-44ac-bfce-861a3498fa85 · outbound
This paper cites an unresolved cited work.
New results similar to Lagrange's four-square theorem Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T15:30:15.272225Z
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 b2a8222b-dfb7-4796-a763-f2e3315b477d · outbound
This paper cites an unresolved cited work.
New results similar to Lagrange's four-square theorem Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T15:30:15.255710Z
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 0303819c-7268-4107-9988-162fc4eb8e39 · outbound
This paper cites Sun, On universal sums of polygonal numbers , Sci.
New results similar to Lagrange's four-square theorem Sun, On universal sums of polygonal numbers , Sci
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.240736Z
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 fd51ae74-fd9d-4ac3-9ca5-d57fce198436 · outbound
This paper cites Sun, A result similar to Lagrange’s theorem , J.
New results similar to Lagrange's four-square theorem Sun, A result similar to Lagrange’s theorem , J
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.223635Z
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 a36c7452-f6bc-42eb-92bb-d996d5cb103f · outbound
This paper cites Sun, On universal sums x(ax + b)/2 +y(cy + d)/2 +z(ez + f )/2, Nanjing Univ.
New results similar to Lagrange's four-square theorem Sun, On universal sums x(ax + b)/2 +y(cy + d)/2 +z(ez + f )/2, Nanjing Univ
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.208636Z
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 52931334-6f50-4d50-899b-05bff8a589bd · outbound
This paper cites Sun, Universal sums of three quadratic polynomia ls, Sci.
New results similar to Lagrange's four-square theorem Sun, Universal sums of three quadratic polynomia ls, Sci
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.194952Z
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 9be3c570-5787-470c-9260-c1d0daf55656 · outbound
This paper cites Sun, Sequence A377224 in OEIS (On-Line Encyclope dia of Integer Sequences), http://oeis.org/A377224.
New results similar to Lagrange's four-square theorem Sun, Sequence A377224 in OEIS (On-Line Encyclope dia of Integer Sequences), http://oeis.org/A377224
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.178894Z
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 f310afad-e6b9-4c63-a5d2-ece9f950bff8 · outbound
This paper cites Wu and Z.-W.
New results similar to Lagrange's four-square theorem Wu and Z.-W
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T15:30:15.164586Z
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 11dfe51d-1338-49f5-912a-5dd66b974500 · inbound
Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions cites this paper.
Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions New results similar to Lagrange's four-square theorem
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:28:11.253589Z
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.