Paper Citation Record · LEDGER

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions

As of 15 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2507.13645.

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

pith.paper-citation-record.v1
2507.13645 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:28:11.074253Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

23 of 23 outbound references displayed

verified exact1
verified fuzzy10
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f74e33cd-13c8-4455-a297-c8acd7052471 · outbound

This paper cites Adiga, B.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Adiga, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:16.060925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ab9ba5f8-fae8-4119-adf7-59d4fc3af358 · outbound

This paper cites Adiga and N.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Adiga and N

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:15.893890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4407020c-4cd6-4a66-a346-ff7037aa7cc7 · outbound

This paper cites Bosma and B.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Bosma and B

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:15.713650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 59b40a37-31e0-4798-b40c-6003cc4d03dd · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:15.565715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed880bbd-e789-4606-94b4-d4899f2eee01 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:15.434247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4fff1456-c8d1-404d-9c35-643886fa8eac · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:15.149092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 237e5db3-2228-4adc-b3d4-e9c0350f6c8f · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:14.876204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 87c50c34-f6d7-4607-b7de-2e8a95c908fe · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:14.575059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8aec3ef7-4726-43aa-9cbf-c9cc03101a70 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:14.203683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5e42f2ab-b89b-4552-891a-a84c59fab672 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:13.877978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2c94b883-957f-4e0e-8e11-81b926669ed0 · outbound

This paper cites Ju, Universal sums of generalized pentagonal numbers, Ramanujan J.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Ju, Universal sums of generalized pentagonal numbers, Ramanujan J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:13.628585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b0a65df6-d228-459a-b26c-e8a04458ab0f · outbound

This paper cites Ju and B.-K.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Ju and B.-K

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:13.435289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c48ad803-1331-4c46-9262-e9dbc04b3cb0 · outbound

This paper cites Ju and B.-K.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Ju and B.-K

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:13.234733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4ed4a1d8-45c9-4091-a125-68b13d6c06ba · outbound

This paper cites Kamaraj, B.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Kamaraj, B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:13.002289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f857ebf7-0165-4f56-bf3f-dffcb4d25603 · outbound

This paper cites Krachun And Z.-W.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Krachun And Z.-W

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:12.753049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4e8fe0e7-e1ca-4f43-8218-8302560fb103 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:12.566491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 92808134-19d8-4a44-8266-377e4b019de1 · outbound

This paper cites Ramanujan, On the expression of a number in the form ax2 +by2 +cz2 +dw2, Math.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Ramanujan, On the expression of a number in the form ax2 +by2 +cz2 +dw2, Math

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:12.426211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 33a14201-65ee-41d7-a1a6-ea62656f7e5d · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:12.271516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 58dae39f-5b2e-4368-98c1-087cfa6a68ce · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:12.016763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0e25db54-92d5-4cc9-8814-4eae578d3e17 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:11.798170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 11dfe51d-1338-49f5-912a-5dd66b974500 · outbound

This paper cites New results similar to Lagrange's four-square theorem.

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 2026-08-14T06:32:32.682623+00:00.

Observation 19b23c56-ce03-4175-8384-87aecb100712 · outbound

This paper cites an unresolved cited work.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:28:11.611314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b59d97d1-49f1-4ac5-bfbf-e3e757bec2e3 · outbound

This paper cites Yang, Universal sums of triangular numbers and squares, J.

Universal quaternary mixed sums involving generalized 3-, 4-, 5- and 8-gonal numbers via products of Ramanujan's theta functions Yang, Universal sums of triangular numbers and squares, J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:28:11.420166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.