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Paper Citation Record · LEDGER

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation

As of 9 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2506.04638.

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

pith.paper-citation-record.v1
2506.04638 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:48:08.323387Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:26:50.047589Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T04:26:50.921386Z

Reference resolution

16 of 16 outbound references displayed

  • verified exact0
  • verified fuzzy5
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6a6a569c-6352-4992-b31d-af8136ad94c7 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.583864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.257329Z digest=sha256:140c20da035d725cad7bdb55181f67aad3eae4b2935de699fa0fec800335efc0

Observation b150e95e-5159-4347-aaff-39cf839ea5e8 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.571043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.262392Z digest=sha256:39a559d33f3d15eb7b297321633d41feb2e22b4dc7d4726af7fada58f21a949d

Observation d41aa24e-f0ba-40c4-9094-0f9b91cc87ec · outbound

This paper cites et al., Higher transcendental functions, vol I,II, R.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation et al., Higher transcendental functions, vol I,II, R

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:48:08.555958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.269484Z digest=sha256:6808aae8ef1cc57fa1e9b62c1d37ac9bd5fc5b270ba4699c767ad3eba32a35e7

Observation e963bc87-644f-48e6-8bfd-b43c13d08661 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.541339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.273426Z digest=sha256:530cf56fcce039261921ea4ab100fcf31e3c9eff3d76408646cb329eb48e8d47

Observation ebb1a867-1445-4dd9-8385-9e4e2511e3f6 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.525934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.277490Z digest=sha256:f216f1c60109f5750aa8998bc6ad2addc88e10570e1e4616631998cfa6984b40

Observation 54140907-1947-4458-aa79-d6c29bc5e66d · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.512200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.282419Z digest=sha256:f30b5e999bc90f2a85d1bcec26bf9a7f03df7ca7794d8b10536d0578699e8515

Observation 71c48385-672b-4cb3-a3d7-975b8e4f2fff · outbound

This paper cites Yoshida, M., From Gauss to Painlevé, Vieweg Verlag, (1991).

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Yoshida, M., From Gauss to Painlevé, Vieweg Verlag, (1991)

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:48:08.493425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.287289Z digest=sha256:9ad7bced9dd5b10a6980e07ecf97cb843fb74ae887784bce99c652445c69cb53

Observation ca7eff00-0b2b-4ee9-b38a-01ae73135ac8 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.479834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.291298Z digest=sha256:1fe3e7dea6ec3cd47140b1b0a8ff6658d2e815440c7fec971af4cf078d6e5d77

Observation 958a0f8b-a80f-4ba7-b27a-28220d75f9e6 · outbound

This paper cites Kimura, Y.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Kimura, Y

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:48:08.464638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.295352Z digest=sha256:240065595017ba8eb2fe2e2b500ff4f11d4e78150d095deb61fd772a8cdee0f7

Observation 7816b831-0431-4ca3-93c1-93a9ad31e36d · outbound

This paper cites Japan Acad.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Japan Acad

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:48:08.450811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.299107Z digest=sha256:d64520521be00a1e1df157d36df2559cb5eebb850b1a9faf14442410374108c4

Observation d7c855c0-f0dc-4ae7-bd4d-dcc2662f0061 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.430751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.303179Z digest=sha256:93750c43897d86bfc62d3abea92bb0ec636641bc798ae12d0c1fd49961dc1fe0

Observation dfc669ee-be3a-4356-bb3a-c0349d3c1803 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.415624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.306822Z digest=sha256:757957e16e803f0c3e2ca32407156202448c71f85ad634f256c5b11ef635ba88

Observation 57cb5714-f8fe-4791-954a-b3f52c5ea7f1 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.402302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.310579Z digest=sha256:a98a0842c3222a851fc52777a89acb835418c0c9c33f0a3ae3c4d6c6a9619667

Observation e453041e-36e6-496a-970e-ffc2bbf94ba8 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.388024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.314551Z digest=sha256:4f7ec072d2e96413401446897e87cf573e07f3e04c430091ac409bf1c27a49cd

Observation 54b1a508-d3e1-40e2-ad7a-539b10d8e454 · outbound

This paper cites an unresolved cited work.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:48:08.371796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.319601Z digest=sha256:0a4ecb46b61ece8ff1cdc92928734ecb960fad7613adb8a6142a009d40e25f92

Observation d0df2a7b-07a2-4e15-b296-8016e6d33a5f · outbound

This paper cites Physics Letters A 236 (1997) 21-29.

Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation Physics Letters A 236 (1997) 21-29

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:48:08.357464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T10:48:08.323387Z digest=sha256:c09cf238f7b09039bd38434eb31bb832e13b0a7f370fc3a5cd4556dd6b493a12

Pith citing papers

Observation be941e23-4c41-4d90-a725-4f4001f6b82e · inbound

Gelfand hypergeometric functions as solutions to the 2-dimensional Toda-Hirota equations II cites this paper.

Gelfand hypergeometric functions as solutions to the 2-dimensional Toda-Hirota equations II Gelfand hypergeometric function as a solution to the 2-dimensional Toda-Hirota equation

Reference 9

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:26:51.100557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-07T04:26:50.047589Z digest=sha256:f02a8a70ac12acc2920b4689de6fa2062a30170f0e541883cbbf4f3ba6c9e898