Paper Citation Record · LEDGER

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian

As of 23 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2505.02941.

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

pith.paper-citation-record.v1
2505.02941 v3

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:53:36.904374Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T20:11:46.988377Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T22:10:48.617131Z

Reference resolution

30 of 30 outbound references displayed

verified exact4
verified fuzzy15
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16f8e0df-2cda-49e0-9506-fc621272071f · outbound

This paper cites On the quantum K-ring of the flag manifold.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian On the quantum K-ring of the flag manifold

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:53:37.284489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 097ceb99-08bd-49d8-b9ff-8626b38da924 · outbound

This paper cites Blasiak, J.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Blasiak, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:38.152636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 05e8c584-aba9-4453-a9b6-b9b425044386 · outbound

This paper cites Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Quantum $K$-theory of $G/P$ and $K$-homology of affine Grassmannian

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T00:53:36.583498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f522a35f-0fb1-42dd-a309-baa823bec2bd · outbound

This paper cites Ginzburg.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Ginzburg

Reference 4

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:53:37.240114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 68585f29-f9ee-4638-8827-c11b72d9d579 · outbound

This paper cites Givental and B.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Givental and B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:38.138817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3f4a52dd-f8fc-44b1-b4f7-ca921eaf90f3 · outbound

This paper cites Ikeda, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Ikeda, S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:38.121760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b6fab5ec-01e9-44e1-b5bc-4bcbce030cca · outbound

This paper cites Ikeda, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Ikeda, S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:38.102407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 32cf3078-6771-4e53-adea-255de9b5cee5 · outbound

This paper cites Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Equivariant $K$-homology of affine Grassmannian and $K$-theoretic double $k$-Schur functions

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:53:37.117213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4d364b09-45d1-46ea-ac6d-69084cc1ce0d · outbound

This paper cites Kato, Frobenius splitting of Schubert varieties of semi-infinite flag manifolds, Forum of Mathematics, Vol 9 P e5, (2021).

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Kato, Frobenius splitting of Schubert varieties of semi-infinite flag manifolds, Forum of Mathematics, Vol 9 P e5, (2021)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:38.087913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8a82622b-558d-4d67-ad21-6f18d79972e4 · outbound

This paper cites Loop structure on equivariant $K$-theory of semi-infinite flag manifolds.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Loop structure on equivariant $K$-theory of semi-infinite flag manifolds

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T00:53:36.679881Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa71bc7f-201a-4fde-ad68-d7466a0ab1b9 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:38.033178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b2253a85-0044-4e89-863c-d323fe8bd4d1 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.899670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d6ba4867-1a48-49a6-b950-ad10901353e7 · outbound

This paper cites Ishii, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Ishii, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.796281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b259e337-90ce-4a39-9758-078650a6feaf · outbound

This paper cites Kouno, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Kouno, S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.744136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d10357a7-5f6a-4710-b5df-ac4f1b64dec0 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.731857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0859e98f-9c9d-442d-ac58-b4b3c80cfd48 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.718969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3b342a09-80a6-4db6-b9e8-6ef4a697ad6a · outbound

This paper cites Lenart, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Lenart, S

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.706098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 70bd5e15-efa7-44bb-8508-d22d6c3efcab · outbound

This paper cites Lam and M.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Lam and M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.688768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 990963d9-faa0-4d89-a19a-4c55d55e904f · outbound

This paper cites From double quantum Schubert polynomials to k-double Schur functions via the Toda lattice.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian From double quantum Schubert polynomials to k-double Schur functions via the Toda lattice

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:53:36.984318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 53b6db80-5ac3-4fc1-bff6-a7eea61c4cab · outbound

This paper cites Lam and M.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Lam and M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.547991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e7780535-0986-43d8-88e3-baaf783afdd5 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.536549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b503738d-19a7-43ab-94b8-11320217f75c · outbound

This paper cites Quantum Grothendieck Polynomials.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Quantum Grothendieck Polynomials

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T00:53:36.804603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da24bd65-c43c-4152-9a94-a8743ffc3ecb · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.522395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5e6e6499-101d-4482-8b8d-80f217e451c4 · outbound

This paper cites Maeno, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Maeno, S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.477364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 10305613-531d-4262-a543-e0e6ef16f91a · outbound

This paper cites Maeno, S.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Maeno, S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.419014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c68a7b44-a284-42bb-aded-a1de5d369465 · outbound

This paper cites Orr, EquivariantK-theory of the semi-infinite flag manifold as a nil-DAHA module, Selecta Mathematica (New Series), Vol.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Orr, EquivariantK-theory of the semi-infinite flag manifold as a nil-DAHA module, Selecta Mathematica (New Series), Vol

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.361130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3ae8f617-4478-4aaf-9c1e-5cc394c2b425 · outbound

This paper cites Peterson.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Peterson

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.340336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8f1dacba-52de-4ef1-b91d-80f70c33bd2b · outbound

This paper cites Takigiku, A Pieri formula and a factorization formula for sums ofK-theoretick-Schur functions.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Takigiku, A Pieri formula and a factorization formula for sums ofK-theoretick-Schur functions

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:53:37.327944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation acf1d327-8cfa-496a-9c53-0b228a1f9b03 · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.313279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 95a3d39e-30b8-4579-a4a4-8f5befc7443f · outbound

This paper cites an unresolved cited work.

Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:53:37.299344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation 3cc6dea5-3608-47e0-8463-74f6bdc16f18 · inbound

Relativistic Toda lattice of type B and quantum $K$-theory of type C flag variety cites this paper.

Relativistic Toda lattice of type B and quantum $K$-theory of type C flag variety Relativistic Toda Lattice and Equivariant $K$-Homology of Affine Grassmannian

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-07T04:17:53.466809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.