Paper Citation Record · LEDGER

Upper cluster structure on Kac--Moody Richardson varieties

As of 10 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 3 inbound Pith citation observations for arXiv:2506.10382.

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

pith.paper-citation-record.v1
2506.10382 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:42:07.812550Z

measured 41 of 41 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T00:12:31.555868Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T20:10:07.067821Z

Reference resolution

38 of 38 outbound references displayed

verified exact0
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External citation measurements

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Outbound references

Observation a7e552f3-e2bf-4e77-906e-99c500804f35 · outbound

This paper cites Bao and X.

Upper cluster structure on Kac--Moody Richardson varieties Bao and X

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.968144Z

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.

Observation 13ace924-4bf6-4385-b480-2b64afcbf07c · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:12.848596Z

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

Observation 5062e82b-6c25-45b0-856d-001124ca21ba · outbound

This paper cites Total positivity in twisted product of flag varieties.

Upper cluster structure on Kac--Moody Richardson varieties Total positivity in twisted product of flag varieties

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:04.542438Z

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Unavailable: canonical work link unavailable.

Observation b86fc1a2-7c4e-47f4-8a46-32b2ecddd3ea · outbound

This paper cites Berenstein, S.

Upper cluster structure on Kac--Moody Richardson varieties Berenstein, S

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.735415Z

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.

Observation 045223ea-5eb7-40ef-9f54-41c64f0f87b7 · outbound

This paper cites Casals, E.

Upper cluster structure on Kac--Moody Richardson varieties Casals, E

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.599767Z

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

Observation cca72710-8415-497d-b856-355aee41d395 · outbound

This paper cites Comparing cluster algebras on braid varieties.

Upper cluster structure on Kac--Moody Richardson varieties Comparing cluster algebras on braid varieties

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:04.807178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 815ec3e5-8c57-473e-91df-ba1f27abaae3 · outbound

This paper cites Cerulli Irelli, B.

Upper cluster structure on Kac--Moody Richardson varieties Cerulli Irelli, B

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.487431Z

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

Observation 7cf4e455-7d92-45c4-bd0d-7b6a092b2336 · outbound

This paper cites Demonet and B.

Upper cluster structure on Kac--Moody Richardson varieties Demonet and B

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.347726Z

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

Observation b30f5821-97e4-41db-af4a-1b4396fac984 · outbound

This paper cites Deodhar, On some geometric aspects of Bruhat orderings.

Upper cluster structure on Kac--Moody Richardson varieties Deodhar, On some geometric aspects of Bruhat orderings

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:12.250813Z

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

Observation 0f7f1ced-665e-43dd-bf79-5ae561383467 · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:12.097830Z

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

Observation 288a8c29-e74f-4347-a3e4-d431e0a8f9ac · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:11.944643Z

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

Observation 046a0997-45b0-4f98-af9a-42e50cc4d098 · outbound

This paper cites Introduction to Cluster Algebras. Chapter 6.

Upper cluster structure on Kac--Moody Richardson varieties Introduction to Cluster Algebras. Chapter 6

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:05.385599Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8384563-47d4-4836-bdc6-8080d9b63f7f · outbound

This paper cites Fomin and A.

Upper cluster structure on Kac--Moody Richardson varieties Fomin and A

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:11.771521Z

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

Observation 10c9c37d-985a-47f2-8f86-c0ac7aa3ded8 · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:05.602842Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d79dfb3-b5d0-4ef1-88f5-f194b88a9015 · outbound

This paper cites Fraser, Quasi-homomorphisms of cluster algebras , Adv.

Upper cluster structure on Kac--Moody Richardson varieties Fraser, Quasi-homomorphisms of cluster algebras , Adv

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:11.574152Z

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.

Observation f79a7309-898d-4480-8c6c-ef54c452924a · outbound

This paper cites Galashin and T.

Upper cluster structure on Kac--Moody Richardson varieties Galashin and T

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:05.785360Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac178cea-bfdf-4291-9ce7-965552cf565c · outbound

This paper cites Braid variety cluster structures, I: 3D plabic graphs.

Upper cluster structure on Kac--Moody Richardson varieties Braid variety cluster structures, I: 3D plabic graphs

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:05.877783Z

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Unavailable: canonical work link unavailable.

Observation 7dddb7db-5b53-4d80-bc19-a354d66e2208 · outbound

This paper cites Galashin, T.

Upper cluster structure on Kac--Moody Richardson varieties Galashin, T

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:05.961041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 230d0dbf-4349-4b86-bbf9-a79771f216a2 · outbound

This paper cites Geiss, B.

Upper cluster structure on Kac--Moody Richardson varieties Geiss, B

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:11.386828Z

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.

Observation 6ac33c36-4778-4e0c-b175-205fe1469dc1 · outbound

This paper cites Gross, P.

Upper cluster structure on Kac--Moody Richardson varieties Gross, P

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:11.230484Z

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.

Observation a06e4211-349a-49a8-bd38-e6391caa865d · outbound

This paper cites Quantum geometry of moduli spaces of local systems and representation theory.

Upper cluster structure on Kac--Moody Richardson varieties Quantum geometry of moduli spaces of local systems and representation theory

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:06.290009Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53970815-7db7-4e34-a5ca-f081211fdd7d · outbound

This paper cites Gekhtman, M.

Upper cluster structure on Kac--Moody Richardson varieties Gekhtman, M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:11.061582Z

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.

Observation 399439e9-afd2-4e6b-8c6b-7ab26f94f610 · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:10.921076Z

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

Observation 4a7b659b-56f9-4367-8a57-01dfed39bd1e · outbound

This paper cites Kashiwara, M.

Upper cluster structure on Kac--Moody Richardson varieties Kashiwara, M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:10.761479Z

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

Observation c0ce49d9-2f7e-486c-a04c-fed067255d6c · outbound

This paper cites Kazhdan and G.

Upper cluster structure on Kac--Moody Richardson varieties Kazhdan and G

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:10.608599Z

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

Observation a396e448-9b05-4a78-a598-6565342397e6 · outbound

This paper cites Kumar, Kac–Moody groups, their flag varieties and representation theory , Progress in Mathematics, vol.

Upper cluster structure on Kac--Moody Richardson varieties Kumar, Kac–Moody groups, their flag varieties and representation theory , Progress in Mathematics, vol

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:10.418510Z

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

Observation 63778259-88f7-4579-84fc-2a17118910a3 · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:10.208750Z

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

Observation 9d27269e-ff2e-4320-9743-07431b5cae5b · outbound

This paper cites Knutson, A.

Upper cluster structure on Kac--Moody Richardson varieties Knutson, A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:09.898460Z

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

Observation 58f02785-e4d0-4eb1-8ebd-a86428b240fa · outbound

This paper cites Leclerc, Cluster structures on strata of flag varieties , Adv.

Upper cluster structure on Kac--Moody Richardson varieties Leclerc, Cluster structures on strata of flag varieties , Adv

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:09.627332Z

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.

Observation d09b9dcd-51cf-4904-bfca-d07e592e0c75 · outbound

This paper cites Lusztig, Total positivity in reductive groups, Lie theory and geometry, Progr.

Upper cluster structure on Kac--Moody Richardson varieties Lusztig, Total positivity in reductive groups, Lie theory and geometry, Progr

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:09.364190Z

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.

Observation e3ebb8c6-24db-447f-bf64-0c535b72bc85 · outbound

This paper cites an unresolved cited work.

Upper cluster structure on Kac--Moody Richardson varieties Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:42:09.174315Z

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

Observation e7f9d789-736d-429b-a10b-8a9dd80cc315 · outbound

This paper cites Muller, Locally acyclic cluster algebras , Adv.

Upper cluster structure on Kac--Moody Richardson varieties Muller, Locally acyclic cluster algebras , Adv

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:08.961329Z

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.

Observation 82c670ef-d50c-4f80-9bde-7af91b36f01f · outbound

This paper cites Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds.

Upper cluster structure on Kac--Moody Richardson varieties Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:07.371443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8d0c1a0-99a5-4a21-8513-390602ee5cf7 · outbound

This paper cites Muller, The existence of a maximal green sequence is not invariant under quiver mutation , Electron.

Upper cluster structure on Kac--Moody Richardson varieties Muller, The existence of a maximal green sequence is not invariant under quiver mutation , Electron

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:08.731497Z

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

Observation 8c5bb030-05f9-4c2f-8186-8cdcb04e7ccd · outbound

This paper cites Serhiyenko and M.

Upper cluster structure on Kac--Moody Richardson varieties Serhiyenko and M

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T04:42:07.561114Z

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Unavailable: canonical work link unavailable.

Observation 7c14b12b-ac35-408a-99c4-7f0b0c207c11 · outbound

This paper cites Shen and D.

Upper cluster structure on Kac--Moody Richardson varieties Shen and D

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:08.515692Z

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

Observation f0d0bf14-7cd3-4d30-811b-072572722b2b · outbound

This paper cites Tits, Uniqueness and presentation of Kac–Moody groups over fields, J.

Upper cluster structure on Kac--Moody Richardson varieties Tits, Uniqueness and presentation of Kac–Moody groups over fields, J

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:08.365259Z

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

Observation c0aa4f8f-a7c8-4f60-bf8c-8ad39e844fb7 · outbound

This paper cites Williams, Cluster ensembles and Kac–Moody groups , Adv.

Upper cluster structure on Kac--Moody Richardson varieties Williams, Cluster ensembles and Kac–Moody groups , Adv

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:42:08.177580Z

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

Pith citing papers

Observation 24296d17-5a05-4a9b-a038-466d0f4b5fd1 · inbound

Towards Monoidal Categorifications of Twisted Products of Flag Varieties cites this paper.

Towards Monoidal Categorifications of Twisted Products of Flag Varieties Upper cluster structure on Kac--Moody Richardson varieties

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T00:12:31.555868Z

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Unavailable: canonical work link unavailable.

Observation dd9849d6-96bc-49e3-8de1-adcaedb904d8 · inbound

Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type cites this paper.

Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type Upper cluster structure on Kac--Moody Richardson varieties

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-04T20:10:07.069956Z

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

Observation 36aaaf8b-ee2c-49d4-a268-280c5437b51f · inbound

Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts cites this paper.

Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts Upper cluster structure on Kac--Moody Richardson varieties

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T13:46:59.537869Z

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.