Paper Citation Record · LEDGER

Cluster structures on Cox rings

As of 16 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 0 inbound Pith citation observations for arXiv:2412.04173.

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

pith.paper-citation-record.v1
2412.04173 v1

Coverage vector

measured 44 of 44 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-11T21:48:08.519130Z

measured 44 of 44 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

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Reference resolution

44 of 44 outbound references displayed

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verified fuzzy27
unresolved15
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Outbound references

Observation 7cac380e-364c-432f-895d-fc58700e2c91 · outbound

This paper cites Cox rings , volume 144 of Cambridge Studies in Advanced Mathematics.

Cluster structures on Cox rings Cox rings , volume 144 of Cambridge Studies in Advanced Mathematics

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.403145Z

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Observation 0114fa8d-0144-4b81-ac99-b2f744137be7 · outbound

This paper cites an unresolved cited work.

Cluster structures on Cox rings Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:48:08.902691Z

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Observation 5e5cbe5c-6261-44e1-b3c5-da21c3dd0fd5 · outbound

This paper cites Hacon, and James McKernan.

Cluster structures on Cox rings Hacon, and James McKernan

Reference 3

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Observation a62e476b-2a20-420c-8212-8a4922a2a4cf · outbound

This paper cites Newton- O kounkov bodies and minimal models for cluster varieties.

Cluster structures on Cox rings Newton- O kounkov bodies and minimal models for cluster varieties

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.891788Z

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Observation 95982d60-37f1-44f1-9fc8-3fdd8064d892 · outbound

This paper cites Cluster algebras.

Cluster structures on Cox rings Cluster algebras

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.415368Z

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Observation 8f8454b1-c3cb-4816-a166-91afa10edcc4 · outbound

This paper cites Upper cluster algebras and choice of ground ring.

Cluster structures on Cox rings Upper cluster algebras and choice of ground ring

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.879541Z

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Observation b5ac5ae7-0963-4b99-9f1c-6ba42493ea4e · outbound

This paper cites The valuation pairing on an upper cluster algebra.

Cluster structures on Cox rings The valuation pairing on an upper cluster algebra

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.871583Z

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Observation 08899efd-ba2f-4036-be28-5f0f49a8723b · outbound

This paper cites an unresolved cited work.

Cluster structures on Cox rings Unresolved cited work

Reference 8

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Observation df1fae87-0506-412c-b217-b24765b3b691 · outbound

This paper cites an unresolved cited work.

Cluster structures on Cox rings Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:48:08.859567Z

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Observation 093a529c-a512-4013-8143-165d8a5fd34d · outbound

This paper cites Quivers with potentials and their representations.

Cluster structures on Cox rings Quivers with potentials and their representations

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.852069Z

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Observation dba022ee-1350-4e87-9ee8-116930f1369d · outbound

This paper cites Quivers with potentials and their representations II : applications to cluster algebras.

Cluster structures on Cox rings Quivers with potentials and their representations II : applications to cluster algebras

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.844462Z

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Observation a2b7f3bf-5212-4a8b-ada4-668f117799d3 · outbound

This paper cites Cluster algebras and semi-invariant rings I.

Cluster structures on Cox rings Cluster algebras and semi-invariant rings I

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.835989Z

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Observation 3b002878-75c4-4d71-accb-50b3547a641d · outbound

This paper cites Cluster algebras and semi-invariant rings II : projections.

Cluster structures on Cox rings Cluster algebras and semi-invariant rings II : projections

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.828420Z

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Observation 0e9eeaeb-92e6-4864-81fb-1282ffff5db5 · outbound

This paper cites Tensor product multiplicities via upper cluster algebras.

Cluster structures on Cox rings Tensor product multiplicities via upper cluster algebras

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.819310Z

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Observation a6c1add1-0bee-4087-96ea-5a510eb91923 · outbound

This paper cites Fock and Alexander B.

Cluster structures on Cox rings Fock and Alexander B

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.809448Z

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Observation 5da75f9e-cafc-46ab-bdc2-8fafef237493 · outbound

This paper cites The minimal monomial lfting of cluster algebras I: branching problems.

Cluster structures on Cox rings The minimal monomial lfting of cluster algebras I: branching problems

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-11T21:48:08.622962Z

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Observation b358ad4f-15ed-4f3d-9b88-4204c99587f0 · outbound

This paper cites Introduction to toric varieties , volume 131 of Annals of Mathematics Studies.

Cluster structures on Cox rings Introduction to toric varieties , volume 131 of Annals of Mathematics Studies

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.448503Z

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Observation 926d0d3d-df3c-43d8-af0e-b7208f10258f · outbound

This paper cites Introduction to Cluster Algebras. Chapter 6.

Cluster structures on Cox rings Introduction to Cluster Algebras. Chapter 6

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.450927Z

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Observation b108a294-e84c-4794-b6d9-dd91d4794be3 · outbound

This paper cites Double B ruhat cells and total positivity.

Cluster structures on Cox rings Double B ruhat cells and total positivity

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.797034Z

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Observation a5db6e76-2cc1-4faa-9581-4f1e0c0215e8 · outbound

This paper cites Cluster algebras.

Cluster structures on Cox rings Cluster algebras

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.455966Z

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Observation ec2e21d5-50fd-4bd1-9cb8-aa9e1d5e2920 · outbound

This paper cites Cluster algebras.

Cluster structures on Cox rings Cluster algebras

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.458885Z

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Observation 653706f1-bd70-4631-800d-7dae701a80fe · outbound

This paper cites Birational geometry of cluster algebras.

Cluster structures on Cox rings Birational geometry of cluster algebras

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.461937Z

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Observation bbb70d5c-6ddb-4b86-aab5-e4c63e722273 · outbound

This paper cites Canonical bases for cluster algebras.

Cluster structures on Cox rings Canonical bases for cluster algebras

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.776770Z

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Observation cd4f8d16-de44-4298-ae0a-754f1cee4be2 · outbound

This paper cites Partial flag varieties and preprojective algebras.

Cluster structures on Cox rings Partial flag varieties and preprojective algebras

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.768916Z

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Observation 5d731059-fd95-49cf-87c1-8e45530e4395 · outbound

This paper cites Kac- M oody groups and cluster algebras.

Cluster structures on Cox rings Kac- M oody groups and cluster algebras

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.760197Z

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Observation 4a69bdd4-1af0-4901-aef9-ebd23b5857da · outbound

This paper cites Factorial cluster algebras.

Cluster structures on Cox rings Factorial cluster algebras

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.751871Z

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Observation e1d22485-9ab9-4419-ba2d-222c5e8eb2a5 · outbound

This paper cites Braid variety cluster structures, II : general type.

Cluster structures on Cox rings Braid variety cluster structures, II : general type

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.473395Z

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Observation 6537b8bf-99a8-4cc8-bebb-02142c78627e · outbound

This paper cites Grabowski.

Cluster structures on Cox rings Grabowski

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.743560Z

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Observation 2e4b616b-8687-4989-a046-f5689222992c · outbound

This paper cites Grothendieck.

Cluster structures on Cox rings Grothendieck

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.734811Z

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Observation 6bc1c1da-d4a3-4254-b7c1-67ebbae09c61 · outbound

This paper cites Drinfeld double of GL_n and generalized cluster structures.

Cluster structures on Cox rings Drinfeld double of GL_n and generalized cluster structures

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.726509Z

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Observation 2bde8cff-bfe3-4cf4-967d-aea05d03548c · outbound

This paper cites an unresolved cited work.

Cluster structures on Cox rings Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:48:08.719467Z

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Observation 9345b1b3-f94f-41a1-8bde-e7c0e87a2fa8 · outbound

This paper cites Algebraic geometry , volume No.

Cluster structures on Cox rings Algebraic geometry , volume No

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T21:48:08.485808Z

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Observation abf67529-67ca-434d-960d-db26f999da11 · outbound

This paper cites Equivariant embeddings into smooth toric varieties.

Cluster structures on Cox rings Equivariant embeddings into smooth toric varieties

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.707854Z

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Observation 3fb775dd-34a2-4de1-86d1-9728d606b857 · outbound

This paper cites Mori dream spaces and GIT.

Cluster structures on Cox rings Mori dream spaces and GIT

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.700185Z

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Observation ba26f30d-ce01-4a01-ba3f-3984681d1145 · outbound

This paper cites A cluster structure on the coordinate ring of partial flag varieties.

Cluster structures on Cox rings A cluster structure on the coordinate ring of partial flag varieties

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.692593Z

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Observation b23e164f-b2c4-47e5-bd19-acfbde3d7862 · outbound

This paper cites Cluster algebras and derived categories.

Cluster structures on Cox rings Cluster algebras and derived categories

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.685102Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1f82b688-8c00-4ca9-a234-4826230124f7 · outbound

This paper cites Littlewood- R ichardson coefficients via mirror symmetry for cluster varieties.

Cluster structures on Cox rings Littlewood- R ichardson coefficients via mirror symmetry for cluster varieties

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.676647Z

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Observation 75640581-2959-416d-8717-ceb3aabb13d4 · outbound

This paper cites Cluster algebras are C ox rings.

Cluster structures on Cox rings Cluster algebras are C ox rings

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.669222Z

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Observation 8eb29204-eac6-495b-adf1-9323ca6f19ff · outbound

This paper cites Locally acyclic cluster algebras.

Cluster structures on Cox rings Locally acyclic cluster algebras

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.661587Z

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Observation 1092b4d0-88bc-4bdf-b600-d8e8284a13a2 · outbound

This paper cites Triangular bases in quantum cluster algebras and monoidal categorification conjectures.

Cluster structures on Cox rings Triangular bases in quantum cluster algebras and monoidal categorification conjectures

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.654154Z

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Observation d1695621-262d-4844-8e29-7dd1c515679f · outbound

This paper cites Bases for upper cluster algebras and tropical points.

Cluster structures on Cox rings Bases for upper cluster algebras and tropical points

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.645665Z

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Observation 9d731619-089d-4bbc-bed6-ee506ac1d2fc · outbound

This paper cites an unresolved cited work.

Cluster structures on Cox rings Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:48:08.637857Z

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Observation c741c9c0-88b4-4c1f-b8e6-2aa783ed72d3 · outbound

This paper cites An Infinitely Generated Upper Cluster Algebra.

Cluster structures on Cox rings An Infinitely Generated Upper Cluster Algebra

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-11T21:48:08.542138Z

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Observation 897c5cb5-ef99-4bfe-a682-a9ff77a025cd · outbound

This paper cites Vinberg and V.

Cluster structures on Cox rings Vinberg and V

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:48:08.630530Z

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