Paper Citation Record · LEDGER

A cluster theory approach from mutation invariants to Diophantine equations

As of 22 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2501.09435.

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

pith.paper-citation-record.v1
2501.09435 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:12:38.105562Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:05:58.511933Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T19:06:03.263722Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy21
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6f6ef7cb-c7b0-45da-8bc2-5fc29a9b09a6 · outbound

This paper cites Aigner Markov's theorem and 100 years of the uniqueness conjecture: a mathematical journal from irrational numbers to perfect matchings Springer 2013.

A cluster theory approach from mutation invariants to Diophantine equations Aigner Markov's theorem and 100 years of the uniqueness conjecture: a mathematical journal from irrational numbers to perfect matchings Springer 2013

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.681384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 511f7b64-c1db-4cec-8f0c-91f00332c464 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.655700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a8ae570c-efac-4c5c-9167-0d4b93ec6cf0 · outbound

This paper cites Beineke, T.

A cluster theory approach from mutation invariants to Diophantine equations Beineke, T

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.640876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 307dd519-4789-47f0-ba1b-c6010f739d78 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.623618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c5801860-ba61-4209-9c82-0202cc02b8aa · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.606683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 659e6711-f8e2-454e-a167-bc27ddc46920 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.591906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b1025b8a-c61f-4748-8863-208ceb942be8 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.577707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8a1450d8-e6dd-41d8-8fe6-77feb48b65ec · outbound

This paper cites Derksen, J.

A cluster theory approach from mutation invariants to Diophantine equations Derksen, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.560888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 14a79dd4-7bdd-4317-af57-1d7281215fb1 · outbound

This paper cites Derksen, J.

A cluster theory approach from mutation invariants to Diophantine equations Derksen, J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:37.992517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87fff36c-6ad0-4a36-85b6-d7c35d5455a2 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.525976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d5cdf94b-c0aa-4f0a-94fa-9503a2bfbdcb · outbound

This paper cites Fujiwara, Y.

A cluster theory approach from mutation invariants to Diophantine equations Fujiwara, Y

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.506800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2425da3f-78bf-4948-b1e5-ed077e5f319f · outbound

This paper cites Fomin, N.

A cluster theory approach from mutation invariants to Diophantine equations Fomin, N

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.491594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 46fb6529-1a35-46e9-bc1a-f80e322a59b3 · outbound

This paper cites Felikson, S.

A cluster theory approach from mutation invariants to Diophantine equations Felikson, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.473387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b99ea196-3b85-41bd-bc3b-ce1157058910 · outbound

This paper cites Felikson, S.

A cluster theory approach from mutation invariants to Diophantine equations Felikson, S

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.458417Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 37176e54-1474-4084-9ec0-994d9da795ee · outbound

This paper cites Fomin, A.

A cluster theory approach from mutation invariants to Diophantine equations Fomin, A

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.017875Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 772a7d0c-c867-4870-a7f6-2835d36139a7 · outbound

This paper cites Fomin, A.

A cluster theory approach from mutation invariants to Diophantine equations Fomin, A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.433541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d67b8893-1f92-4443-a50c-45d3c87f4778 · outbound

This paper cites Fomin, A.

A cluster theory approach from mutation invariants to Diophantine equations Fomin, A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.418736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 53e361b2-14f8-4e29-9b58-ef89cbd819b7 · outbound

This paper cites Fomin, A.

A cluster theory approach from mutation invariants to Diophantine equations Fomin, A

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.029291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6d98743-9fa9-45c7-8904-543b6b256988 · outbound

This paper cites Gantmacher The Theory of Matrices , AMS Chelsea, American Mathematical Society: Providence, Rhode Island, 1998 , Volume II.

A cluster theory approach from mutation invariants to Diophantine equations Gantmacher The Theory of Matrices , AMS Chelsea, American Mathematical Society: Providence, Rhode Island, 1998 , Volume II

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.393546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 988939d4-e6e0-42dc-8845-c2492bdde2e6 · outbound

This paper cites Gross, P.

A cluster theory approach from mutation invariants to Diophantine equations Gross, P

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.036171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 911f7933-12e9-4385-b43a-1e5f46d53ac4 · outbound

This paper cites Gyoda, K.

A cluster theory approach from mutation invariants to Diophantine equations Gyoda, K

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.366035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 42742b48-9378-46e8-8034-ad840778b423 · outbound

This paper cites Gekhtman, M.

A cluster theory approach from mutation invariants to Diophantine equations Gekhtman, M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.348306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 798f35a8-b3e3-45ce-8754-4e36e15ed214 · outbound

This paper cites Gekhtman, M.

A cluster theory approach from mutation invariants to Diophantine equations Gekhtman, M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.330640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c0e7bd74-441f-49f9-9801-696446b085fc · outbound

This paper cites On the monotonicity of the generalized Markov numbers.

A cluster theory approach from mutation invariants to Diophantine equations On the monotonicity of the generalized Markov numbers

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.051589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3a2623c-e49a-4953-b9c8-abaf2905c617 · outbound

This paper cites Hernandez, B.

A cluster theory approach from mutation invariants to Diophantine equations Hernandez, B

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.317081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cac880fb-b306-490f-aec8-ec9771c1174b · outbound

This paper cites Keller, D.

A cluster theory approach from mutation invariants to Diophantine equations Keller, D

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.301611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 72d83d14-a98c-4ec0-868b-7fabb42478cd · outbound

This paper cites Kuniba, T.

A cluster theory approach from mutation invariants to Diophantine equations Kuniba, T

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.288442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 83de07c8-2b95-45d3-acfd-9002ce73af04 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.273850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bf17c1e3-8930-45d8-9c20-b44f3e3d4bf4 · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.259243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bbd556d0-fb5d-42bf-9c1e-dc18fd48dd46 · outbound

This paper cites Lampe Diophantine equations via cluster transformations J.

A cluster theory approach from mutation invariants to Diophantine equations Lampe Diophantine equations via cluster transformations J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.242183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 628dcb43-6207-4b07-91f6-fe19c8abd2be · outbound

This paper cites Muller Locally acyclic cluster algebras Adv.

A cluster theory approach from mutation invariants to Diophantine equations Muller Locally acyclic cluster algebras Adv

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.228590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6486ce8b-5ab6-467f-a1aa-1e75f54a2efb · outbound

This paper cites Muller = for locally acyclic cluster algebras SIGMA Symmetry Integrability Geom.

A cluster theory approach from mutation invariants to Diophantine equations Muller = for locally acyclic cluster algebras SIGMA Symmetry Integrability Geom

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.215781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 19b9f8c9-d33b-4593-b7ee-8406d9e5f02f · outbound

This paper cites Nakanishi Cluster algebras and scattering diagrams MSJ Mem.

A cluster theory approach from mutation invariants to Diophantine equations Nakanishi Cluster algebras and scattering diagrams MSJ Mem

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.088828Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ec8b36b-6655-4ca4-a60b-774c19c3015c · outbound

This paper cites Nakanishi, A.

A cluster theory approach from mutation invariants to Diophantine equations Nakanishi, A

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:38.092697Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7154aac3-28ab-484c-8e55-535794f70412 · outbound

This paper cites Propp The combinatorics of frieze patterns and Markoff numbers Integers 20 2020.

A cluster theory approach from mutation invariants to Diophantine equations Propp The combinatorics of frieze patterns and Markoff numbers Integers 20 2020

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.185144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3d10baa3-218a-458c-853d-cc049cce3c0d · outbound

This paper cites an unresolved cited work.

A cluster theory approach from mutation invariants to Diophantine equations Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:12:38.170453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 432927c8-0295-4544-ae00-db6789f88b19 · outbound

This paper cites Reading, S.

A cluster theory approach from mutation invariants to Diophantine equations Reading, S

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:38.158033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation b53f0e95-3231-427b-8531-8e7c33da5eb8 · inbound

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations cites this paper.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations A cluster theory approach from mutation invariants to Diophantine equations

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:06:03.319910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.