Paper Citation Record · LEDGER

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

As of 14 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 9 inbound Pith citation observations for arXiv:2507.06900.

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

pith.paper-citation-record.v1
2507.06900 v2

Coverage vector

measured 53 of 53 reference resolution

Typed states for the displayed outbound observations.

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measured 62 of 62 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 9 of 9 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:01:23.251057Z

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

Source: arxiv_reference, observed 2026-06-30T23:25:07.104696Z

Reference resolution

53 of 53 outbound references displayed

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External citation measurements

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Outbound references

Observation da1240c6-bfec-4911-85b9-676a0406b3be · outbound

This paper cites A mathematical journey from irrational numbers to perfect matchings.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations A mathematical journey from irrational numbers to perfect matchings

Reference 1

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This paper cites Socially-Aware Robot Navigation Enhanced by Bidirectional Natural Language Conversations Using Large Language Models.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Socially-Aware Robot Navigation Enhanced by Bidirectional Natural Language Conversations Using Large Language Models

Reference 2

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Observation 1a26f799-f6ce-4274-a3d7-fb6f9a48411f · outbound

This paper cites 63 (2024), no.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations 63 (2024), no

Reference 3

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This paper cites Algebra674 (2025), 77–116.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Algebra674 (2025), 77–116

Reference 4

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This paper cites Represent.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Represent

Reference 5

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 6

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Observation e322e722-afc7-489b-86cd-7b515fb5adf6 · outbound

This paper cites Positivity of generalized cluster scattering diagrams.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Positivity of generalized cluster scattering diagrams

Reference 7

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 8

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This paper cites Algebra 382 (2013), 240–281.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Algebra 382 (2013), 240–281

Reference 9

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 10

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 11

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 12

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

This paper cites A cluster theory approach from mutation invariants to Diophantine equations.

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

Reference 13

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 14

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This paper cites 18 (1971), 125–136.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations 18 (1971), 125–136

Reference 15

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This paper cites an unresolved cited work.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 16

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Observation f5266850-47e8-4da0-b8b2-1e320470ace4 · outbound

This paper cites 15(2002), 497–529.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations 15(2002), 497–529

Reference 17

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Observation ce8302a1-a6f4-44a7-9112-b840ead8350a · outbound

This paper cites Math.143 (2007), no.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Math.143 (2007), no

Reference 18

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Observation 6d7c40a2-db85-4554-952b-4941138c60ab · outbound

This paper cites Homological conditions on locally gentle algebras.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Homological conditions on locally gentle algebras

Reference 19

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 20

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 21

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This paper cites Math.290 (2016), 364–452.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Math.290 (2016), 364–452

Reference 22

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Observation 35ba09ca-6a1b-454e-87dc-3dd9d4a89959 · outbound

This paper cites SL(2,Z)-matrixizations of generalized Markov numbers.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations SL(2,Z)-matrixizations of generalized Markov numbers

Reference 23

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 24

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Reihe, Bd

Reference 25

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This paper cites 348 (2025), no.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations 348 (2025), no

Reference 26

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Observation a8b40de8-5b79-4b1d-bb7f-bd521639817f · outbound

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations MR4863786

Reference 27

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Observation 59e387a0-e223-4551-a3a0-4054fd6e29f4 · outbound

This paper cites $q$-Deformations and $t$-deformations of Markov triples.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations $q$-Deformations and $t$-deformations of Markov triples

Reference 28

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Algebra520 (2019), 90–135

Reference 29

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 30

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 31

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 32

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This paper cites Differential Geom.48 (1998), no.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Differential Geom.48 (1998), no

Reference 33

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This paper cites Markoff,Sur les formes quadratiques binaires indéfinies, Math.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Markoff,Sur les formes quadratiques binaires indéfinies, Math

Reference 34

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This paper cites Math.233 (2013), 207–247.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Math.233 (2013), 207–247

Reference 35

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This paper cites Super Markov Numbers and Signed Double Dimer Covers.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Super Markov Numbers and Signed Double Dimer Covers

Reference 36

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations MR2721552

Reference 37

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 38

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 39

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 40

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 41

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Math.277 (2015), no

Reference 42

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations 41, Mathematical Society of Japan, Tokyo, 2023

Reference 43

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Observation 0a83cffa-f9d4-453e-b193-8225fa4f7a51 · outbound

This paper cites Addendum to "Structure of seeds in generalized cluster algebras".

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Addendum to "Structure of seeds in generalized cluster algebras"

Reference 44

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations MR3643935

Reference 45

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 46

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Observation e3182ff5-1da1-4f48-a6a6-3833aa21fef5 · outbound

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 47

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This paper cites Posets for $F$-polynomials in cluster algebras from surfaces.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Posets for $F$-polynomials in cluster algebras from surfaces

Reference 48

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations MR4067101

Reference 49

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Observation ea79caf2-a4d6-4859-afb8-0618c7fa3681 · outbound

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-06T19:06:04.008004Z

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Observation c1b7b28c-9016-49eb-b087-a629e182b3db · outbound

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Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 51

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Observation 8c12ed40-1509-43de-8373-c5d715656177 · outbound

This paper cites an unresolved cited work.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations Unresolved cited work

Reference 52

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Observation 4e678b44-2854-4a25-aa4f-78bfdba109d7 · outbound

This paper cites An elementary proof of uniqueness of Markoff numbers which are prime powers.

Cluster algebraic interpretation of generalized Markov numbers and their matrixizations An elementary proof of uniqueness of Markoff numbers which are prime powers

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:06:02.355271Z

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Pith citing papers

Observation 8ad4b375-0306-40f0-b236-08e4be131927 · inbound

Divisibility by $p$ for Markoff-like Surfaces cites this paper.

Divisibility by $p$ for Markoff-like Surfaces Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 1

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Observation 279ad765-3c06-4d08-a3a6-c1fa5a2d9bd4 · inbound

Orderings of k-Markov Numbers cites this paper.

Orderings of k-Markov Numbers Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 2

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Observation 464f1693-46d6-46e8-8497-e70b6bb160ef · inbound

Generalized discrete Markov spectra cites this paper.

Generalized discrete Markov spectra Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-17T01:53:51.011918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f3e0c6c6-1901-4c2c-be6c-1aa965228f8f · inbound

Orderings of Generalized k-Markov Numbers cites this paper.

Orderings of Generalized k-Markov Numbers Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-10T06:01:13.289096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9911c404-a65a-42d2-baff-b493a38d183c · inbound

Cluster Expansions from Punctured Orbifolds cites this paper.

Cluster Expansions from Punctured Orbifolds Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T17:56:06.192784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 22759343-d3a9-4e3b-9fff-fa3c246041a6 · inbound

Cluster Expansions from Punctured Orbifolds cites this paper.

Cluster Expansions from Punctured Orbifolds Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T23:25:07.107164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 48b33f3b-1f1d-4a01-8247-a0bae03f056c · inbound

Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver cites this paper.

Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 17

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:21:24.663786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2c8949a6-0222-4232-ad36-af52ed84f43b · inbound

Words for generalized Markov numbers cites this paper.

Words for generalized Markov numbers Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-06-29T16:03:33.996453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a291ce3a-e0dd-4c6f-a919-eced591f2bc4 · inbound

Monoidal categorification of generalized cluster algebras and conjectures of Fraser and Gleitz cites this paper.

Monoidal categorification of generalized cluster algebras and conjectures of Fraser and Gleitz Cluster algebraic interpretation of generalized Markov numbers and their matrixizations

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-12T13:49:50.081465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.