Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T15:00:45.606990Z
Paper Citation Record · LEDGER
Arithmetic and geometry of Markov polynomials
As of 18 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 3 inbound Pith citation observations for arXiv:2501.14882.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T18:13:58.692079Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-11T11:56:31.644751Z
Reference resolution
27 of 27 outbound references displayed
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- verified fuzzy24
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 70bc54fc-2257-4031-bb35-cc70d141860e · outbound
This paper cites Aigner Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings.
Arithmetic and geometry of Markov polynomials Aigner Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings
Reference 1
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation c7c80062-b5f9-47cd-92e3-6d5aa078fdb8 · outbound
This paper cites Arnold Continued fractions.
Arithmetic and geometry of Markov polynomials Arnold Continued fractions
Reference 2
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 549b5e4e-65fe-49ac-a6c1-d98f55abe226 · outbound
This paper cites Bourgain, A.
Arithmetic and geometry of Markov polynomials Bourgain, A
Reference 3
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 53772fd2-7d12-4948-bc26-cb6666225c7c · outbound
This paper cites Caldero, A.V.
Arithmetic and geometry of Markov polynomials Caldero, A.V
Reference 4
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 86fcbfdf-95ee-4ce3-aed2-2dadc7266ab6 · outbound
This paper cites C ¸ anak¸ cı, R.
Arithmetic and geometry of Markov polynomials C ¸ anak¸ cı, R
Reference 5
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 6a6b3e0c-8786-440b-83e6-b8377fd43a20 · outbound
This paper cites Conway The Sensual (Quadratic) Form, Carus Mathematical Monographs, Vol.26.
Arithmetic and geometry of Markov polynomials Conway The Sensual (Quadratic) Form, Carus Mathematical Monographs, Vol.26
Reference 6
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- raw_fallback, observed 2026-08-10T15:00:45.858516Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 217c9106-a939-4385-a973-925efb372db4 · outbound
This paper cites Connectivity of Markoff mod-p graphs and maximal divisors.
Arithmetic and geometry of Markov polynomials Connectivity of Markoff mod-p graphs and maximal divisors
Reference 7
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- verified exact
- local_arxiv, observed 2026-08-10T15:00:45.652693Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 0f9e55e5-37a0-4c61-bb81-851cb67a5fd6 · outbound
This paper cites Fei Combinatorics of F -polynomials.
Arithmetic and geometry of Markov polynomials Fei Combinatorics of F -polynomials
Reference 8
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- raw_fallback, observed 2026-08-10T15:00:45.848289Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 3fd9a3e8-e265-4a67-adae-f2584b36d7cc · outbound
This paper cites Felikson, M.
Arithmetic and geometry of Markov polynomials Felikson, M
Reference 9
- Resolution
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- raw_fallback, observed 2026-08-10T15:00:45.838916Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cdb10dd8-1f75-4413-b4a3-09a62eadcd5b · outbound
This paper cites Dual Teichm\" uller spaces.
Arithmetic and geometry of Markov polynomials Dual Teichm\" uller spaces
Reference 10
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- no resolver link, observed 2026-08-10T15:00:45.547846Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9d0893b7-c9b7-4fe1-baba-e0c8a7778bb3 · outbound
This paper cites Fomin and A.
Arithmetic and geometry of Markov polynomials Fomin and A
Reference 11
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- raw_fallback, observed 2026-08-10T15:00:45.829418Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 53b2175f-9d29-4ef9-90f1-aec38306d181 · outbound
This paper cites Frobenius ¨Uber die Markoffschen Zahlen.
Arithmetic and geometry of Markov polynomials Frobenius ¨Uber die Markoffschen Zahlen
Reference 12
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- raw_fallback, observed 2026-08-10T15:00:45.820168Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 601786d3-e860-42a4-8490-dce77ff5448b · outbound
This paper cites Itsara, G.
Reference 13
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 54018d8c-19f3-4a7f-98c3-c0d5875a6afa · outbound
This paper cites Karpenkov Geometry of Continued Fractions.
Arithmetic and geometry of Markov polynomials Karpenkov Geometry of Continued Fractions
Reference 14
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- raw_fallback, observed 2026-08-10T15:00:45.799917Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 878e86cc-e9bf-4fbf-95cf-ee1007e1d0e2 · outbound
This paper cites Leclere, S.
Reference 15
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Observation f40c59cb-2423-4cde-a306-f30d009a3743 · outbound
This paper cites an unresolved cited work.
Arithmetic and geometry of Markov polynomials Unresolved cited work
Reference 16
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- unresolved
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1f8a26c9-0b33-48d5-8008-c45196fe729a · outbound
This paper cites Markoff Sur les formes quadratiques binaires ind´ efinies.
Arithmetic and geometry of Markov polynomials Markoff Sur les formes quadratiques binaires ind´ efinies
Reference 17
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- raw_fallback, observed 2026-08-10T15:00:45.767114Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 89c0047f-bd7f-46b2-9462-31622e8a9e97 · outbound
This paper cites Morier-Genoud and V.
Arithmetic and geometry of Markov polynomials Morier-Genoud and V
Reference 18
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- raw_fallback, observed 2026-08-10T15:00:45.756234Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation cee97307-a90f-417f-84f5-ff3f29e2533d · outbound
This paper cites Newton Arithmetica Universalis: Sive De Compositione Et Resolutione Arithmetica Liber.
Arithmetic and geometry of Markov polynomials Newton Arithmetica Universalis: Sive De Compositione Et Resolutione Arithmetica Liber
Reference 19
- Resolution
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- raw_fallback, observed 2026-08-10T15:00:45.745857Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 998cdf4c-be8a-4c14-a3d8-5e3f911e01d9 · outbound
This paper cites MARKOV POLYNOMIALS 25.
Arithmetic and geometry of Markov polynomials MARKOV POLYNOMIALS 25
Reference 20
- Resolution
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 199a6cbe-a0a1-4ace-a571-0c01acce8f3e · outbound
This paper cites Penner The decorated Teichm¨ uller space of punctured surfaces.Comm.
Arithmetic and geometry of Markov polynomials Penner The decorated Teichm¨ uller space of punctured surfaces.Comm
Reference 21
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- raw_fallback, observed 2026-08-10T15:00:45.724775Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 97080dfc-0fbb-4235-a3f2-0fedc3b0e7a8 · outbound
This paper cites Propp The combinatorics of frieze patterns and Markoff numbers.
Arithmetic and geometry of Markov polynomials Propp The combinatorics of frieze patterns and Markoff numbers
Reference 22
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 7ccfdd44-1575-4bc3-a3e4-98dfe185f53e · outbound
This paper cites Sorrentino and A.P.
Arithmetic and geometry of Markov polynomials Sorrentino and A.P
Reference 23
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 903265ec-8b41-4dc7-8480-b30acae7c46a · outbound
This paper cites Spalding, A.P.
Arithmetic and geometry of Markov polynomials Spalding, A.P
Reference 24
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- raw_fallback, observed 2026-08-10T15:00:45.694441Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 049c521a-1bf5-451d-97d1-44dac14b1f15 · outbound
This paper cites Stanley Log-concave and unimodal sequences in algebra, combinatorics, and geometry.
Arithmetic and geometry of Markov polynomials Stanley Log-concave and unimodal sequences in algebra, combinatorics, and geometry
Reference 25
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation b246be7b-e8ce-497f-8a38-c0b442aa9a4c · outbound
This paper cites Ustinov Geometric proof of Rødseth’s formula for Frobenius numbers.
Arithmetic and geometry of Markov polynomials Ustinov Geometric proof of Rødseth’s formula for Frobenius numbers
Reference 26
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dfb466b8-910b-4236-b330-2b45897ea44f · outbound
This paper cites Zelevinsky Semicanonical basis generators of the cluster algebra of type A(1) 1.
Arithmetic and geometry of Markov polynomials Zelevinsky Semicanonical basis generators of the cluster algebra of type A(1) 1
Reference 27
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
Observation 5d815fae-e53a-4eb5-8a26-c5ba2121a4ce · inbound
On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges cites this paper.
On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges Arithmetic and geometry of Markov polynomials
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T18:13:58.692079Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3c3a0c48-086e-4104-a3a6-ef799da24df7 · inbound
Wug-snake graphs and Markov numbers of matrix semigroups cites this paper.
Wug-snake graphs and Markov numbers of matrix semigroups Arithmetic and geometry of Markov polynomials
Reference 16
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- metadata mismatch
- arxiv_id, observed 2026-05-10T06:26:27.008161Z
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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 926156f2-e5f7-42b8-a997-6a509f37840c · inbound
Saturation of Markov Polynomials cites this paper.
Saturation of Markov Polynomials Arithmetic and geometry of Markov polynomials
Reference 4
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- arxiv_id, observed 2026-05-11T11:56:31.648639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.