Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T21:04:24.664729Z
Paper Citation Record · LEDGER
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$
As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 2 inbound Pith citation observations for arXiv:2501.06779.
A citation records a reference. It does not transfer a finding from one paper to another.
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One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-15T16:42:25.266082Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-15T16:46:18.215983Z
Reference resolution
31 of 31 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 0140fe06-ba0c-4997-a53c-ada06342a58d · outbound
This paper cites Aigner Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Math- ematical Journey from Irrational Numbers to Perfect Matchings.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Aigner Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Math- ematical Journey from Irrational Numbers to Perfect Matchings
Reference 1
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- raw_fallback, observed 2026-08-10T21:04:28.784676Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 327d3752-978e-45d4-a669-119a09861f38 · outbound
This paper cites Baragar On the unicity conjecture for Markoff numbers.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Baragar On the unicity conjecture for Markoff numbers
Reference 2
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0cf7aaf8-9f82-442c-b98f-9d6a13f5a9e0 · outbound
This paper cites Bourgain, A.Gamburd, P.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Bourgain, A.Gamburd, P
Reference 3
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 688a7776-d2e6-4e0a-a146-b8c650a1fc80 · outbound
This paper cites Buchstaber and A.P.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Buchstaber and A.P
Reference 4
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation bb8f394c-46f7-4bc2-b61d-b8d71dad8d53 · outbound
This paper cites Cassels An Introduction to Diophantine Approximation.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Cassels An Introduction to Diophantine Approximation
Reference 5
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6373ce48-62c4-4580-b08b-48fa79113cc1 · outbound
This paper cites Cohn Approach to Markoff ’s minimal forms through modular functions.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Cohn Approach to Markoff ’s minimal forms through modular functions
Reference 6
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- raw_fallback, observed 2026-08-10T21:04:28.218014Z
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 563df184-587d-4dc3-9007-aa11dba34fae · outbound
This paper cites Conway The Sensual (Quadratic) Form , Carus Mathematical Monographs, Vol.26.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Conway The Sensual (Quadratic) Form , Carus Mathematical Monographs, Vol.26
Reference 7
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- raw_fallback, observed 2026-08-10T21:04:28.112978Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 49433410-6d77-431d-937c-409116ee1c0f · outbound
This paper cites Dr` ezet and J.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Dr` ezet and J
Reference 8
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 19ab3025-87a0-4801-b93f-2257b42f0aad · outbound
This paper cites Dubrovin Geometry of 2D topological field theories.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Dubrovin Geometry of 2D topological field theories
Reference 9
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7c30240d-d9d6-4b9a-90d4-fb831dd5e4bd · outbound
This paper cites Dubrovin Geometry and analytic theory of Frobenius manifolds.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Dubrovin Geometry and analytic theory of Frobenius manifolds
Reference 10
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0579b9d2-ccb6-43bc-a20b-c43788d61210 · outbound
This paper cites Dual Teichm\" uller spaces.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Dual Teichm\" uller spaces
Reference 11
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ad56c31b-6238-47e7-ad67-5435a10efa94 · outbound
This paper cites Frobenius ¨Uber die Markoffschen Zahlen.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Frobenius ¨Uber die Markoffschen Zahlen
Reference 12
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 84c18f58-7637-4400-b1fc-eb80d6c43cab · outbound
This paper cites Gbur On the minimum of zero indefinite binary quadratic forms.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Gbur On the minimum of zero indefinite binary quadratic forms
Reference 13
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8daa41fb-c3cc-4d48-bc14-b3a9ced2581f · outbound
This paper cites Gorshkov Geometry of Lobachevskii in connection with certain questions of arith- metic.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Gorshkov Geometry of Lobachevskii in connection with certain questions of arith- metic
Reference 14
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation da962132-5aab-43bb-9270-a84e6a083999 · outbound
This paper cites Hacking, Y.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Hacking, Y
Reference 15
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 8b1c0255-2de1-4890-b146-48aa74afc291 · outbound
This paper cites Karpov, D.Yu.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Karpov, D.Yu
Reference 16
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation ee83bcce-fbc2-4cfa-b230-229407bb120d · outbound
This paper cites Kuleshov, D.O.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Kuleshov, D.O
Reference 17
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 7273b4b4-2c07-44d5-9fac-fbe6450bf051 · outbound
This paper cites LeVeque Fundamentals of Number Theory.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ LeVeque Fundamentals of Number Theory
Reference 18
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a2db9426-c385-497f-b824-403c0257ede9 · outbound
This paper cites Le Potier Lectures on Vector Bundles.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Le Potier Lectures on Vector Bundles
Reference 19
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation be0db66c-2231-426e-ac9f-dd025a47fe84 · outbound
This paper cites Markov Sur les formes quadratiques binaires ind´ efinies.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Markov Sur les formes quadratiques binaires ind´ efinies
Reference 20
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 070560af-1427-4de9-bbf8-2cfe799e4d60 · outbound
This paper cites McShane Simple geodesics and a series constant over Teichmuller space.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ McShane Simple geodesics and a series constant over Teichmuller space
Reference 21
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation a55733e4-e570-453e-af97-14ed0e4988bb · outbound
This paper cites Minkowski Zur Geometrie der Zahlen.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Minkowski Zur Geometrie der Zahlen
Reference 22
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- raw_fallback, observed 2026-08-10T21:04:26.332992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b0c4e543-51de-48d1-9154-d57a1f14eee1 · outbound
This paper cites Dubrovin conjecture and the second structure connection.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Dubrovin conjecture and the second structure connection
Reference 23
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- no resolver link, observed 2026-08-10T21:04:24.346607Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9a9abfd0-a9b7-419d-b1ae-cef5152664e3 · outbound
This paper cites Riesz, B.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Riesz, B
Reference 24
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9dd9ebae-6973-44a0-b8c1-53109479f940 · outbound
This paper cites Rosenberger ¨Uber die Diophantische Gleichung ax2 + by2 + cz2 = dxyz.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Rosenberger ¨Uber die Diophantische Gleichung ax2 + by2 + cz2 = dxyz
Reference 25
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2305351a-5c01-42a8-ada1-181a445cfe1a · outbound
This paper cites an unresolved cited work.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Unresolved cited work
Reference 26
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- raw_fallback, observed 2026-08-10T21:04:25.904758Z
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1dceb3e1-d372-405a-b3de-bea4548fb310 · outbound
This paper cites Rudakov Exceptional vector bundles on quadrics.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Rudakov Exceptional vector bundles on quadrics
Reference 27
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1d7b53d4-3eb6-4feb-b899-0537e48c3a95 · outbound
This paper cites Salem On some singular monotonic functions which are strictly increasing.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Salem On some singular monotonic functions which are strictly increasing
Reference 28
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 1536bc7f-d8c7-4b62-8989-8c69a2dfed7e · outbound
This paper cites Spalding and A.P.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Spalding and A.P
Reference 29
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 04a3bcc3-1694-4dca-a40f-09d3501e5666 · outbound
This paper cites Springborn The worst approximable rational numbers.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Springborn The worst approximable rational numbers
Reference 30
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 2a8c1c48-db38-48aa-86bd-df0434b8657e · outbound
This paper cites Viader, J.
Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Viader, J
Reference 31
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Pith citing papers
Observation bf08d4a1-5ae9-490d-a897-ad1d25fc46e9 · inbound
Plane geometry of $q$-rationals and Springborn Operations cites this paper.
Plane geometry of $q$-rationals and Springborn Operations Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$
Reference 31
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- arxiv_id, observed 2026-05-15T16:46:18.219334Z
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5efadd9e-071a-46e2-831b-bb40a248d364 · inbound
Markov fractions and Cohn matrices cites this paper.
Markov fractions and Cohn matrices Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$
Reference 12
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- arxiv_id, observed 2026-05-10T06:06:18.692683Z
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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.