Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-15T16:42:25.266082Z
Paper Citation Record · LEDGER
Plane geometry of $q$-rationals and Springborn Operations
As of 15 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2603.04295.
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 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T05:25:04.750824Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
31 of 31 outbound references displayed
- verified exact23
- verified fuzzy5
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 2bafac5a-022d-4baf-89e6-1ecd0bde0e5e · outbound
This paper cites Aigner.Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings.
Plane geometry of $q$-rationals and Springborn Operations Aigner.Markov’s Theorem and 100 Years of the Uniqueness Conjecture: A Mathematical Journey from Irrational Numbers to Perfect Matchings
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T16:51:18.680285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4e4a9572-e87d-4c5f-8790-6d31b645f4df · outbound
This paper cites Aval and S.
Plane geometry of $q$-rationals and Springborn Operations Aval and S
Reference 2
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.306113Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 989f79d4-dbb1-4289-b6ea-edb11b97f587 · outbound
This paper cites $q$-deformed rational numbers and the 2-Calabi--Yau category of type $A_2$.
Plane geometry of $q$-rationals and Springborn Operations $q$-deformed rational numbers and the 2-Calabi--Yau category of type $A_2$
Reference 3
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.262232Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6c766060-94c6-499d-96af-a3ac70e676bf · outbound
This paper cites Bittmann, P.
Plane geometry of $q$-rationals and Springborn Operations Bittmann, P
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.293116Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 71ad94c4-9f49-4ddb-b572-a53238b8e5cb · outbound
This paper cites Bounding deformation spaces of Kleinian groups with two generators.
Plane geometry of $q$-rationals and Springborn Operations Bounding deformation spaces of Kleinian groups with two generators
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-06-23T04:13:37.472272Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 502969a1-8a7e-4a86-b9e7-05e1a13660c9 · outbound
This paper cites On $q$-real and $q$-complex numbers.
Plane geometry of $q$-rationals and Springborn Operations On $q$-real and $q$-complex numbers
Reference 6
- Resolution
- verified exact
- arxiv_id, observed 2026-08-07T00:51:06.975017Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 911f2897-1b40-4a51-9bc7-23bdb237bfe4 · outbound
This paper cites On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges.
Plane geometry of $q$-rationals and Springborn Operations On $q$-deformed Markov numbers. Cohn matrices and perfect matchings with weighted edges
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.312767Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d87e7599-1785-4204-a0ab-6d6626990b4b · outbound
This paper cites an unresolved cited work.
Plane geometry of $q$-rationals and Springborn Operations Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T16:51:18.688549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 87812429-cdcc-47fd-adc1-fdf50f2cac3e · outbound
This paper cites an unresolved cited work.
Plane geometry of $q$-rationals and Springborn Operations Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T16:51:18.671434Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a728d08e-acf8-4f22-ad99-59671bece4cd · outbound
This paper cites Symmetries of the q-deformed real projective line.
Plane geometry of $q$-rationals and Springborn Operations Symmetries of the q-deformed real projective line
Reference 10
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.238265Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4e9a6813-d3a3-46a8-9047-11dd956cb8ed · outbound
This paper cites Oriented posets, Rank Matrices and q-deformed Markov Numbers.
Plane geometry of $q$-rationals and Springborn Operations Oriented posets, Rank Matrices and q-deformed Markov Numbers
Reference 11
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.250259Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6919b50d-c589-4b8e-a42a-8aafd9371681 · outbound
This paper cites $q$-Deformations and $t$-deformations of Markov triples.
Plane geometry of $q$-rationals and Springborn Operations $q$-Deformations and $t$-deformations of Markov triples
Reference 12
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.280847Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5189d3aa-61fb-47a0-9e70-47e69d8bcfec · outbound
This paper cites Arithmetic on $q$-deformed rational numbers.
Plane geometry of $q$-rationals and Springborn Operations Arithmetic on $q$-deformed rational numbers
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.224856Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 47d6728e-b422-43fe-a5cb-43ea2af026b4 · outbound
This paper cites The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence.
Plane geometry of $q$-rationals and Springborn Operations The $q$-analog of the Markoff injectivity conjecture over the language of a balanced sequence
Reference 14
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.343926Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 76b104d8-4392-4899-8009-f85dc0bf5e13 · outbound
This paper cites A $q$-analog of the Markoff injectivity conjecture holds.
Plane geometry of $q$-rationals and Springborn Operations A $q$-analog of the Markoff injectivity conjecture holds
Reference 15
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.325350Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e479a9e8-c51d-4070-ad54-57bbecb2b65c · outbound
This paper cites Leclere.q-analogues des nombres r´ eels et des matrices unimodulaires : aspects alg´ ebriques, combinatoires et analytiques.
Plane geometry of $q$-rationals and Springborn Operations Leclere.q-analogues des nombres r´ eels et des matrices unimodulaires : aspects alg´ ebriques, combinatoires et analytiques
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T16:51:18.667356Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a154bc93-8acf-48b7-95c4-a0fcfd428e96 · outbound
This paper cites $q$-deformations of the modular group and of the real quadratic irrational numbers.
Plane geometry of $q$-rationals and Springborn Operations $q$-deformations of the modular group and of the real quadratic irrational numbers
Reference 17
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.299750Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 82f64571-9c89-4766-b3c5-fc6edcfb9360 · outbound
This paper cites On radius of convergence of $q$-deformed real numbers.
Plane geometry of $q$-rationals and Springborn Operations On radius of convergence of $q$-deformed real numbers
Reference 18
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.268430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5776d304-13e9-4c4b-bce8-c04d0811960e · outbound
This paper cites Manecke and A.
Plane geometry of $q$-rationals and Springborn Operations Manecke and A
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T16:51:18.675576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d52234f6-fee4-4ea6-af69-90681b874a72 · outbound
This paper cites an unresolved cited work.
Plane geometry of $q$-rationals and Springborn Operations Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-05-15T16:51:18.693064Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 829a1727-7e87-41d5-9589-61f491149e07 · outbound
This paper cites Farey boat I. Continued fractions and triangulations, modular group and polygon dissections.
Plane geometry of $q$-rationals and Springborn Operations Farey boat I. Continued fractions and triangulations, modular group and polygon dissections
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-05-15T16:46:18.337788Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 75aabd72-1443-44b1-971b-296a6ff03b91 · outbound
This paper cites $q$-deformed rationals and $q$-continued fractions.
Plane geometry of $q$-rationals and Springborn Operations $q$-deformed rationals and $q$-continued fractions
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.275120Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ac33624e-5877-4656-a1d0-640eb7468332 · outbound
This paper cites Morier-Genoud and V.
Plane geometry of $q$-rationals and Springborn Operations Morier-Genoud and V
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T16:51:18.684484Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3f80f5df-31af-4de5-98bc-50e2920172db · outbound
This paper cites Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group.
Plane geometry of $q$-rationals and Springborn Operations Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.256141Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation bfe0f5a6-ab73-4f4a-88a6-766be5f4d393 · outbound
This paper cites On $q$-deformed Farey sum and a homological interpretation of $q$-deformed real quadratic irrational numbers.
Plane geometry of $q$-rationals and Springborn Operations On $q$-deformed Farey sum and a homological interpretation of $q$-deformed real quadratic irrational numbers
Reference 25
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.286628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation dfc0c88d-6618-412a-8f46-dbf9a35db6b2 · outbound
This paper cites Ren and K.
Plane geometry of $q$-rationals and Springborn Operations Ren and K
Reference 26
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.244085Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a23feffb-237f-494a-8b7e-6a1bd4d433ad · outbound
This paper cites an unresolved cited work.
Plane geometry of $q$-rationals and Springborn Operations Unresolved cited work
Reference 27
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.331788Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4bba5ca9-056c-44e7-8f30-036ae9eaf521 · outbound
This paper cites The worst approximable rational numbers.
Plane geometry of $q$-rationals and Springborn Operations The worst approximable rational numbers
Reference 28
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.232072Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f1565346-c8a5-4059-be77-1cb147d617a8 · outbound
This paper cites Sullivan.
Plane geometry of $q$-rationals and Springborn Operations Sullivan
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-15T16:51:18.662894Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation cde4f883-df6c-49f7-be85-bb64616e2377 · outbound
This paper cites Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra.
Plane geometry of $q$-rationals and Springborn Operations Infinitesimal Modular Group: $q$-Deformed $\mathfrak{sl}_2$ and Witt Algebra
Reference 30
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.206644Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation bf08d4a1-5ae9-490d-a897-ad1d25fc46e9 · outbound
This paper cites Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$.
Plane geometry of $q$-rationals and Springborn Operations Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$
Reference 31
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T16:46:18.219334Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Pith citing papers
Observation 48ab3e5e-9979-4145-9e81-800df97dcc27 · inbound
Nuancing the unicity of $q$-rationals cites this paper.
Nuancing the unicity of $q$-rationals Plane geometry of $q$-rationals and Springborn Operations
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T05:25:04.750824Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.