Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T22:57:39.606032Z
Paper Citation Record · LEDGER
Tropical linear systems and the realizability problem
As of 22 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2506.21268.
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 2026-08-22T06:32:14.747728+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T15:21:45.642479Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T15:21:45.757669Z
Reference resolution
12 of 12 outbound references displayed
- verified exact2
- verified fuzzy1
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch6
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 8badb5bc-0b4f-4bda-b361-26266fab2fd4 · outbound
This paper cites Riemann-Roch and Abel-Jacobi theory on a finite graph.
Tropical linear systems and the realizability problem Riemann-Roch and Abel-Jacobi theory on a finite graph
Reference 3
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.699150Z
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 795c2b40-abce-429f-8578-1dcc13991c30 · outbound
This paper cites Realizability of tropical pluri-canonical divisors.
Tropical linear systems and the realizability problem Realizability of tropical pluri-canonical divisors
Reference 11
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.650955Z
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 bddcfc19-1764-4f8d-a098-39fdad0b6e39 · outbound
This paper cites Towards a Tropical Hodge Bundle.
Tropical linear systems and the realizability problem Towards a Tropical Hodge Bundle
Reference 2002
- Resolution
- verified exact
- doi, observed 2026-08-06T22:57:39.630648Z
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 50f6fd40-1f84-44f0-b46c-ef51fbc777aa · outbound
This paper cites Specialization of linear systems from curves to graphs.
Tropical linear systems and the realizability problem Specialization of linear systems from curves to graphs
Reference 2007
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.708983Z
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 002222af-4039-4192-91b3-c55be4882cd1 · outbound
This paper cites Linear Systems on Tropical Curves.
Tropical linear systems and the realizability problem Linear Systems on Tropical Curves
Reference 2009
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.682780Z
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 f4a99575-adf7-422d-908e-3c9f59add6d8 · outbound
This paper cites Reduced Divisors and Embeddings of Tropical Curves.
Tropical linear systems and the realizability problem Reduced Divisors and Embeddings of Tropical Curves
Reference 2012
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.719481Z
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 84588131-3859-4842-afcd-14307c85217e · outbound
This paper cites Tropicalizing vs Compactifying the Torelli morphism.
Tropical linear systems and the realizability problem Tropicalizing vs Compactifying the Torelli morphism
Reference 2013
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T22:57:39.640848Z
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 f8d33550-de84-4001-b817-33b496b24aed · outbound
This paper cites Realizability of tropical canonical divisors.
Tropical linear systems and the realizability problem Realizability of tropical canonical divisors
Reference 2017
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T22:57:39.661351Z
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 ec69e9b4-89f0-43f9-b104-b729e862c4fa · outbound
This paper cites Idempotent Analysis, Tropical Convexity and Reduced Divisors.
Tropical linear systems and the realizability problem Idempotent Analysis, Tropical Convexity and Reduced Divisors
Reference 2018
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T22:57:39.595012Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 245f534b-6910-436b-afb2-a951c1bb5699 · outbound
This paper cites 07549 [math.CO].
Tropical linear systems and the realizability problem 07549 [math.CO]
Reference 2021
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T22:57:39.727035Z
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 6fd0e761-cb7a-4ee2-9205-a8f62ca4fc61 · outbound
This paper cites Tropical Linear Series and Tropical Independence.
Tropical linear systems and the realizability problem Tropical Linear Series and Tropical Independence
Reference 2022
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T22:57:39.589514Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b61d9c75-ecb7-4d54-a03f-1ae9358e2beb · outbound
This paper cites The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$.
Tropical linear systems and the realizability problem The Kodaira dimensions of $\overline{\mathcal{M}}_{22}$ and $\overline{\mathcal{M}}_{23}$
Reference 2023
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T22:57:39.582733Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation d5541509-7632-4cbc-a62f-6d3e543a2022 · inbound
Tropical linear series and matroids cites this paper.
Tropical linear series and matroids Tropical linear systems and the realizability problem
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T15:21:45.761423Z
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.