Paper Citation Record · LEDGER

Tropical linear systems and the realizability problem

As of 20 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.

pith.paper-citation-record.v1
2506.21268 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:57:39.606032Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:21:45.642479Z

measured 0 of 1 external citation measurements

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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+00:00.