Paper Citation Record · LEDGER

Closure operators and geometric modules of valuated matroids

As of 14 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2606.18562.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2606.18562 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T20:49:43.897662Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

verified exact2
verified fuzzy0
unresolved22
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malformed identifier0
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External citation measurements

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Outbound references

Observation 4318fa5f-10e1-4838-bf1d-777b2fa70ea1 · outbound

This paper cites Matroid Powers in Tropical Geometry.

Closure operators and geometric modules of valuated matroids Matroid Powers in Tropical Geometry

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7d2d451-2493-4a46-ab75-65092b5bce59 · outbound

This paper cites Matroids over partial hyperstructures.

Closure operators and geometric modules of valuated matroids Matroids over partial hyperstructures

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 92dcb1dc-e623-45df-924d-8280c4958a56 · outbound

This paper cites Axioms for infinite matroids.

Closure operators and geometric modules of valuated matroids Axioms for infinite matroids

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 3450ec01-5cd5-454e-9912-c73a7af4126d · outbound

This paper cites Large convex sets in oriented matroids.

Closure operators and geometric modules of valuated matroids Large convex sets in oriented matroids

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 47eb4f56-3a46-4f6f-b3e4-e914ade7b565 · outbound

This paper cites Lorentzian polynomials and matroids over triangular hyperfields 1: T opological aspects.

Closure operators and geometric modules of valuated matroids Lorentzian polynomials and matroids over triangular hyperfields 1: T opological aspects

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:59:20.132424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 13a25a86-f3ac-44b6-8512-edc098fecd7e · outbound

This paper cites The moduli space of matroids.

Closure operators and geometric modules of valuated matroids The moduli space of matroids

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 208a9660-0abf-4770-87e3-30482733e78e · outbound

This paper cites A module-theoretic approach to matroids.

Closure operators and geometric modules of valuated matroids A module-theoretic approach to matroids

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 238567c4-a4b6-401b-876d-9d2c4fb9c220 · outbound

This paper cites Duality theory for finite and infinite matroids with coefficients.

Closure operators and geometric modules of valuated matroids Duality theory for finite and infinite matroids with coefficients

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation d87ced42-e562-4507-947e-3ca6d822bfe1 · outbound

This paper cites Valuated matroids.

Closure operators and geometric modules of valuated matroids Valuated matroids

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cc2a7171-3c78-40dc-b764-5bfc2a38a1e4 · outbound

This paper cites On infinite matroids with strong maps: Proto-exactness and finiteness conditions.

Closure operators and geometric modules of valuated matroids On infinite matroids with strong maps: Proto-exactness and finiteness conditions

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation bf19e16f-1fdb-44cf-925b-a720a4c4e56f · outbound

This paper cites Extensions of transversal valuated matroids.

Closure operators and geometric modules of valuated matroids Extensions of transversal valuated matroids

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 4ee671ad-1700-4096-9ed1-fd14b0be032f · outbound

This paper cites Equations of tropical varieties.

Closure operators and geometric modules of valuated matroids Equations of tropical varieties

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 05e5eaa0-3a4e-4499-9acf-e5a7715d6206 · outbound

This paper cites A G rassmann algebra for matroids.

Closure operators and geometric modules of valuated matroids A G rassmann algebra for matroids

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e60cb6e9-da08-4e34-b128-f71014741156 · outbound

This paper cites Uniform semimodular lattices and valuated matroids.

Closure operators and geometric modules of valuated matroids Uniform semimodular lattices and valuated matroids

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 18cf4193-adfd-457c-9663-4a53fb5338d4 · outbound

This paper cites Vector bundles on tropical schemes.

Closure operators and geometric modules of valuated matroids Vector bundles on tropical schemes

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 5d5f62af-b41d-4eb6-98ca-090155b2cdbb · outbound

This paper cites Tropical representations and valuated matroids.

Closure operators and geometric modules of valuated matroids Tropical representations and valuated matroids

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-04T00:59:20.137301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 408686fc-737f-474f-89da-e9747c0953d6 · outbound

This paper cites Tropical schemes, tropical cycles, and valuated matroids.

Closure operators and geometric modules of valuated matroids Tropical schemes, tropical cycles, and valuated matroids

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation a760407d-f28f-4b89-9a5b-e6ca2de214d1 · outbound

This paper cites Introduction to tropical geometry , volume 161.

Closure operators and geometric modules of valuated matroids Introduction to tropical geometry , volume 161

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 40cd28bd-b949-4550-a1e9-ee231aaf850a · outbound

This paper cites On circuit valuation of matroids.

Closure operators and geometric modules of valuated matroids On circuit valuation of matroids

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 40425f7f-b7eb-4702-9df3-ba20342ba80b · outbound

This paper cites Zur axiomatik der linearen abh \"a ngigkeit.

Closure operators and geometric modules of valuated matroids Zur axiomatik der linearen abh \"a ngigkeit

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Observation 81819e2f-0b78-4b04-a0c7-f59d1aea4e9d · outbound

This paper cites an unresolved cited work.

Closure operators and geometric modules of valuated matroids Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

Source-reported events for the cited work

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Observation cecea2b8-b32a-4b53-969a-d280419acaba · outbound

This paper cites Tropical linear spaces.

Closure operators and geometric modules of valuated matroids Tropical linear spaces

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

Source-reported events for the cited work

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Observation f685b78d-5e15-4490-9034-4998dd4714ef · outbound

This paper cites Finite lattices and J ordan- H \"o lder sets.

Closure operators and geometric modules of valuated matroids Finite lattices and J ordan- H \"o lder sets

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Unavailable: canonical work link unavailable.

Observation eda17863-0a03-4bca-8899-74e006032628 · outbound

This paper cites On the abstract properties of linear dependence.

Closure operators and geometric modules of valuated matroids On the abstract properties of linear dependence

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T20:49:43.897662Z

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Pith citing papers

No inbound Pith citation observations are available.