Paper Citation Record · LEDGER

Vector-valued Laurent polynomial equations, toric vector bundles and matroids

As of 10 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2507.09793.

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

pith.paper-citation-record.v1
2507.09793 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:58:04.915942Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact2
verified fuzzy17
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9a9b5611-1982-4c75-ae0a-63dfffbf8c60 · outbound

This paper cites Hodge theory for combinatorial geometries.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Hodge theory for combinatorial geometries

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:08.436200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation eb21b0a5-dd9a-4e58-ba7b-5debe5db2ccc · outbound

This paper cites Lagrangian geometry of matroids.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Lagrangian geometry of matroids

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:08.422167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c0de7e7e-2a33-45ee-854f-4174605da87a · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:08.403259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 80cfccde-a2dd-4664-88c6-6114e435d03a · outbound

This paper cites Tautological classes of matroids.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Tautological classes of matroids

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:08.382957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation febd30b1-dfc3-4eb5-a8fc-d83ea55b1c11 · outbound

This paper cites N.; Kushnirenko, A.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids N.; Kushnirenko, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:08.188596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 232d8dde-8d76-435b-ab32-54ae82f9d197 · outbound

This paper cites E.; Chun, C.; Fife, T.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids E.; Chun, C.; Fife, T

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.810458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2cc2180e-f0af-4d06-86dc-5749a2882ff8 · outbound

This paper cites Piecewise polynomial functions, convex polytopes and enumerative geometry.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Piecewise polynomial functions, convex polytopes and enumerative geometry

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.579046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 09568880-509a-4c99-97fd-1b459cb231d0 · outbound

This paper cites I.; Khovanskii, A.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids I.; Khovanskii, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.457766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation edd31667-7f5f-4806-9714-aa41d118187c · outbound

This paper cites Complete symmetric varieties II.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Complete symmetric varieties II

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.294504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 67354dad-f7b6-4783-880f-e24291a43571 · outbound

This paper cites Sch\"on complete intersections.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Sch\"on complete intersections

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:02.639692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5573fe37-550d-4bc2-a5c1-1c4e15d6a7ac · outbound

This paper cites Engineered complete intersections: slightly degenerate Bernstein--Kouchnirenko--Khovanskii.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Engineered complete intersections: slightly degenerate Bernstein--Kouchnirenko--Khovanskii

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:02.740449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68a6ea10-bd04-49c4-8b9c-6e54b8c5dff2 · outbound

This paper cites Engineered complete intersections: eliminating variables and understanding topology.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Engineered complete intersections: eliminating variables and understanding topology

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:02.876851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a29f44a8-93a7-4a75-af23-bab3ce0c1403 · outbound

This paper cites Signed permutohedra, delta-matroids, and beyond.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Signed permutohedra, delta-matroids, and beyond

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.116889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f40d7851-0661-47bc-847a-05b763c3b3a0 · outbound

This paper cites Stellahedral geometry of matroids.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Stellahedral geometry of matroids

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:07.019878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 992f3b22-398d-4891-bb02-e3c8d6bd091b · outbound

This paper cites Ya; Khovanskii, A.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Ya; Khovanskii, A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:06.926171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2db28c8e-0acb-4cbe-b006-8546986c0ba6 · outbound

This paper cites Intersection theory on toric varieties.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Intersection theory on toric varieties

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:06.839108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7292e670-e72a-4e01-8144-c08dce3f0fa3 · outbound

This paper cites Helgason, Aspects of the theory of hypermatroids, in Hypergraph Seminar (Proc.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Helgason, Aspects of the theory of hypermatroids, in Hypergraph Seminar (Proc

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:06.728405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6ad0154a-f530-4b3e-a87d-a8e7ea3ab9b9 · outbound

This paper cites Rota’s conjecture and positivity of algebraic cycles in permutohedral varieties.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Rota’s conjecture and positivity of algebraic cycles in permutohedral varieties

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:06.638960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1b76a515-3edf-40db-a2db-b912be13df63 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:06.501045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 296ea646-f13b-4d80-8134-a6c1055d2a48 · outbound

This paper cites A short survey on Newton polytopes, tropical geometry and ring of conditions of algebraic torus.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids A short survey on Newton polytopes, tropical geometry and ring of conditions of algebraic torus

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:58:05.307055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 297cb965-d8a2-494e-a338-8a7673b5e574 · outbound

This paper cites Toric vector bundles, valuations and tropical geometry.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Toric vector bundles, valuations and tropical geometry

Reference 21

Resolution: verified exact; doi, observed 2026-08-06T17:58:05.135370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0f3f5ac8-d739-43a6-9ba9-4fdf0f051a48 · outbound

This paper cites Tropical vector bundles and matroids.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Tropical vector bundles and matroids

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:03.965232Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe005a90-a1a0-4cd3-88cd-4cb95ec5e540 · outbound

This paper cites Tropical Vector Bundles.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Tropical Vector Bundles

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:04.040101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6721f0c2-1af8-4373-b89b-338b6285d181 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:06.410245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 25ca99d5-8a61-44fa-ad07-03d516d655d9 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:06.305576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 18c46643-28f8-4779-9ac0-cc5e5e0cf3d6 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:06.198789Z

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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1556e1cc-f44c-4c78-a4cd-866d8d94b9ff · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:06.089674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d97fee89-2ce7-4fae-8fba-5877a1ee21c3 · outbound

This paper cites G.; Pukhlikov, A.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids G.; Pukhlikov, A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:05.995516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1061f97c-9342-428c-96b6-c3c08e256cb3 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:05.898117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 79a8f96e-2341-412c-9192-2ac5ee188fbe · outbound

This paper cites Moduli of toric vector bundles.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Moduli of toric vector bundles

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:05.767896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c9aba9c2-e535-4881-a400-cbc3c1ff77b9 · outbound

This paper cites Toric vector bundles, branched covers of fans, and the resolution property , J.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Toric vector bundles, branched covers of fans, and the resolution property , J

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:05.635671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3035be2e-6345-4af9-a5fb-63a0087cafa8 · outbound

This paper cites an unresolved cited work.

Vector-valued Laurent polynomial equations, toric vector bundles and matroids Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:05.499237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

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