Paper Citation Record · LEDGER

Toric ideals of Minkowski sums of unit simplices

As of 23 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:1908.01415.

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

pith.paper-citation-record.v1
1908.01415 v2

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:23:29.416698Z

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

10 of 10 outbound references displayed

verified exact1
verified fuzzy7
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 07d18bc5-aa43-4ff8-9709-84b78d9723b9 · outbound

This paper cites an unresolved cited work.

Toric ideals of Minkowski sums of unit simplices Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:23:30.058877Z

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 29f94ad0-7956-4c96-8c10-1bcb10ccdd78 · outbound

This paper cites an unresolved cited work.

Toric ideals of Minkowski sums of unit simplices Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-14T15:23:30.043254Z

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 b7a7b363-2195-4f6f-9c48-358773d851b1 · outbound

This paper cites Bruns, The quest for counterexamples in toric geometry, Commutative algebra and alge- braic geometry, 45–61, Ramanujan Math.

Toric ideals of Minkowski sums of unit simplices Bruns, The quest for counterexamples in toric geometry, Commutative algebra and alge- braic geometry, 45–61, Ramanujan Math

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:30.027217Z

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 b9f73934-fc02-45ad-b894-304d8eef96b0 · outbound

This paper cites Toric Topology.

Toric ideals of Minkowski sums of unit simplices Toric Topology

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.997256Z

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 dae9f343-268e-4993-9443-4ccd2d1af00e · outbound

This paper cites Binomial ideals.

Toric ideals of Minkowski sums of unit simplices Binomial ideals

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.901628Z

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 5ee72700-c158-40c4-bcae-283fb77020a3 · outbound

This paper cites Pitman and R.

Toric ideals of Minkowski sums of unit simplices Pitman and R

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.805204Z

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 afe7f266-3301-4941-b47d-e26896d3fecc · outbound

This paper cites Postnikov, Permutohedra, associahedra, and beyond, Int.

Toric ideals of Minkowski sums of unit simplices Postnikov, Permutohedra, associahedra, and beyond, Int

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.788629Z

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 c6549d8f-0e69-4849-84bd-a42da62ef9fc · outbound

This paper cites Shibuta, Gr¨ obner bases of contraction ideals, J.

Toric ideals of Minkowski sums of unit simplices Shibuta, Gr¨ obner bases of contraction ideals, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.770256Z

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 6e0b8f7f-b196-4d56-912d-0b641701e3d3 · outbound

This paper cites Gr¨ obner bases and convex polytopes.

Toric ideals of Minkowski sums of unit simplices Gr¨ obner bases and convex polytopes

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T15:23:29.756411Z

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 35902fb9-4c32-46da-95d0-ea66c43e4b1f · outbound

This paper cites Cayley sums and Minkowski sums of lattice polytopes.

Toric ideals of Minkowski sums of unit simplices Cayley sums and Minkowski sums of lattice polytopes

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-14T15:23:29.596464Z

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.

Pith citing papers

No inbound Pith citation observations are available.