Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:36:07.681414Z
Paper Citation Record · LEDGER
Syzygies of polymatroidal ideals
As of 8 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2507.13153.
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 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T11:14:51.495182Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
24 of 24 outbound references displayed
- verified exact5
- verified fuzzy5
- unresolved13
- parse uncertain0
- malformed identifier1
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 304e7a51-8c66-4331-a480-c47dad0479ca · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.736496Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 99ea1e14-194a-436d-9e59-55372288e8c1 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.612419Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5d82d279-0c23-4f70-a7ef-07a87ccf1d78 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.526640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 85b40790-69a2-4d6e-a3c7-4a557a470ba3 · outbound
This paper cites Math., vol.
Syzygies of polymatroidal ideals Math., vol
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:10.407548Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b1192183-e514-405f-a58c-55c010f3654b · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.282158Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation df173e6d-63fd-4ddf-b865-3eea1ff9399d · outbound
This paper cites K-polynomials of multiplicity-free varieties.
Syzygies of polymatroidal ideals K-polynomials of multiplicity-free varieties
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T16:36:06.219709Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 10f38ca2-b40e-403c-8efa-c678677c8db9 · outbound
This paper cites The Bergman fan of a polymatroid.
Syzygies of polymatroidal ideals The Bergman fan of a polymatroid
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:08.436052Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b6cb8143-483d-470b-b6e2-82fb1164bcbe · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.171473Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a1c1d5f0-b38d-4083-9940-79132e98ef5c · outbound
This paper cites K-theoretic positivity for matroids.
Syzygies of polymatroidal ideals K-theoretic positivity for matroids
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:08.319708Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 284f40c9-2153-429b-8df0-074aa4d6ef72 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:10.035696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 21a4da80-a745-4073-a2c7-78beaf5aa6a3 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:09.893819Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1f4b1a7a-d64e-46bf-b25c-f2f4725c017c · outbound
This paper cites Homological shifts of polymatroidal ideals.
Syzygies of polymatroidal ideals Homological shifts of polymatroidal ideals
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:08.151455Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4b4dd174-ae1d-4932-8ee9-e6ba74ff13d6 · outbound
This paper cites 260, Springer-Verlag London, Ltd., London, 2011.
Syzygies of polymatroidal ideals 260, Springer-Verlag London, Ltd., London, 2011
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:09.799371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 95ccc52b-9c29-483d-8cd4-20731b09ad01 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:09.687936Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 90f1ddce-6d26-4d0e-a51f-6e3cc94e8da1 · outbound
This paper cites 3, 1245--1318.
Syzygies of polymatroidal ideals 3, 1245--1318
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:09.578074Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8987eb5b-cfb9-49e5-a557-3768e9396e7f · outbound
This paper cites Frobenius splitting and M\"obius inversion.
Syzygies of polymatroidal ideals Frobenius splitting and M\"obius inversion
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:07.985178Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 723652a7-4788-4ca9-b693-0bfdc94da0fa · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:09.464234Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 40341a0f-0e2c-4df1-89d2-bc0118ffe16a · outbound
This paper cites 227, Springer-Verlag, New York, 2005.
Syzygies of polymatroidal ideals 227, Springer-Verlag, New York, 2005
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:09.344268Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 39929c5d-551f-4219-85d0-ac203652cc8e · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:09.184430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9a8e9a10-68c5-4c64-ad29-1684351b1522 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:09.042327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bcdea516-a445-417d-95f8-fa0a9d01fe16 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:36:08.890848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6fc81920-52e6-4256-842c-f62285f7e2e1 · outbound
This paper cites Dually Lorentzian Polynomials.
Syzygies of polymatroidal ideals Dually Lorentzian Polynomials
Reference 22
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:36:07.852211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 77145acc-14ec-4086-88a4-2bd8364dce71 · outbound
This paper cites an unresolved cited work.
Syzygies of polymatroidal ideals Unresolved cited work
Reference 23
- Resolution
- malformed identifier
- raw_fallback, observed 2026-08-06T16:36:08.716010Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 668c9b0e-a985-4365-a814-79e60f0c59a3 · outbound
This paper cites P olyhedra and efficiency.
Syzygies of polymatroidal ideals P olyhedra and efficiency
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:36:08.566203Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
Observation 3d2e3cf3-a9fd-43cc-8dc4-fcd08aa1026e · inbound
Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid cites this paper.
Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid Syzygies of polymatroidal ideals
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T11:14:51.495182Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.