Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials
As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 3 inbound Pith citation observations for arXiv:2108.08370.
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 2026-08-07T05:49:32.785018Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T15:58:37.948054Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation 9eb3ff15-eab3-47bf-862f-125a50c8e8b1 · inbound
Changing Bases with Pipe Dream Combinatorics cites this paper.
Changing Bases with Pipe Dream Combinatorics Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:49:32.785018Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation abe48d34-a421-4e10-91f8-a4feb51ffd73 · inbound
Hybrid pipe dreams for the lower-upper scheme cites this paper.
Hybrid pipe dreams for the lower-upper scheme Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T12:16:24.345937Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f40551d5-fcb9-4709-853f-bcacd5756ca0 · inbound
Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams cites this paper.
Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials
Reference 11
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T15:58:37.949480Z
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.