Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T12:16:24.399793Z
Paper Citation Record · LEDGER
Hybrid pipe dreams for the lower-upper scheme
As of 8 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2509.01857.
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
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
21 of 21 outbound references displayed
- verified exact7
- verified fuzzy4
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 4f8da360-a97b-4760-9742-6333b0b7176f · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T12:16:25.159366Z
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 e93cc836-6425-422e-b057-f002d4151cda · outbound
This paper cites 4, 257 -- 269.
Hybrid pipe dreams for the lower-upper scheme 4, 257 -- 269
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T12:16:25.139759Z
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 1cc4dcde-5e1e-43ca-9392-330ac59d56c2 · outbound
This paper cites Borho, J.-L.
Hybrid pipe dreams for the lower-upper scheme Borho, J.-L
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T12:16:25.122074Z
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 7c8685a4-4004-4634-8836-3657fcc38f25 · outbound
This paper cites Inhomogenous model of crossing loops and multidegrees of some algebraic varieties.
Hybrid pipe dreams for the lower-upper scheme Inhomogenous model of crossing loops and multidegrees of some algebraic varieties
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T12:16:24.964694Z
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 8be13bd7-018b-4368-abab-b30511b3b8d2 · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T12:16:25.100635Z
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 f82a121d-e761-42a1-846a-381667f4120f · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T12:16:24.303871Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a03d4e65-c2e6-4892-908a-7cfe4e213aca · outbound
This paper cites 21, 18629--18663.
Hybrid pipe dreams for the lower-upper scheme 21, 18629--18663
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T12:16:25.068618Z
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 a805e8e3-9449-4dc9-af7c-bb8e9f9b5123 · outbound
This paper cites Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams.
Hybrid pipe dreams for the lower-upper scheme Bijective Proofs of Monk's rule for Schubert and Double Schubert Polynomials with Bumpless Pipe Dreams
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T12:16:24.927939Z
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 1358bdae-553a-4f00-a6bb-93b272221275 · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T12:16:25.049050Z
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 d63add84-77ad-4aed-b5e3-82fb6836b98b · outbound
This paper cites Algebraic Geom.
Hybrid pipe dreams for the lower-upper scheme Algebraic Geom
Reference 10
- Resolution
- verified exact
- raw_fallback, observed 2026-08-05T12:16:24.888767Z
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 394d4b43-08dd-4a7d-bccb-3d4db2babfe1 · outbound
This paper cites Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula.
Hybrid pipe dreams for the lower-upper scheme Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T12:16:24.332984Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3d8d80bb-ac78-4616-b073-c7f89a742177 · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T12:16:25.023978Z
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 abe48d34-a421-4e10-91f8-a4feb51ffd73 · outbound
This paper cites Bumpless pipe dreams encode Gr\"obner geometry of Schubert polynomials.
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 dd646b97-b037-4265-9013-1ed027250496 · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 14
- Resolution
- verified exact
- raw_fallback, observed 2026-08-05T12:16:24.733067Z
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 82127585-b3d9-4885-998c-cdd64ae3b4dc · outbound
This paper cites The Brauer loop scheme and orbital varieties.
Hybrid pipe dreams for the lower-upper scheme The Brauer loop scheme and orbital varieties
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T12:16:24.583410Z
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 8f2515f9-6eee-421c-8cf5-2e9e81a78b5b · outbound
This paper cites Generic pipe dreams, lower-upper varieties, and Schwartz-MacPherson classes.
Hybrid pipe dreams for the lower-upper scheme Generic pipe dreams, lower-upper varieties, and Schwartz-MacPherson classes
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T12:16:24.365085Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9145b689-2154-4bcd-a9f6-9adeaab5960b · outbound
This paper cites Back stable Schubert calculus.
Hybrid pipe dreams for the lower-upper scheme Back stable Schubert calculus
Reference 17
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-05T12:16:24.528855Z
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 c0011671-2c03-4336-8412-3188c9219df9 · outbound
This paper cites 227, Springer-Verlag, New York, 2005.
Hybrid pipe dreams for the lower-upper scheme 227, Springer-Verlag, New York, 2005
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T12:16:25.002731Z
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 d30e2b45-f9db-4a94-9688-95f79c5f81dd · outbound
This paper cites an unresolved cited work.
Hybrid pipe dreams for the lower-upper scheme Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T12:16:24.983764Z
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 dd06e46f-df1a-4781-8b35-654431082bdd · outbound
This paper cites Bumpless pipe dreams and alternating sign matrices.
Hybrid pipe dreams for the lower-upper scheme Bumpless pipe dreams and alternating sign matrices
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T12:16:24.495234Z
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 96bbbb3e-1b8d-4cb4-adc5-269a732684f7 · outbound
This paper cites Changing Bases with Pipe Dream Combinatorics.
Hybrid pipe dreams for the lower-upper scheme Changing Bases with Pipe Dream Combinatorics
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T12:16:24.464238Z
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
No inbound Pith citation observations are available.