Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:07:22.991780Z
Paper Citation Record · LEDGER
Graham positivity of triple Schubert calculus
As of 11 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 3 inbound Pith citation observations for arXiv:2506.09421.
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 2026-08-11T06:34:44.6726+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T20:00:26.501210Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-04T11:49:50.862521Z
Reference resolution
22 of 22 outbound references displayed
- verified exact1
- verified fuzzy17
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 43920830-a473-4ab1-8305-1731e1467cfb · outbound
This paper cites Cambridge University Press, Cambridge, 2024.
Graham positivity of triple Schubert calculus Cambridge University Press, Cambridge, 2024
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.334155Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5cb16169-70d2-4e70-a484-cc2af63c0e4e · outbound
This paper cites Skew divided difference operators in the Nichols algebra associated to a finite Coxeter group.J.
Graham positivity of triple Schubert calculus Skew divided difference operators in the Nichols algebra associated to a finite Coxeter group.J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.320211Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 01e0aa18-f245-4797-8cbc-9d0899b5624b · outbound
This paper cites Littlewood-Richardson coefficients for reflection groups.
Graham positivity of triple Schubert calculus Littlewood-Richardson coefficients for reflection groups
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.304834Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation b68652d0-ebae-48ec-a691-967b127fb5a2 · outbound
This paper cites RC-graphs and Schubert polynomials.Experiment.
Graham positivity of triple Schubert calculus RC-graphs and Schubert polynomials.Experiment
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.291491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7244a36e-2e10-43f5-ae41-d5b3a6339ff3 · outbound
This paper cites an unresolved cited work.
Graham positivity of triple Schubert calculus Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:07:23.277922Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c0fd581a-92b7-4d2f-a6bd-5783a426b922 · outbound
This paper cites an unresolved cited work.
Graham positivity of triple Schubert calculus Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:07:23.264662Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c4c6f00b-1ee3-4ddc-9de3-50f9a8bb9c39 · outbound
This paper cites Kirillov.
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.251489Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation a8abb826-85f6-4247-b449-ca73846ad3d8 · outbound
This paper cites Positivity in equivariant Schubert calculus.Duke Math.
Graham positivity of triple Schubert calculus Positivity in equivariant Schubert calculus.Duke Math
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.237965Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation b5579960-c97f-48e6-8a0e-8a63548bcc35 · outbound
This paper cites Schubert products for permutations with separated descents.Int.
Graham positivity of triple Schubert calculus Schubert products for permutations with separated descents.Int
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.223438Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation da9da013-ceb0-4ec2-82f2-600ae9b76f09 · outbound
This paper cites Humphreys.Linear algebraic groups, volume No.
Graham positivity of triple Schubert calculus Humphreys.Linear algebraic groups, volume No
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.209834Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 84402d22-e644-4354-a19c-44e3097ffdea · outbound
This paper cites Kirillov.
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.196345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation ce2f27d5-e8ac-4a11-bd0b-21e33d1685a5 · outbound
This paper cites Gr¨ obner geometry of Schubert polynomials.Ann.
Graham positivity of triple Schubert calculus Gr¨ obner geometry of Schubert polynomials.Ann
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.182667Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c23c62bf-fe15-477d-a561-4f65f63ce649 · outbound
This paper cites Puzzles and (equivariant) cohomology of Grassmannians.Duke Math.
Graham positivity of triple Schubert calculus Puzzles and (equivariant) cohomology of Grassmannians.Duke Math
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.169296Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2a501745-fe94-41e4-a798-841a7faaeb56 · outbound
This paper cites Schubert puzzles and integrability III: separated descents.
Graham positivity of triple Schubert calculus Schubert puzzles and integrability III: separated descents
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:07:23.035519Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 37e0bccb-9943-4f9b-bc74-a4c8fa6e6cbd · outbound
This paper cites Back stable Schubert calculus.Compos.
Graham positivity of triple Schubert calculus Back stable Schubert calculus.Compos
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.155485Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2f681d63-c5be-4e8b-9ef5-48742e5e71fe · outbound
This paper cites Back stableK-theory Schubert calculus.Int.
Graham positivity of triple Schubert calculus Back stableK-theory Schubert calculus.Int
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.140149Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c795b146-928b-4637-a882-48b4712c0121 · outbound
This paper cites Positive expressions for skew divided difference operators.J.
Graham positivity of triple Schubert calculus Positive expressions for skew divided difference operators.J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.125371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 673ece96-bfea-4f2a-83d3-547ef0a124d5 · outbound
This paper cites an unresolved cited work.
Graham positivity of triple Schubert calculus Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:07:23.109897Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 47212ef1-72d7-43e8-9559-c5987102dc16 · outbound
This paper cites Mihalcea, Hiroshi Naruse, and Changjian Su.
Graham positivity of triple Schubert calculus Mihalcea, Hiroshi Naruse, and Changjian Su
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.095277Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5d4e4810-af5d-4f8f-865c-cf278b4d7c0e · outbound
This paper cites Molev and Bruce E.
Graham positivity of triple Schubert calculus Molev and Bruce E
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.080446Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation f0c6b372-8c8f-4f66-8006-6664ba5fb5a5 · outbound
This paper cites an unresolved cited work.
Graham positivity of triple Schubert calculus Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:07:23.065760Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2b052b73-11d3-437d-b85d-b84d6fe495c7 · outbound
This paper cites Billey’s formula in combinatorics, geometry, and topology.
Graham positivity of triple Schubert calculus Billey’s formula in combinatorics, geometry, and topology
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:07:23.051647Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Pith citing papers
Observation 3bd9e492-8534-4687-be9a-6146db5c2dae · inbound
Equivariant Quantum Cohomology of Grassmannians via the Clifford algebra cites this paper.
Equivariant Quantum Cohomology of Grassmannians via the Clifford algebra Graham positivity of triple Schubert calculus
Reference 56
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-07-02T14:37:03.719251Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c48ba322-f660-4e26-ae22-8873f8bd0e92 · inbound
A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra cites this paper.
A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra Graham positivity of triple Schubert calculus
Reference 103
- Resolution
- verified exact
- arxiv_id, observed 2026-07-04T11:49:50.863841Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 9e564fd7-2267-41b8-967c-1de8c8a4731b · inbound
Equivariant Schubert Calculus for Inverse Grassmannian Permutations cites this paper.
Equivariant Schubert Calculus for Inverse Grassmannian Permutations Graham positivity of triple Schubert calculus
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T20:00:26.501210Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.