Paper Citation Record · LEDGER

Divided difference operators for Hessenberg representations

As of 19 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2507.05614.

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

pith.paper-citation-record.v1
2507.05614 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:33:15.255122Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

16 of 16 outbound references displayed

verified exact13
verified fuzzy0
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e6dd5ed2-4e1a-491a-a7ad-9921eb1efaf8 · outbound

This paper cites Chromatic symmetric functions from the modular law.

Divided difference operators for Hessenberg representations Chromatic symmetric functions from the modular law

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.609445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c875fee-7f38-49c1-aa1d-059a72183620 · outbound

This paper cites Unit Interval Orders and the Dot Action on the Cohomology of Regular Semisimple Hessenberg Varieties.

Divided difference operators for Hessenberg representations Unit Interval Orders and the Dot Action on the Cohomology of Regular Semisimple Hessenberg Varieties

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.595969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 66d57d67-80cf-48b8-abc5-d10897984850 · outbound

This paper cites A proof of the shuffle conjecture.

Divided difference operators for Hessenberg representations A proof of the shuffle conjecture

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.582398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7254b9d4-61de-4320-aa97-94471097019c · outbound

This paper cites A modular relation for the chromatic symmetric functions of (3+1)-free posets.

Divided difference operators for Hessenberg representations A modular relation for the chromatic symmetric functions of (3+1)-free posets

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T19:33:14.647658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80bb8480-6d60-4af3-8fb5-b02e0a713c0d · outbound

This paper cites A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra.

Divided difference operators for Hessenberg representations A second proof of the Shareshian--Wachs conjecture, by way of a new Hopf algebra

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T19:33:14.754877Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e562c223-e603-43b1-bcba-185d8afd405f · outbound

This paper cites Poset pinball, GKM-compatible subspaces, and Hessenberg varieties.

Divided difference operators for Hessenberg representations Poset pinball, GKM-compatible subspaces, and Hessenberg varieties

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.545938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f3d0ea8d-e54e-4469-9b84-9d1202a0a748 · outbound

This paper cites Modular law through GKM theory.

Divided difference operators for Hessenberg representations Modular law through GKM theory

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.530231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d9b3ebf1-404d-4398-9264-cbb44ab822ef · outbound

This paper cites Three presentations of torus equivariant cohomology of flag manifolds.

Divided difference operators for Hessenberg representations Three presentations of torus equivariant cohomology of flag manifolds

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.514341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8551db0e-60a1-4cbd-8453-48912efbdbb1 · outbound

This paper cites an unresolved cited work.

Divided difference operators for Hessenberg representations Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T19:33:15.287098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 128b3223-c8a0-49da-9356-ce66a492f9ce · outbound

This paper cites Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties.

Divided difference operators for Hessenberg representations Ribbon Tableaux, Hall-Littlewood Functions, Quantum Affine Algebras and Unipotent Varieties

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.498964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 71c1a0ac-f8c2-40f2-b0fc-fbd38fd35e51 · outbound

This paper cites Graphs with Equal Chromatic Symmetric Functions.

Divided difference operators for Hessenberg representations Graphs with Equal Chromatic Symmetric Functions

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.483450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ccb967f1-3b4e-44a5-8aea-eccba564b8aa · outbound

This paper cites Chromatic quasisymmetric functions and Hessenberg varieties.

Divided difference operators for Hessenberg representations Chromatic quasisymmetric functions and Hessenberg varieties

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.467909Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cef36908-887a-4efd-88f6-78f966bd57ba · outbound

This paper cites Chromatic quasisymmetric functions.

Divided difference operators for Hessenberg representations Chromatic quasisymmetric functions

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.451968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 00e6fc12-bb21-4c56-a151-8e2f490ce725 · outbound

This paper cites Stanley, 1995, A symmetric function generalization of the chromatic polynomial of a graph, doi:10.1006/aima.1995.1020.

Divided difference operators for Hessenberg representations Stanley, 1995, A symmetric function generalization of the chromatic polynomial of a graph, doi:10.1006/aima.1995.1020

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T19:33:15.248684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b17135ab-62a5-4dae-8db3-0950b73d567c · outbound

This paper cites An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson.

Divided difference operators for Hessenberg representations An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.318289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fee7c6ee-9751-4d9e-a640-b91fe9ff2d98 · outbound

This paper cites Permutation actions on equivariant cohomology.

Divided difference operators for Hessenberg representations Permutation actions on equivariant cohomology

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T19:33:15.303614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.