Paper Citation Record · LEDGER

Schur positivity of nabla on Petrie symmetric functions

As of 14 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2607.06351.

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

pith.paper-citation-record.v1
2607.06351 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T09:20:56.123227Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

32 of 32 outbound references displayed

verified exact29
verified fuzzy2
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9c1bb40e-fc07-4e5a-b53d-b61099146354 · outbound

This paper cites and Morse, J.

Schur positivity of nabla on Petrie symmetric functions and Morse, J

Reference 1

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.307989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c8e4fc3a-57c2-427e-9c1b-03393ddac6d5 · outbound

This paper cites an unresolved cited work.

Schur positivity of nabla on Petrie symmetric functions Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-07-08T09:24:49.081665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5de47d74-c481-429b-a559-ac638169a9c6 · outbound

This paper cites TITLE =.

Schur positivity of nabla on Petrie symmetric functions TITLE =

Reference 3

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.301764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d1328c41-eda1-4fce-af88-615faea80610 · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 4

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.311994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ba081f04-8458-4841-8aa2-e910751795c7 · outbound

This paper cites 2008 , PAGES =.

Schur positivity of nabla on Petrie symmetric functions 2008 , PAGES =

Reference 5

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.267888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 28a23908-4392-4f5f-ae50-582708fec3a8 · outbound

This paper cites and Garsia, A.

Schur positivity of nabla on Petrie symmetric functions and Garsia, A

Reference 6

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.313925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 46e80476-64e7-4736-baf3-e1907ec1de1f · outbound

This paper cites an unresolved cited work.

Schur positivity of nabla on Petrie symmetric functions Unresolved cited work

Reference 7

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.270264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 06bd20fa-12b1-4edf-b7ba-9e96700c8f38 · outbound

This paper cites Haiman, Hilbert schemes, polygraphs and the M acdonald positivity conjecture , J.

Schur positivity of nabla on Petrie symmetric functions Haiman, Hilbert schemes, polygraphs and the M acdonald positivity conjecture , J

Reference 8

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.256413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ce7a0df1-0771-43b0-a643-cc387ca0aa05 · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 9

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.272475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9a610386-193d-4cf6-a550-f833e85352b8 · outbound

This paper cites an unresolved cited work.

Schur positivity of nabla on Petrie symmetric functions Unresolved cited work

Reference 10

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.258420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 277308c3-6e9a-4434-9db5-c06f6cd34f05 · outbound

This paper cites and Garsia, A.

Schur positivity of nabla on Petrie symmetric functions and Garsia, A

Reference 11

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.315826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ddeca79b-f802-4c25-a1a3-c6491256cb57 · outbound

This paper cites [CM18] Erik Carlsson and Anton Mellit.

Schur positivity of nabla on Petrie symmetric functions [CM18] Erik Carlsson and Anton Mellit

Reference 12

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.240712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4edaccc1-2e45-448d-b465-c60045782501 · outbound

This paper cites Remmel, and Alexander Ulyanov.

Schur positivity of nabla on Petrie symmetric functions Remmel, and Alexander Ulyanov

Reference 13

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.303861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c0bf7052-a9fb-4a48-ab2e-bd0f72c24411 · outbound

This paper cites and Leclerc, B.

Schur positivity of nabla on Petrie symmetric functions and Leclerc, B

Reference 14

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.317815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f768eb2c-acb4-49fa-86c5-656d1024a402 · outbound

This paper cites an unresolved cited work.

Schur positivity of nabla on Petrie symmetric functions Unresolved cited work

Reference 15

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.264795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fb429d22-e3ed-4dab-9601-ea2ece83953f · outbound

This paper cites an unresolved cited work.

Schur positivity of nabla on Petrie symmetric functions Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.244468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b4907b5e-bbd3-4b62-bb2b-c40480b09f1d · outbound

This paper cites and Haiman, M.

Schur positivity of nabla on Petrie symmetric functions and Haiman, M

Reference 17

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.254405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dbd7d2ef-43c7-4bb5-9e23-192f743cab28 · outbound

This paper cites and Haiman, M.

Schur positivity of nabla on Petrie symmetric functions and Haiman, M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T09:24:49.085186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dc38dc78-67f1-4d25-b2a2-7f1afb0fcca5 · outbound

This paper cites Extending the science fiction and the Loehr--Warrington formula.

Schur positivity of nabla on Petrie symmetric functions Extending the science fiction and the Loehr--Warrington formula

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-08T09:24:48.453810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e62a8e37-43d2-4c29-bf64-d16e161ca9b2 · outbound

This paper cites Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials.

Schur positivity of nabla on Petrie symmetric functions Schur positivity of the nabla operator on two-column modified Hall--Littlewood polynomials

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-07-08T09:24:48.459385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a3ad9107-6034-445c-867a-3720839060e0 · outbound

This paper cites and Xin, G.

Schur positivity of nabla on Petrie symmetric functions and Xin, G

Reference 21

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.249582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37bf8b9a-7924-4f7c-a683-25275c463dd6 · outbound

This paper cites The Schur positivity of $\nabla m_\mu$.

Schur positivity of nabla on Petrie symmetric functions The Schur positivity of $\nabla m_\mu$

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-07-08T09:24:48.451043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 07f85203-85a7-4f0b-a0fd-2ba0907ae479 · outbound

This paper cites and Remmel, J.

Schur positivity of nabla on Petrie symmetric functions and Remmel, J

Reference 23

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.299018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 129d7c47-bbdf-4253-8a33-b6cad6db61c3 · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T09:24:49.083434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5bfb5dc9-a4b6-4899-bf10-ca8db41d13d4 · outbound

This paper cites and Haiman, M.

Schur positivity of nabla on Petrie symmetric functions and Haiman, M

Reference 25

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.247269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1eb01e4d-33c5-4393-9c3f-79d504c95fcb · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 26

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.310082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 021cf5a4-ebb0-414a-8752-6845b5585b7f · outbound

This paper cites and Chou, M.-C.

Schur positivity of nabla on Petrie symmetric functions and Chou, M.-C

Reference 27

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.305986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 530d3173-1633-4989-bacf-bad17a31859c · outbound

This paper cites Grinberg, Z.-W.

Schur positivity of nabla on Petrie symmetric functions Grinberg, Z.-W

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-07-08T09:24:48.295939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4f7a6742-b92d-4f03-8b8f-eba2ef3078b2 · outbound

This paper cites and Polo, P.

Schur positivity of nabla on Petrie symmetric functions and Polo, P

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-07-08T09:24:48.275635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cba31317-d7eb-4960-bfa3-c75f67672dce · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 30

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.252114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cbcb5a1d-370c-4bb0-9859-7c922deae2fe · outbound

This paper cites and Garsia, A.

Schur positivity of nabla on Petrie symmetric functions and Garsia, A

Reference 31

Resolution: verified exact; doi, observed 2026-07-08T09:24:48.277554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 14544118-7484-4587-9c8e-7ad3cff1b723 · outbound

This paper cites , TITLE =.

Schur positivity of nabla on Petrie symmetric functions , TITLE =

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-08T09:24:48.261662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.