Paper Citation Record · LEDGER

Positivity of Schubert Coefficients

As of 12 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2412.18984.

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

pith.paper-citation-record.v1
2412.18984 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T01:04:45.207505Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:04:11.330210Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-12T00:04:11.479198Z

Reference resolution

38 of 38 outbound references displayed

verified exact4
verified fuzzy13
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 27421f9b-63e8-4ac5-bc47-0a467b86774e · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.815007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9d211ca2-5cb1-47bb-bcea-d3030feaad00 · outbound

This paper cites A parametric version of the Hilbert Nullstellensatz.

Positivity of Schubert Coefficients A parametric version of the Hilbert Nullstellensatz

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-11T01:04:45.451823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c6491bc1-e9bf-4517-a04f-05484e4e14f9 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.034367Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81a7c24e-08c7-4f3c-b98f-84ee73ddaa09 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.040314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ef2cb58-43ef-4a46-945f-479e947bf42a · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.781263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e56ae43a-6e58-46cd-b6a0-bec22407642e · outbound

This paper cites Buch, Frank Sottile and Alexander Yong, Quiver coefficients are Schubert structure constants, Math.\ Res.\ Lett.

Positivity of Schubert Coefficients Buch, Frank Sottile and Alexander Yong, Quiver coefficients are Schubert structure constants, Math.\ Res.\ Lett

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.766513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6d0f87b2-6b90-498e-9ff9-8601615582bb · outbound

This paper cites Pi 12 (2024), Paper No.

Positivity of Schubert Coefficients Pi 12 (2024), Paper No

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.058485Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f25e586-f1f9-4318-988d-7dcb8510c8b6 · outbound

This paper cites 1015 (2024), Paper No.

Positivity of Schubert Coefficients 1015 (2024), Paper No

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.065279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 693f6b20-454c-448f-a672-146992d1c4b7 · outbound

This paper cites Equality cases of the Stanley--Yan log-concave matroid inequality.

Positivity of Schubert Coefficients Equality cases of the Stanley--Yan log-concave matroid inequality

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.071245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1010a059-17bc-4f63-8cf2-f61c8b2a4db7 · outbound

This paper cites Farmer, Currently there are no reasons to doubt the Riemann Hypothesis, preprint (2022), 58 pp.; arXiv:2211.11671.

Positivity of Schubert Coefficients Farmer, Currently there are no reasons to doubt the Riemann Hypothesis, preprint (2022), 58 pp.; arXiv:2211.11671

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-11T01:04:45.418754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 55035f6d-1ba8-4518-b64f-066290db9783 · outbound

This paper cites Gasarch, The third =?\.

Positivity of Schubert Coefficients Gasarch, The third =?\

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.732670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 86d397c8-9812-4337-b6f3-6f8a4bdaa731 · outbound

This paper cites A conceptual perspective, Cambridge Univ.\ Press, Cambridge, UK, 2008, 606 pp.

Positivity of Schubert Coefficients A conceptual perspective, Cambridge Univ.\ Press, Cambridge, UK, 2008, 606 pp

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.715659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e5cfc5f1-00d1-41ef-8073-e74f73a06c36 · outbound

This paper cites Symbolic Comput.

Positivity of Schubert Coefficients Symbolic Comput

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.098945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f954c8ce-d20a-4c2f-b87b-a96d8c28a898 · outbound

This paper cites What is in #P and what is not?.

Positivity of Schubert Coefficients What is in #P and what is not?

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.103004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5363498d-9bf3-40ae-b076-393323be25cd · outbound

This paper cites (2024), no.

Positivity of Schubert Coefficients (2024), no

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.694005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 232b11b8-f953-454e-b4db-7e6098c1bc36 · outbound

This paper cites 10 (2001), 345--353.

Positivity of Schubert Coefficients 10 (2001), 345--353

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.679455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b793f758-df95-4bcf-b29f-65034311fe57 · outbound

This paper cites VI, EMS Press, 4582--4605.

Positivity of Schubert Coefficients VI, EMS Press, 4582--4605

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.114949Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ccc6220-3b89-45a8-9c7f-689d6dac311e · outbound

This paper cites Schubert puzzles and integrability I: invariant trilinear forms.

Positivity of Schubert Coefficients Schubert puzzles and integrability I: invariant trilinear forms

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.118920Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fcce8e12-c142-43b4-8da3-c8346bbd9cd5 · outbound

This paper cites Schubert puzzles and integrability III: separated descents.

Positivity of Schubert Coefficients Schubert puzzles and integrability III: separated descents

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.123390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cece361-cbc2-44f2-8f0b-96edab517e67 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.657539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 928184ec-7a3f-4462-b576-0019d3d24464 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.643386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 558fe21a-d3b7-4e5c-ad66-1c5c287b5afb · outbound

This paper cites Macdonald, Notes on Schubert polynomials, Publ.\ LaCIM, UQAM, Montreal, 1991, 116 pp.

Positivity of Schubert Coefficients Macdonald, Notes on Schubert polynomials, Publ.\ LaCIM, UQAM, Montreal, 1991, 116 pp

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.629684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dfcf9feb-e0cd-43eb-a059-109e84a2c125 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.141859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0548c55-0877-494e-b1e5-ae90082d187a · outbound

This paper cites Miltersen and N.

Positivity of Schubert Coefficients Miltersen and N

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.604186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fe4e76fc-017b-41fd-861a-b06956415801 · outbound

This paper cites IV, World Sci., Hackensack, NJ, 2018, 3153--3180.

Positivity of Schubert Coefficients IV, World Sci., Hackensack, NJ, 2018, 3153--3180

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.592152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dc1a9b99-2230-41e5-813a-b050cc9cf952 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.154435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 886547c3-0be2-4238-a39f-f5e9d2659ad9 · outbound

This paper cites Signed combinatorial interpretations in algebraic combinatorics.

Positivity of Schubert Coefficients Signed combinatorial interpretations in algebraic combinatorics

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-11T01:04:45.284656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7f87ff84-8eb7-4e74-9091-7358c062afe8 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.569940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 379c0fd8-cdc0-42f7-956d-31b662fc5081 · outbound

This paper cites Computational Complexity in Algebraic Combinatorics.

Positivity of Schubert Coefficients Computational Complexity in Algebraic Combinatorics

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.167766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4faea2c8-fd63-4b10-a5fa-9944ee38fd73 · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.554468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e7579214-f9af-4b70-a6cc-44257216e7ff · outbound

This paper cites 24590, 38 pp.

Positivity of Schubert Coefficients 24590, 38 pp

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.540715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ef5e3d5-f966-45ef-9be1-00e0c1785485 · outbound

This paper cites Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz.

Positivity of Schubert Coefficients Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-11T01:04:45.252041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b977ee39-0469-4d07-9339-8d5f702b120f · outbound

This paper cites Dizier and Alexander Yong, Generalized permutahedra and S chubert calculus, Arnold Math.

Positivity of Schubert Coefficients Dizier and Alexander Yong, Generalized permutahedra and S chubert calculus, Arnold Math

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.527886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2a1ced86-2930-4b63-8204-c0d5b512cb55 · outbound

This paper cites Stanley, Positivity problems and conjectures in algebraic combinatorics, in Mathematics: frontiers and perspectives, AMS, Providence, RI, 2000, 295--319.

Positivity of Schubert Coefficients Stanley, Positivity problems and conjectures in algebraic combinatorics, in Mathematics: frontiers and perspectives, AMS, Providence, RI, 2000, 295--319

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T01:04:45.191296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b69bc46c-e3f9-4a8f-b242-edde524bba5d · outbound

This paper cites Stanley, Enumerative Combinatorics , vol.

Positivity of Schubert Coefficients Stanley, Enumerative Combinatorics , vol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.502850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cf055f85-9c7a-4faa-ada2-85d90b601ca5 · outbound

This paper cites Vadhan, Pseudorandomness, Found.\ Trends Theor.\ Comput.\ Sci.

Positivity of Schubert Coefficients Vadhan, Pseudorandomness, Found.\ Trends Theor.\ Comput.\ Sci

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.489838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 57e2d392-80be-4860-a583-9627cd9183bd · outbound

This paper cites an unresolved cited work.

Positivity of Schubert Coefficients Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-11T01:04:45.476612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6e284b22-8684-4eaa-a8f8-7e64efd5a352 · outbound

This paper cites Wilf, What is an answer?, Amer.\ Math.\ Monthly 89 (1982), no.

Positivity of Schubert Coefficients Wilf, What is an answer?, Amer.\ Math.\ Monthly 89 (1982), no

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T01:04:45.464049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation f9bf263b-57de-477c-a085-2be74ebacc85 · inbound

Vanishing of Schubert Coefficients cites this paper.

Vanishing of Schubert Coefficients Positivity of Schubert Coefficients

Reference 90

Resolution: verified exact; local_arxiv, observed 2026-08-12T00:04:11.497471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.