Paper Citation Record · LEDGER

Saturation property fails for Schubert coefficients

As of 9 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 1 inbound Pith citation observation for arXiv:2601.04182.

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

pith.paper-citation-record.v1
2601.04182 v2

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T12:20:15.781875Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-07T08:23:09.084562Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T10:01:28.447352Z

Reference resolution

47 of 47 outbound references displayed

verified exact0
verified fuzzy0
unresolved47
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 23054c48-9df9-4f2c-a909-d8df6da98687 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.073926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55624341-ee2b-431d-bf02-0947dc7ffa3c · outbound

This paper cites 383 (2021), Paper No.

Saturation property fails for Schubert coefficients 383 (2021), Paper No

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.184446Z

Source-reported events for the cited work

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Observation 8ad1dca5-9be9-4453-ae40-5ee83e8a9eb6 · outbound

This paper cites 28 (2019), 115--120.

Saturation property fails for Schubert coefficients 28 (2019), 115--120

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.268246Z

Source-reported events for the cited work

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Observation ec90069a-5e14-4757-ba93-330587b7d3bd · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.419928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4281d215-66b1-4924-a095-2e17f8514159 · outbound

This paper cites 149 (2013), 1569--1582.

Saturation property fails for Schubert coefficients 149 (2013), 1569--1582

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.531190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eca057bb-dc35-4f95-9032-3a4ec46da2ae · outbound

This paper cites 15 (2006), 133--173.

Saturation property fails for Schubert coefficients 15 (2006), 133--173

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.670004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 707eb566-3cab-4a73-a89f-8ce7fef9eeb7 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:10.788494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d092403b-721b-41ed-a67a-6d951557d65f · outbound

This paper cites Algebraic Geom.

Saturation property fails for Schubert coefficients Algebraic Geom

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.014524Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b72497b9-60b0-440e-8e0d-16f816a82250 · outbound

This paper cites 354 (2012), 401--425.

Saturation property fails for Schubert coefficients 354 (2012), 401--425

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.146507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22ab5d47-3e31-44da-9ed6-65dbd053829c · outbound

This paper cites 63 (2017), 403--470.

Saturation property fails for Schubert coefficients 63 (2017), 403--470

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.328859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation baf2969d-c8f2-4022-bf2f-96547c62418b · outbound

This paper cites Mulmuley), Comp.\ Complexity 18 (2009), 577--600.

Saturation property fails for Schubert coefficients Mulmuley), Comp.\ Complexity 18 (2009), 577--600

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.470953Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db1f77c2-678b-41e3-9806-200a9693a9b4 · outbound

This paper cites Buch, The saturation conjecture (after A.

Saturation property fails for Schubert coefficients Buch, The saturation conjecture (after A

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.653484Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cafb3e2-1134-4609-b0d9-c2e4a0002d6c · outbound

This paper cites Buch, A Littlewood--Richardson rule for the K -theory of Grassmannians, Acta Math.

Saturation property fails for Schubert coefficients Buch, A Littlewood--Richardson rule for the K -theory of Grassmannians, Acta Math

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.830065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56c6d8e5-f36c-489f-a604-ea48eae41111 · outbound

This paper cites Buch, Andrew Kresch, Kevin Purbhoo and Harry Tamvakis, The puzzle conjecture for the cohomology of two-step flag manifolds, J.

Saturation property fails for Schubert coefficients Buch, Andrew Kresch, Kevin Purbhoo and Harry Tamvakis, The puzzle conjecture for the cohomology of two-step flag manifolds, J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:11.993953Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4d68c55-2ac2-465d-85bc-2629b0c5e5f2 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.080826Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 582516b5-045d-41d6-aa30-f32694a1c2e3 · outbound

This paper cites 176 (2009), 325--395.

Saturation property fails for Schubert coefficients 176 (2009), 325--395

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.138884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c404ae70-472c-4ddf-b4e9-57cb28b56b44 · outbound

This paper cites De Loera and Tyrrell B.

Saturation property fails for Schubert coefficients De Loera and Tyrrell B

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.220151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48839b3a-55a2-45e9-8a1e-85ac28fab707 · outbound

This paper cites AMS 13 (2000), 467--479.

Saturation property fails for Schubert coefficients AMS 13 (2000), 467--479

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.275958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b91a8d7-f885-4df6-b5bd-00d79066ce7b · outbound

This paper cites \`Elashvili, Invariant algebras, in Lie groups, their discrete subgroups, and invariant theory, AMS, Providence, RI, 1992, 57--64.

Saturation property fails for Schubert coefficients \`Elashvili, Invariant algebras, in Lie groups, their discrete subgroups, and invariant theory, AMS, Providence, RI, 1992, 57--64

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.329242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba51383d-f2e3-4a68-8666-2e9edc07820e · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.379149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e6e65e7-d038-462a-84d2-d754023bd64d · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.390115Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d40fa009-33d3-4a7f-91d5-a23f235b36c9 · outbound

This paper cites AMS 374 (2021), 6331--6366.

Saturation property fails for Schubert coefficients AMS 374 (2021), 6331--6366

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.514062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e151e22-8c87-4334-97d7-330df2ad5104 · outbound

This paper cites Mulmuley and Michael Walter, On vanishing of Kronecker coefficients, Comp.\ Complexity 26 (2017), 949--992.

Saturation property fails for Schubert coefficients Mulmuley and Michael Walter, On vanishing of Kronecker coefficients, Comp.\ Complexity 26 (2017), 949--992

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.674631Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6dda7bf9-21e1-4015-be55-b0af16c46e18 · outbound

This paper cites Millson, A path model for geodesics in Euclidean buildings and its applications to representation theory, Groups Geom.\ Dyn.

Saturation property fails for Schubert coefficients Millson, A path model for geodesics in Euclidean buildings and its applications to representation theory, Groups Geom.\ Dyn

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.799935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b18e56c-da48-44c3-927f-1f1cf3d5957f · outbound

This paper cites King, Christophe Tollu and Fr\'ed\'eric Toumazet, Stretched Littlewood--Richardson and Kostka coefficients, in Symmetry in physics, AMS, Providence, RI, 2004, 99--112.

Saturation property fails for Schubert coefficients King, Christophe Tollu and Fr\'ed\'eric Toumazet, Stretched Littlewood--Richardson and Kostka coefficients, in Symmetry in physics, AMS, Providence, RI, 2004, 99--112

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:12.925766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c79b7223-79c8-4a04-afd7-4077daaf6664 · outbound

This paper cites Kirillov, An invitation to the generalized saturation conjecture, Publ.\ RIMS 40 (2004), 1147--1239.

Saturation property fails for Schubert coefficients Kirillov, An invitation to the generalized saturation conjecture, Publ.\ RIMS 40 (2004), 1147--1239

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.071907Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f158134-ed12-4ddf-84e8-b6f9ffc58705 · outbound

This paper cites Quantum marginal problem and representations of the symmetric group.

Saturation property fails for Schubert coefficients Quantum marginal problem and representations of the symmetric group

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.178004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b995788e-73de-4c6d-a200-cdff9cd693d7 · outbound

This paper cites 71, Math.\ Soc.\ Japan, Tokyo, 2016, 185--209.

Saturation property fails for Schubert coefficients 71, Math.\ Soc.\ Japan, Tokyo, 2016, 185--209

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.341166Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 200e3702-9955-4ecd-ae55-603af47939ce · outbound

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

Saturation property fails for Schubert coefficients VI, EMS Press, 4582--4605

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.415106Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd7c187a-e81f-48fd-a0c1-5836d3209c7f · outbound

This paper cites AMS 12 (1999), 1055--1090.

Saturation property fails for Schubert coefficients AMS 12 (1999), 1055--1090

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.542808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5ac5272-8318-4aa1-9a85-18da7cd5f9a9 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.658808Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9faf2a3e-f46b-48d9-8827-25f59e3ca0bf · outbound

This paper cites The honeycomb model of GL_n( C ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone.

Saturation property fails for Schubert coefficients The honeycomb model of GL_n( C ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.787655Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4620b82a-1ac0-430b-8b75-cd7177ca6195 · outbound

This paper cites With an appendix by M.

Saturation property fails for Schubert coefficients With an appendix by M

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:13.938920Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 672e8002-81c2-4994-a3a0-9ee2e0f15011 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.063930Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57a7dd99-85e8-441a-81a3-c8c6df5f3b37 · outbound

This paper cites Macdonald, Symmetric functions and Hall polynomials (Second ed.), Oxford U.

Saturation property fails for Schubert coefficients Macdonald, Symmetric functions and Hall polynomials (Second ed.), Oxford U

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.249752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed33429f-8a35-40ca-896a-49405724941e · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.396974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e91b2fb1-eb42-4ed6-9465-c0752c8734cf · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.542089Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b148b93-4a86-4d64-94f8-271a9b5fd554 · outbound

This paper cites Geometric Complexity Theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry.

Saturation property fails for Schubert coefficients Geometric Complexity Theory VI: the flip via saturated and positive integer programming in representation theory and algebraic geometry

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.635821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e1ecf9f-c3a8-4ec2-911e-d45d56ac90ca · outbound

This paper cites Mulmuley, Hariharan Narayanan and Milind Sohoni, Geometric complexity theory III.

Saturation property fails for Schubert coefficients Mulmuley, Hariharan Narayanan and Milind Sohoni, Geometric complexity theory III

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.765588Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e08ff87-fc17-4c05-a546-12f0f2c2082c · outbound

This paper cites R.\ Math.\ Acad.\ Sci.\ Paris 358 (2020), no.

Saturation property fails for Schubert coefficients R.\ Math.\ Acad.\ Sci.\ Paris 358 (2020), no

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:14.891770Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e56a096-1080-487f-9984-7549498f0a38 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.024912Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3324a71-f83a-4905-babc-06751d25996d · outbound

This paper cites II, Cambridge Univ.\ Press, Cambridge, UK, 2022, 284--335.

Saturation property fails for Schubert coefficients II, Cambridge Univ.\ Press, Cambridge, UK, 2022, 284--335

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.148497Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91bd2f4d-5747-413f-89db-54f32f13d764 · outbound

This paper cites Rosas, The Kronecker product of Schur functions indexed by two-row shapes or hook shapes, J.\ Algebraic Combin.

Saturation property fails for Schubert coefficients Rosas, The Kronecker product of Schur functions indexed by two-row shapes or hook shapes, J.\ Algebraic Combin

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.288447Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7b60f79-7fc9-411d-b547-dddf90e2f43d · outbound

This paper cites Sam and Andrew Snowden, Proof of Stembridge's conjecture on stability of Kronecker coefficients, J.

Saturation property fails for Schubert coefficients Sam and Andrew Snowden, Proof of Stembridge's conjecture on stability of Kronecker coefficients, J

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.405443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0a6280c-ac09-48e5-af2d-b0a55e3d335c · outbound

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

Saturation property fails for Schubert coefficients Dizier and Alexander Yong, Generalized permutahedra and S chubert calculus, Arnold Math

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.529831Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60325fb8-da10-4c3d-bc21-f2ef6274a4df · outbound

This paper cites Stanley, Enumerative Combinatorics , vol.

Saturation property fails for Schubert coefficients Stanley, Enumerative Combinatorics , vol

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.650688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a854d283-d95b-4abf-9615-94649043e3a7 · outbound

This paper cites an unresolved cited work.

Saturation property fails for Schubert coefficients Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-03T12:20:15.781875Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 03bb3625-97df-4898-a54c-d50c8d8008b8 · inbound

Stretched Schubert coefficients are eventually quasi-polynomial cites this paper.

Stretched Schubert coefficients are eventually quasi-polynomial Saturation property fails for Schubert coefficients

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-07-13T02:18:53.777388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.