Paper Citation Record · LEDGER

Grothendieck positivity for normal square root crystals

As of 15 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2501.16640.

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

pith.paper-citation-record.v1
2501.16640 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T11:53:32.290933Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:27:09.625833Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T14:27:10.982605Z

Reference resolution

31 of 31 outbound references displayed

verified exact3
verified fuzzy25
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 65446179-1b8a-4c94-a606-1b1b088be5a3 · outbound

This paper cites R C -graphs and S chubert polynomials.

Grothendieck positivity for normal square root crystals R C -graphs and S chubert polynomials

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.649287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation aec21264-0c8e-4089-9f4c-2076de2f5cc2 · outbound

This paper cites Combinatorics of C oxeter groups.

Grothendieck positivity for normal square root crystals Combinatorics of C oxeter groups

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.496829Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f04dc779-8579-40bb-b8f2-bd3a096faf6e · outbound

This paper cites Stable G rothendieck polynomials and K -theoretic factor sequences.

Grothendieck positivity for normal square root crystals Stable G rothendieck polynomials and K -theoretic factor sequences

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.423824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 711d6b33-e5d9-4e34-88f7-6e7ed24e18a6 · outbound

This paper cites Crystal bases: representations of combinatorics.

Grothendieck positivity for normal square root crystals Crystal bases: representations of combinatorics

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.414108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ec033a43-2574-493a-9fad-cd94daef57db · outbound

This paper cites A L ittlewood- R ichardson rule for the K -theory of G rassmannians.

Grothendieck positivity for normal square root crystals A L ittlewood- R ichardson rule for the K -theory of G rassmannians

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.403543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 67fa05c6-1768-4e35-8ed0-0274b43d49ec · outbound

This paper cites Balanced tableaux.

Grothendieck positivity for normal square root crystals Balanced tableaux

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.392311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b9f719e5-35d2-441f-a093-45f489bffeab · outbound

This paper cites Kirillov.

Grothendieck positivity for normal square root crystals Kirillov

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.383784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0bcbddd0-d781-4875-aa3f-667dc8c6664d · outbound

This paper cites Characterization of queer supercrystals.

Grothendieck positivity for normal square root crystals Characterization of queer supercrystals

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.374071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 270f0d89-4ef3-4a92-8d4e-b663c77f6bf1 · outbound

This paper cites Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux.

Grothendieck positivity for normal square root crystals Crystal bases for the quantum queer superalgebra and semistandard decomposition tableaux

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.363280Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a95dc8d3-53cf-4a68-b2aa-f80fefc3ed85 · outbound

This paper cites Crystal structures for canonical G rothendieck functions.

Grothendieck positivity for normal square root crystals Crystal structures for canonical G rothendieck functions

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.353246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 419d1b89-59f4-4610-9cd6-a1ff503d5e0c · outbound

This paper cites K -theoretic analogues of factorial S chur P - and Q -functions.

Grothendieck positivity for normal square root crystals K -theoretic analogues of factorial S chur P - and Q -functions

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.342312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 01f873e7-13eb-43c0-b38e-c79fce13abdf · outbound

This paper cites Crystalizing the q -analogue of universal enveloping algebras.

Grothendieck positivity for normal square root crystals Crystalizing the q -analogue of universal enveloping algebras

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.331034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 20f42137-547a-41d7-a785-eb34323ae505 · outbound

This paper cites On crystal bases of the q -analogue of universal enveloping algebras.

Grothendieck positivity for normal square root crystals On crystal bases of the q -analogue of universal enveloping algebras

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.219740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e534ae4-78ee-411a-8271-4f4a8db53f26 · outbound

This paper cites The crystal base and L ittelmann's refined D emazure character formula.

Grothendieck positivity for normal square root crystals The crystal base and L ittelmann's refined D emazure character formula

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.103822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0e426eec-6f3b-4eb7-b786-c56742eaf37a · outbound

This paper cites Subword complexes in coxeter groups.

Grothendieck positivity for normal square root crystals Subword complexes in coxeter groups

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:33.011467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation e26a7c8b-3b26-419f-aa83-d34d852a4ce8 · outbound

This paper cites Gr\"obner geometry of S chubert polynomials.

Grothendieck positivity for normal square root crystals Gr\"obner geometry of S chubert polynomials

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.999272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 28029b65-8ccd-4bbb-a55d-4a84c4afaa72 · outbound

This paper cites Combinatorial aspects of the K -theory of G rassmannians.

Grothendieck positivity for normal square root crystals Combinatorial aspects of the K -theory of G rassmannians

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.988896Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 1ee57320-218b-49a7-b0cb-331a456efc41 · outbound

This paper cites A K -theory version of M onk's formula and some related multiplication formulas.

Grothendieck positivity for normal square root crystals A K -theory version of M onk's formula and some related multiplication formulas

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.978878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b62c5a1a-e130-43d8-af12-ebad329bfc00 · outbound

This paper cites an unresolved cited work.

Grothendieck positivity for normal square root crystals Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T11:53:32.251302Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3952579-7e3f-4a90-baad-e828a99c16f1 · outbound

This paper cites an unresolved cited work.

Grothendieck positivity for normal square root crystals Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-10T11:53:32.962478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0c7441a1-7f38-4509-b3a3-5e0e5b0ea954 · outbound

This paper cites A symplectic refinement of shifted H ecke insertion.

Grothendieck positivity for normal square root crystals A symplectic refinement of shifted H ecke insertion

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.952917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation bc274b57-cedf-4da1-ac34-813f88b707e6 · outbound

This paper cites Set-Valued Skyline Fillings.

Grothendieck positivity for normal square root crystals Set-Valued Skyline Fillings

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-10T11:53:32.633081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 76a9570f-a5d9-4664-ae2a-e97dceb9185c · outbound

This paper cites Crystal structures for symmetric G rothendieck polynomials.

Grothendieck positivity for normal square root crystals Crystal structures for symmetric G rothendieck polynomials

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.942112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation da667bc4-788b-4f2e-8f61-dc19c13291d5 · outbound

This paper cites Crystal approach to affine S chubert calculus.

Grothendieck positivity for normal square root crystals Crystal approach to affine S chubert calculus

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.931597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0653b495-03e5-4ebd-93e2-5c540b0f1c9e · outbound

This paper cites Key and Lascoux polynomials for symmetric orbit closures.

Grothendieck positivity for normal square root crystals Key and Lascoux polynomials for symmetric orbit closures

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-10T11:53:32.550485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 19b6d997-ee64-42e2-af69-861cb0d827e5 · outbound

This paper cites Crystals for set-valued decomposition tableaux, preprint, arXiv:2312.16776 , 2023.

Grothendieck positivity for normal square root crystals Crystals for set-valued decomposition tableaux, preprint, arXiv:2312.16776 , 2023

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-08-10T11:53:32.535870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 7d94a461-14ec-4bc3-b9fc-5e7077525745 · outbound

This paper cites Key polynomials and a flagged L ittlewood-- R ichardson rule.

Grothendieck positivity for normal square root crystals Key polynomials and a flagged L ittlewood-- R ichardson rule

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.920662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 6190a58c-52ae-4821-ae03-7770bb1747b2 · outbound

This paper cites Poset edge densities, nearly reduced words, and barely set-valued tableaux.

Grothendieck positivity for normal square root crystals Poset edge densities, nearly reduced words, and barely set-valued tableaux

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.911272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9e63a4ad-06e5-4160-bf9f-d19cd3e5c392 · outbound

This paper cites an unresolved cited work.

Grothendieck positivity for normal square root crystals Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T11:53:32.900805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 81e8f185-135c-49e9-9e56-46d0bba9c141 · outbound

This paper cites Stembridge.

Grothendieck positivity for normal square root crystals Stembridge

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.849564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 53628db2-a35a-4769-90b8-f33700ee9388 · outbound

This paper cites Set-valued tableaux rule for L ascoux polynomials.

Grothendieck positivity for normal square root crystals Set-valued tableaux rule for L ascoux polynomials

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T11:53:32.717056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation e719af2b-4a40-4226-a7c7-1dc1ca362a4d · inbound

Hybrid Grothendieck polynomials cites this paper.

Hybrid Grothendieck polynomials Grothendieck positivity for normal square root crystals

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-07T14:27:11.073587Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.