Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T11:53:32.290933Z
Paper Citation Record · LEDGER
Grothendieck positivity for normal square root crystals
As of 16 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:27:09.625833Z
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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.