Paper Citation Record · LEDGER

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions

As of 7 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2505.22127.

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

pith.paper-citation-record.v1
2505.22127 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:32:35.355614Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

22 of 22 outbound references displayed

verified exact1
verified fuzzy13
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 27e64baf-c498-4ce9-8a99-2792af705557 · outbound

This paper cites Berenstein and A.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Berenstein and A

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:39.326471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5b1b394a-911a-4332-b1fe-33dd4b561e0a · outbound

This paper cites Bossinger and G.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Bossinger and G

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:39.162901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e7cf320d-d807-40b0-8d73-842bcda18839 · outbound

This paper cites Bump and A.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Bump and A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:38.971804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8c46d272-35ef-4ba5-8e52-49fd1411fccc · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:38.785553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b9c31fd5-1875-46fa-a6eb-74994017fb49 · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:38.628192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a12b3054-1622-47f5-9d0e-3d3f167c00d1 · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:38.441801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 09ad639e-5448-41a0-8d76-5e0d86a561cd · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:38.253893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1145bc23-3f68-4ee6-b186-10001c7bbcb8 · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:38.090344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7050ca60-aa2c-40f5-a196-c3fbba752e0c · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:37.942138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation faa684a9-0619-4847-8ce5-0beaa423de56 · outbound

This paper cites Gleizer and A.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Gleizer and A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:37.756615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c416a447-5be8-439a-9b4f-8c6c00cd0ad9 · outbound

This paper cites Kashiwara.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Kashiwara

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:37.609715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2da5ff30-ec16-48a0-b942-e4a13cade194 · outbound

This paper cites Kashiwara.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Kashiwara

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:37.485416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c9626a32-441b-4af8-8ff3-c9beab1c137f · outbound

This paper cites Kashiwara.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Kashiwara

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:37.349235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 32f4ce0d-989c-4a30-9553-1a6cdebd59a2 · outbound

This paper cites Kashiwara.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Kashiwara

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:37.173092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3b158ca6-c131-4fcb-a58d-08c6e71835dc · outbound

This paper cites Lascoux and M.-P.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Lascoux and M.-P

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:36.997914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 72a201e3-47b4-4590-9676-0ad0cff7f557 · outbound

This paper cites Lecouvey and C.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Lecouvey and C

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:36.808220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a8aacbd0-0451-4554-844e-219d8f9716e1 · outbound

This paper cites Libedinsky, L.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Libedinsky, L

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:36.617424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dda85b20-92cc-4072-bf41-c2a96ec6e520 · outbound

This paper cites Littelmann.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Littelmann

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:36.404573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cb1ef89a-b55e-4a79-8f48-3cce7913ada2 · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:36.229040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8df5708a-0b93-4ec2-aaec-49c371b33793 · outbound

This paper cites an unresolved cited work.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:32:36.014470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3d37a5db-d436-47c9-b0f0-b3f9612bdf98 · outbound

This paper cites Charges via the Affine Grassmannian.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Charges via the Affine Grassmannian

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:32:35.592081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7054a04e-cd07-485d-b9f2-773e51f9e5ea · outbound

This paper cites Patimo and J.

Unveiling Crystal Embeddings: New Perspectives on String Polytopes and Atomic Decompositions Patimo and J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:32:35.807679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.