Paper Citation Record · LEDGER

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature

As of 5 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2606.08006.

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

pith.paper-citation-record.v1
2606.08006 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T19:38:31.237585Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+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

30 of 30 outbound references displayed

verified exact0
verified fuzzy0
unresolved30
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1921596b-fe94-4405-8d78-143ba5472dac · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b265dd0e-8710-4065-aefc-a9e8e8b05706 · outbound

This paper cites Bakry and M.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Bakry and M

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06402d85-ec44-4c29-98eb-e1b00c8d7ced · outbound

This paper cites Bakry, I.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Bakry, I

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22c8a7c2-f062-445a-b8f3-2ea36ad3dc68 · outbound

This paper cites Bauer, F.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Bauer, F

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ff9fda8a-7fe3-46e6-a4f6-f65dc2bd73ba · outbound

This paper cites Bauer, P.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Bauer, P

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8452c2a-1919-4263-8f28-788f60fea33f · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c748baa6-9b30-4a7b-ac9d-291a866ff52d · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75bf865b-8d23-4211-a267-f26f40981741 · outbound

This paper cites Cushing, S.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Cushing, S

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6cdbb24f-7bf8-4a7a-af4d-b453fff66bd0 · outbound

This paper cites Cushing, S.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Cushing, S

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 226951ae-fb06-4b73-b584-506a25ff08b0 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 309bb00d-a444-41f4-80db-08be0ee08205 · outbound

This paper cites Fathi and Y.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Fathi and Y

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc15c971-6d00-4d0a-a29d-1ec22c3cd096 · outbound

This paper cites Gromov.Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Gromov.Metric structures for Riemannian and non-Riemannian spaces, volume 152 of Progress in Mathematics

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe4bf00e-5883-416e-9ed3-9cf4f8198cbe · outbound

This paper cites Harary, J.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Harary, J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c4fe16d-94d3-4173-956f-79b6725c7fe8 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cbdef4c7-1643-40f4-96cf-bf5e75a55a9e · outbound

This paper cites Hu and S.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Hu and S

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0056854-f95b-4768-bdd2-74dfe09a3d32 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a90e7c2-e740-4dd6-8957-149ceb025448 · outbound

This paper cites Hua and F.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Hua and F

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed68fca2-50d5-44ae-9634-8545ff9fa2b4 · outbound

This paper cites Keller and F.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Keller and F

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29d24e79-55e5-44a5-b969-a98a042408ec · outbound

This paper cites Kempton, F.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Kempton, F

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b0a0d5b-1c04-4e5f-862b-56d2ddadec06 · outbound

This paper cites Lichnerowicz.Géométrie des groupes de transformations, volume III ofTravaux et Recherches Mathématiques.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Lichnerowicz.Géométrie des groupes de transformations, volume III ofTravaux et Recherches Mathématiques

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ffe6ffb-9a68-4755-abff-f2da2689d4c8 · outbound

This paper cites Lin and S.-T.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Lin and S.-T

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84c30aa3-89c0-4588-9a2b-99ce848d3d7d · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df78400a-847b-4500-88e9-03ef67bc4603 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e78956db-5364-480b-aa5d-8bc9c2e0de89 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0661575-42c7-4357-a96e-6590b1aa04ec · outbound

This paper cites Münch and C.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Münch and C

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 584275a4-caaa-46b9-9653-7d4b5cdc936b · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d36ddf3-a4c0-42e6-b6b8-bc24b86b8ea6 · outbound

This paper cites Petersen.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Petersen

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72bb3a3b-1ab1-4019-8c68-952da5e7b23c · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edf62c41-8f7c-42f0-9329-212e57fd4647 · outbound

This paper cites an unresolved cited work.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e720d2c9-1e53-4b51-b11c-5f72783326a5 · outbound

This paper cites Schmuckenschläger.

Optimal spectral rigidity of the hypercube via Bakry--\'Emery curvature Schmuckenschläger

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-27T19:38:31.237585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.