Paper Citation Record · LEDGER

Spectral and Isoperimetric Bounds on Flat Tori

As of 21 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2608.13052.

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

pith.paper-citation-record.v1
2608.13052 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:00:39.147081Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

28 of 28 outbound references displayed

verified exact2
verified fuzzy20
unresolved6
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External citation measurements

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Outbound references

Observation 7f3e752f-8057-4f50-8d2d-a0754d2b721f · outbound

This paper cites An improved constant in Banaszczyk's transference theorem.

Spectral and Isoperimetric Bounds on Flat Tori An improved constant in Banaszczyk's transference theorem

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:00:39.210455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e008aa33-dcf2-4db2-81b3-4759146d9067 · outbound

This paper cites Artstein-Avidan, A.

Spectral and Isoperimetric Bounds on Flat Tori Artstein-Avidan, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.393084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b631ce4c-1172-46ec-bfdc-dd174ddb4579 · outbound

This paper cites Autissier, Un lemme matriciel effectif,Math.

Spectral and Isoperimetric Bounds on Flat Tori Autissier, Un lemme matriciel effectif,Math

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.385263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 58419cbe-46c3-49f9-9a05-ff1b2da34264 · outbound

This paper cites Bayle,A differential inequality for the isoperimetric profile, Int.

Spectral and Isoperimetric Bounds on Flat Tori Bayle,A differential inequality for the isoperimetric profile, Int

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.377124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3402ca6d-0f4b-4e45-9bef-75d506f83e21 · outbound

This paper cites Optimal $MM^*$ bounds for convex bodies.

Spectral and Isoperimetric Bounds on Flat Tori Optimal $MM^*$ bounds for convex bodies

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:39.083041Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e53a769-a0ae-476e-8a37-0b621aca9a28 · outbound

This paper cites Buser,A note on the isoperimetric constant, Ann.

Spectral and Isoperimetric Bounds on Flat Tori Buser,A note on the isoperimetric constant, Ann

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.369463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 56aed8d5-c45f-40b9-b300-ed4c58902514 · outbound

This paper cites Cheeger,A lower bound for the smallest eigenvalue of the Laplacian, in: Problems in Analysis (Papers dedicated to Salomon Bochner), Princeton Univ.

Spectral and Isoperimetric Bounds on Flat Tori Cheeger,A lower bound for the smallest eigenvalue of the Laplacian, in: Problems in Analysis (Papers dedicated to Salomon Bochner), Princeton Univ

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.361884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 17e1dfe4-7f0f-4d6d-b0bc-96a8cf665fb5 · outbound

This paper cites Digesting the proof of the sharp thin-shell inequality.

Spectral and Isoperimetric Bounds on Flat Tori Digesting the proof of the sharp thin-shell inequality

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:39.091675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3eab0b37-983f-4940-8e3c-36cbb507ad74 · outbound

This paper cites De Ponti and A.

Spectral and Isoperimetric Bounds on Flat Tori De Ponti and A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.354068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 975bacea-c9cd-4678-9556-31ed18ad7335 · outbound

This paper cites Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem,J.

Spectral and Isoperimetric Bounds on Flat Tori Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem,J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.346573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e5ad899f-c4ad-4bae-b8cd-e9cbfc5d1bb1 · outbound

This paper cites Fradelizi,Hyperplane sections of convex bodies in isotropic position, Beitr.

Spectral and Isoperimetric Bounds on Flat Tori Fradelizi,Hyperplane sections of convex bodies in isotropic position, Beitr

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.338758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b07ef332-2d90-43f8-be2b-94bc11164651 · outbound

This paper cites an unresolved cited work.

Spectral and Isoperimetric Bounds on Flat Tori Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:00:39.330968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c802cfe7-53b7-49a9-8872-d770ec10f064 · outbound

This paper cites Hadwiger,Gitterperiodische Punktmengen und Isoperimetrie, Monatsh.

Spectral and Isoperimetric Bounds on Flat Tori Hadwiger,Gitterperiodische Punktmengen und Isoperimetrie, Monatsh

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.323225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7612c23d-d1ed-4170-a8ba-7149a2982a62 · outbound

This paper cites Hensley,Slicing convex bodies—bounds for slice area in terms of the body’s covariance, Proc.

Spectral and Isoperimetric Bounds on Flat Tori Hensley,Slicing convex bodies—bounds for slice area in terms of the body’s covariance, Proc

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.315454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3294731b-69b1-4e78-b1f0-0a7db76d7727 · outbound

This paper cites Hoshikawa and H.

Spectral and Isoperimetric Bounds on Flat Tori Hoshikawa and H

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.307776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8f47da1b-38cd-4191-9485-438058b8859b · outbound

This paper cites Kannan, L.

Spectral and Isoperimetric Bounds on Flat Tori Kannan, L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.300288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5e450f44-342d-4e43-8390-557901c2ae29 · outbound

This paper cites Klartag,Logarithmic bounds for isoperimetry and slices of convex sets, Ars Inven.

Spectral and Isoperimetric Bounds on Flat Tori Klartag,Logarithmic bounds for isoperimetry and slices of convex sets, Ars Inven

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.292470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ee4c809d-1c45-45e1-9feb-0f02a266cc3e · outbound

This paper cites Klartag and J.

Spectral and Isoperimetric Bounds on Flat Tori Klartag and J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.284724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e99065d4-a99c-468a-940d-8bade3279ec3 · outbound

This paper cites The KLS constant is $O(\log^{1/4} n)$.

Spectral and Isoperimetric Bounds on Flat Tori The KLS constant is $O(\log^{1/4} n)$

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:00:39.122236Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 290d300a-b5cf-4d8e-8f5c-1078bcce5775 · outbound

This paper cites Magazinov,A proof of a conjecture by Haviv, Lyubashevsky and Regev on the second moment of a lattice Voronoi cell, Adv.

Spectral and Isoperimetric Bounds on Flat Tori Magazinov,A proof of a conjecture by Haviv, Lyubashevsky and Regev on the second moment of a lattice Voronoi cell, Adv

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.276845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 1ecc7fa2-3d85-4d36-b85b-83315c0b21a3 · outbound

This paper cites Maggi,Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory, Cambridge Studies in Advanced Mathematics, vol.

Spectral and Isoperimetric Bounds on Flat Tori Maggi,Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory, Cambridge Studies in Advanced Mathematics, vol

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.268692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c6eb4893-f2fa-4aa5-ac1f-8f8dbe1ca33d · outbound

This paper cites Melbourne, M.

Spectral and Isoperimetric Bounds on Flat Tori Melbourne, M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.260522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7eeaba40-d2e9-4961-80b8-6d1cbd39cec7 · outbound

This paper cites Milman, On the role of convexity in isoperimetry, spectral-gap and concentration,Invent.

Spectral and Isoperimetric Bounds on Flat Tori Milman, On the role of convexity in isoperimetry, spectral-gap and concentration,Invent

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.252067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation caba12f3-9ad8-41b5-bd6c-006488ce09d5 · outbound

This paper cites The second minimum of Barnes-Wall lattices.

Spectral and Isoperimetric Bounds on Flat Tori The second minimum of Barnes-Wall lattices

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:00:39.177846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2dc4ccd2-a294-4979-aa50-83d7247c2e9b · outbound

This paper cites an unresolved cited work.

Spectral and Isoperimetric Bounds on Flat Tori Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:00:39.243681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d5c86b64-63b7-4ac6-9990-a6a8a99e0c20 · outbound

This paper cites Ros,The isoperimetric problem, in: Global Theory of Minimal Surfaces, Clay Math.

Spectral and Isoperimetric Bounds on Flat Tori Ros,The isoperimetric problem, in: Global Theory of Minimal Surfaces, Clay Math

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.235784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation c379c26d-5fd3-41ec-871a-1683e11c9496 · outbound

This paper cites an unresolved cited work.

Spectral and Isoperimetric Bounds on Flat Tori Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:00:39.227274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a8d05e43-277d-44c0-a2bb-7cba3e4beff1 · outbound

This paper cites Sternberg and K.

Spectral and Isoperimetric Bounds on Flat Tori Sternberg and K

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:00:39.218985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

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