Paper Citation Record · LEDGER

An arithmetic measure of width for convex bodies

As of 22 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2509.04726.

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

pith.paper-citation-record.v1
2509.04726 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:38:46.906872Z

measured 38 of 38 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:23:13.479331Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-16T00:23:13.535343Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy33
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ec39240b-e536-4026-a472-3a7e0ae9ea43 · outbound

This paper cites The hardness of approximate optima in lattices, codes, and systems of linear equations.Journal of Computer and System Sciences, 54(2):317– 331, 1997.

An arithmetic measure of width for convex bodies The hardness of approximate optima in lattices, codes, and systems of linear equations.Journal of Computer and System Sciences, 54(2):317– 331, 1997

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.496673Z

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 8f081c09-28b0-40b8-ae37-bb5c01dcf4d7 · outbound

This paper cites De Loera, Alexey Garber, Sof´ ıa Garz´ on Mora, Katharina Jochemko, and Josephine Yu.

An arithmetic measure of width for convex bodies De Loera, Alexey Garber, Sof´ ıa Garz´ on Mora, Katharina Jochemko, and Josephine Yu

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.457132Z

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 55b0cece-b085-471a-9796-ad6741068787 · outbound

This paper cites An upper bound on the size of Sidon sets.The American Mathematical Monthly, 130(5):437–445, 2023.

An arithmetic measure of width for convex bodies An upper bound on the size of Sidon sets.The American Mathematical Monthly, 130(5):437–445, 2023

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.425537Z

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 f7517900-0f5b-43c4-8154-4bd92203b1b6 · outbound

This paper cites American Mathematical Society, 2002.

An arithmetic measure of width for convex bodies American Mathematical Society, 2002

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.399084Z

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 ed6fd324-04b6-4241-ad31-bee5b33a5a98 · outbound

This paper cites Pommersheim.

An arithmetic measure of width for convex bodies Pommersheim

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.281014Z

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 09539208-1998-4c3c-be01-8b3d8771a063 · outbound

This paper cites Short rational generating functions for lattice point problems.J.

An arithmetic measure of width for convex bodies Short rational generating functions for lattice point problems.J

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.247889Z

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 ca833696-235a-4ea3-805e-dd52015302ec · outbound

This paper cites On multigraded Hilbert functions and resolutions.Mathematische Proceedings of the Cambridge Philosophical Society, 118:245–257, 1995.

An arithmetic measure of width for convex bodies On multigraded Hilbert functions and resolutions.Mathematische Proceedings of the Cambridge Philosophical Society, 118:245–257, 1995

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.219768Z

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 27dc95ec-d1df-4412-94c0-602d3c29727b · outbound

This paper cites Efficient lattice width computation in arbitrary dimension.

An arithmetic measure of width for convex bodies Efficient lattice width computation in arbitrary dimension

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.181044Z

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 8404b352-8dfc-478b-9382-19e7b4728630 · outbound

This paper cites Generalised flatness constants: A framework applied in dimension 2, 2021.

An arithmetic measure of width for convex bodies Generalised flatness constants: A framework applied in dimension 2, 2021

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.153163Z

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 6a2b1b5e-bf8b-49c9-a8bc-55f0ffa925fe · outbound

This paper cites PhD thesis, Georgia Institute of Technology, 2012.

An arithmetic measure of width for convex bodies PhD thesis, Georgia Institute of Technology, 2012

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.124912Z

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 ba0095ab-1531-4350-aaf1-da29193b614b · outbound

This paper cites De Loera, Raymond Hemmecke, Jeremiah Tauzer, and Ruriko Yoshida.

An arithmetic measure of width for convex bodies De Loera, Raymond Hemmecke, Jeremiah Tauzer, and Ruriko Yoshida

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:49.059652Z

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 b6cc4963-825f-4556-a8f6-a4bfe27a6e6b · outbound

This paper cites Lattice-free polytopes and their diameter.Discrete & Computational Geometry, 13(1):59–76, 1995.

An arithmetic measure of width for convex bodies Lattice-free polytopes and their diameter.Discrete & Computational Geometry, 13(1):59–76, 1995

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.918643Z

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 30327fc2-c44a-448f-89c2-877dfeb5b798 · outbound

This paper cites Parametric integer programming in fixed dimension.Math- ematics of Operations Research, 33(4):839–850, 2008.

An arithmetic measure of width for convex bodies Parametric integer programming in fixed dimension.Math- ematics of Operations Research, 33(4):839–850, 2008

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.846398Z

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 7fd22894-b5aa-458c-9ab1-9d0c99b3b503 · outbound

This paper cites Parrilo, James Saunderson, and Rekha R.

An arithmetic measure of width for convex bodies Parrilo, James Saunderson, and Rekha R

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.766739Z

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 212ac9b8-eb56-401d-ba42-21050e8a6541 · outbound

This paper cites The lattice width and quasi-straightness in digital spaces.

An arithmetic measure of width for convex bodies The lattice width and quasi-straightness in digital spaces

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.599322Z

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 71621225-c7fc-4b5e-b227-fe06f83436a4 · outbound

This paper cites an unresolved cited work.

An arithmetic measure of width for convex bodies Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:38:48.565031Z

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 899ac3cb-52bf-4889-9649-f5a4e0e4dbfa · outbound

This paper cites A structure theorem for sets of lengths.Colloq.

An arithmetic measure of width for convex bodies A structure theorem for sets of lengths.Colloq

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.542849Z

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 1c38fc4b-0de3-416a-af75-76d426bc2f8d · outbound

This paper cites Sets of lengths.Amer.

An arithmetic measure of width for convex bodies Sets of lengths.Amer

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.425987Z

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 bc2fa73d-a1ea-4c62-b730-1227b19b9324 · outbound

This paper cites Chapman & Hall/CRC, Boca Raton, FL, 2006.

An arithmetic measure of width for convex bodies Chapman & Hall/CRC, Boca Raton, FL, 2006

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.312780Z

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 73094146-deb4-4dde-9818-056f3b19e247 · outbound

This paper cites A realization theorem for sets of lengths in numerical monoids.Forum Math., 30(5):1111–1118, 2018.

An arithmetic measure of width for convex bodies A realization theorem for sets of lengths in numerical monoids.Forum Math., 30(5):1111–1118, 2018

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.287023Z

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 b2db1ac3-7f9c-4bc4-a98f-7b556c5219a7 · outbound

This paper cites Computing the integer programming gap.Combinatorica, 27(4):367– 382, 2007.

An arithmetic measure of width for convex bodies Computing the integer programming gap.Combinatorica, 27(4):367– 382, 2007

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.158157Z

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 a18189d6-5bc0-42a8-bfaa-3c8cd2d0b4a2 · outbound

This paper cites an unresolved cited work.

An arithmetic measure of width for convex bodies Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:38:48.119258Z

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 f8f6f586-fe88-401c-b873-674bdfcb050a · outbound

This paper cites an unresolved cited work.

An arithmetic measure of width for convex bodies Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:38:48.081827Z

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 518dd860-130b-4464-8428-552ad84de6a8 · outbound

This paper cites Geometry of numbers and integer programming.Mathematical programming: recent de- velopments and applications, pages 177–210, 1989.

An arithmetic measure of width for convex bodies Geometry of numbers and integer programming.Mathematical programming: recent de- velopments and applications, pages 177–210, 1989

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:48.004606Z

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 63b8a85a-5a3a-4e1a-8f5a-1fae53901c7f · outbound

This paper cites Lattice-free simplices with lattice width 2d - o(d).

An arithmetic measure of width for convex bodies Lattice-free simplices with lattice width 2d - o(d)

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.855746Z

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 54e769a7-6913-4e8f-8730-42f424a9c3a7 · outbound

This paper cites The Kluwer International Series in Engineering and Computer Science.

An arithmetic measure of width for convex bodies The Kluwer International Series in Engineering and Computer Science

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.813973Z

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 be3f9c53-a80e-4190-9ba0-2af603933dda · outbound

This paper cites Springer, 2005.

An arithmetic measure of width for convex bodies Springer, 2005

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.779551Z

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 e9e8d0d7-ad82-4e31-bde8-d28ac40e00bf · outbound

This paper cites The structure theorem for sets of lengths for numerical semi- groups.J.

An arithmetic measure of width for convex bodies The structure theorem for sets of lengths for numerical semi- groups.J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.660167Z

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 c204d5aa-ccd9-4fb2-9b2b-3ea5529dcc5e · outbound

This paper cites Nguyen and Brigitte Vall´ ee.

An arithmetic measure of width for convex bodies Nguyen and Brigitte Vall´ ee

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.630871Z

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 61efedaa-ef79-4f24-a867-446cda5e24f1 · outbound

This paper cites The subspace flatness conjecture and faster integer programming.

An arithmetic measure of width for convex bodies The subspace flatness conjecture and faster integer programming

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.561543Z

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 06b32a3d-a853-45a6-aea9-16ba655da720 · outbound

This paper cites An analog of Freiman’s theorem in groups.Ast´ erisque, 258(199):323–326, 1999.

An arithmetic measure of width for convex bodies An analog of Freiman’s theorem in groups.Ast´ erisque, 258(199):323–326, 1999

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T16:38:46.713952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52773f6f-fd23-4aef-b30d-8cd0ec2b5909 · outbound

This paper cites Salem and D.

An arithmetic measure of width for convex bodies Salem and D

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.404768Z

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 48ef1cef-a1f1-4a47-a6ff-cf019c345ebc · outbound

This paper cites Stanley.Combinatorics and Commutative Algebra.

An arithmetic measure of width for convex bodies Stanley.Combinatorics and Commutative Algebra

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.374196Z

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 2ede59a8-1220-4bfb-b140-3f2c67997452 · outbound

This paper cites Combinatorial secant varieties.Pure and Applied Mathematics Quar- terly, 2(3):867–891, 2006.

An arithmetic measure of width for convex bodies Combinatorial secant varieties.Pure and Applied Mathematics Quar- terly, 2(3):867–891, 2006

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.272890Z

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 fb9c193b-9ab0-45ee-9b61-9d3ad07e8263 · outbound

This paper cites Freiman’s theorem for solvable groups.Contrib.

An arithmetic measure of width for convex bodies Freiman’s theorem for solvable groups.Contrib

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.238887Z

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 de881428-c2bb-48fb-ab6e-581f51f7e057 · outbound

This paper cites Another NP-complete partition problem and the complexity of computing short vectors in a lattice.

An arithmetic measure of width for convex bodies Another NP-complete partition problem and the complexity of computing short vectors in a lattice

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.090209Z

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 15d1c840-4dbf-4198-9c71-a37353733dd2 · outbound

This paper cites Ziegler.Lectures on Polytopes, volume 152 ofGraduate Texts in Mathematics.

An arithmetic measure of width for convex bodies Ziegler.Lectures on Polytopes, volume 152 ofGraduate Texts in Mathematics

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:38:47.030171Z

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

Observation ff9e1733-f76c-4c8f-bccb-dc0ddfa718b5 · inbound

A Sharp Four-Layer Theorem for Integer-Occupied Slices of a Planar Disk-Slab cites this paper.

A Sharp Four-Layer Theorem for Integer-Occupied Slices of a Planar Disk-Slab An arithmetic measure of width for convex bodies

Reference 5

Resolution: metadata mismatch; local_arxiv, observed 2026-08-16T00:23:13.541539Z

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.