Paper Citation Record · LEDGER

Variations on five-dimensional sphere packings

As of 12 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 3 inbound Pith citation observations for arXiv:2412.00937.

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

pith.paper-citation-record.v1
2412.00937 v3

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T05:02:52.914749Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:06:24.003193Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T02:49:24.593146Z

Reference resolution

23 of 23 outbound references displayed

verified exact14
verified fuzzy0
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d35282d7-abb8-438f-95b0-e5397d754245 · outbound

This paper cites Locally optimal 2-periodic sphere packings.

Variations on five-dimensional sphere packings Locally optimal 2-periodic sphere packings

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.229310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 381b0b37-5e51-471b-8fac-b1811b81c4e9 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 2

Resolution: verified exact; doi, observed 2026-08-12T05:02:53.024818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 82e549d0-009a-4b8f-887c-14491d223ec3 · outbound

This paper cites Rigidity of spherical codes.

Variations on five-dimensional sphere packings Rigidity of spherical codes

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.214867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 87582d2d-3f9e-4444-9fb0-ad6ac5922af1 · outbound

This paper cites The sphere packing problem in dimension 24.

Variations on five-dimensional sphere packings The sphere packing problem in dimension 24

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.200814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c5682365-96b2-4ef0-a58a-072635992098 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T05:02:52.840952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d75781f-a35e-4bf7-9d4b-16d4e4294d55 · outbound

This paper cites Optimality and uniqueness of the $D_4$ root system.

Variations on five-dimensional sphere packings Optimality and uniqueness of the $D_4$ root system

Reference 6

Resolution: metadata mismatch; local_arxiv, observed 2026-08-12T05:02:53.185983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fa6c3549-cead-4dd8-b01f-a306f6ef86a6 · outbound

This paper cites A formal proof of the Kepler conjecture.

Variations on five-dimensional sphere packings A formal proof of the Kepler conjecture

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T05:02:52.850148Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70582aa5-c8c5-47b4-bc62-f4f3e4a6b67e · outbound

This paper cites Hales, A proof of the Kepler conjecture , Ann.

Variations on five-dimensional sphere packings Hales, A proof of the Kepler conjecture , Ann

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T05:02:52.854537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83148c2e-170a-4a47-beb8-d760e04ae244 · outbound

This paper cites Korkine and G.

Variations on five-dimensional sphere packings Korkine and G

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T05:02:52.858700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29495339-d7b6-4510-91ca-dde0eb412f30 · outbound

This paper cites Notions of denseness.

Variations on five-dimensional sphere packings Notions of denseness

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.162921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1206fd3e-5ef5-4fea-b80c-b50adf199ce2 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 11

Resolution: verified exact; doi, observed 2026-08-12T05:02:52.995942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e7fb0ff8-aa59-46ca-adf6-4c21aabf3c36 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 12

Resolution: verified exact; doi, observed 2026-08-12T05:02:52.985009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 110da3ea-601f-4578-8fa6-8f86dd533f50 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-08-12T05:02:52.974336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bfa5b161-a0b4-4bd7-9576-f6fdf3d5c0fb · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-12T05:02:53.249663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8121dceb-3f89-4212-982d-6cf7b7b3dabd · outbound

This paper cites High accuracy semidefinite programming bounds for kissing numbers.

Variations on five-dimensional sphere packings High accuracy semidefinite programming bounds for kissing numbers

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.149004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 55e2ec7e-590a-4b44-ac58-c1b7e771c9e7 · outbound

This paper cites The kissing number in four dimensions.

Variations on five-dimensional sphere packings The kissing number in four dimensions

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.134681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c4ce7b35-5f1a-4d6f-844a-8d2bd569d648 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-08-12T05:02:52.963935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a3ec2fc8-6a00-43aa-9140-2cffbe1361fa · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 18

Resolution: metadata mismatch; raw_fallback, observed 2026-08-12T05:02:53.119848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f3d89733-785e-472b-ae4c-28a2c349af23 · outbound

This paper cites Sch¨ utte and B.

Variations on five-dimensional sphere packings Sch¨ utte and B

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T05:02:52.898660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d5f0306c-e436-481d-bb7e-08adaa8e872d · outbound

This paper cites A note on five dimensional kissing arrangements.

Variations on five-dimensional sphere packings A note on five dimensional kissing arrangements

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.054209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 22116611-aada-4b6e-ac56-c59f63569775 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T05:02:53.239321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d6303050-4b18-41e0-bee1-2b48002eb316 · outbound

This paper cites The sphere packing problem in dimension 8.

Variations on five-dimensional sphere packings The sphere packing problem in dimension 8

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:02:53.040290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 019c7d12-0972-428d-a859-62ffdde93673 · outbound

This paper cites an unresolved cited work.

Variations on five-dimensional sphere packings Unresolved cited work

Reference 23

Resolution: verified exact; doi, observed 2026-08-12T05:02:52.945512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation f77309ad-c677-4373-9be7-b4414d96dd44 · inbound

Classification of independent sets in signed Johnson graphs and applications to kissing arrangements cites this paper.

Classification of independent sets in signed Johnson graphs and applications to kissing arrangements Variations on five-dimensional sphere packings

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-07T03:17:07.345051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 90b0b503-b4f2-485b-8a34-8c6d974e969d · inbound

Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere cites this paper.

Structure of kissing arrangements in ${\mathbb R}^{12}$ and a place for the $841$st sphere Variations on five-dimensional sphere packings

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-07T03:17:07.345051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d2652413-ccf2-4195-8b98-b052adcc8bc4 · inbound

Linear Programming Bounds for Fibered Sphere Packings cites this paper.

Linear Programming Bounds for Fibered Sphere Packings Variations on five-dimensional sphere packings

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T03:06:24.003193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.