Paper Citation Record · LEDGER

Remarks on the Brouwer Conjecture

As of 18 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2508.07550.

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

pith.paper-citation-record.v1
2508.07550 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T22:15:34.663574Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:20:46.851965Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

31 of 31 outbound references displayed

verified exact3
verified fuzzy14
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1f08f1b0-acf4-46d9-b781-1535bfbbb611 · outbound

This paper cites Anderson and T.D.

Remarks on the Brouwer Conjecture Anderson and T.D

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.164344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2735e35b-0cd2-4506-b999-c6cedaafccf9 · outbound

This paper cites Balakrishnan and K.

Remarks on the Brouwer Conjecture Balakrishnan and K

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.149117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f3a07bad-6373-4b28-a632-54c3f951079d · outbound

This paper cites Brouwer and H.H Haemers.

Remarks on the Brouwer Conjecture Brouwer and H.H Haemers

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.135979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 231f20e4-584a-4307-82f0-fbbdba7a3797 · outbound

This paper cites Brouwer and W.H.

Remarks on the Brouwer Conjecture Brouwer and W.H

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.121055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2b56f512-79e9-4d31-ba1b-746bd8af22b4 · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:35.105412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a19c8068-15e3-48b4-9fe5-e5334f6aab3e · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:35.091146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6ca8b294-8135-419b-88e6-19766d5ee732 · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:35.076382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d314a101-eeca-4d51-9886-6690b0d8ca74 · outbound

This paper cites Soci´ ete Math´ ematique de France, 1998.

Remarks on the Brouwer Conjecture Soci´ ete Math´ ematique de France, 1998

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.061516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 30c27e54-f3dd-4aff-9e0b-1e79178365e4 · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:35.047097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 912d60f7-f2f3-40b0-8d82-4404968c4e4d · outbound

This paper cites Tayfeh-Rezaie F.

Remarks on the Brouwer Conjecture Tayfeh-Rezaie F

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.032862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4734a29c-67e4-46e8-ace8-a4f4ae27e6e8 · outbound

This paper cites Godsil and G.

Remarks on the Brouwer Conjecture Godsil and G

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.018648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation de6a4a80-2cb5-446f-9bf8-b4f0efcf0d1d · outbound

This paper cites Grone and R.

Remarks on the Brouwer Conjecture Grone and R

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:35.003900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7c685d6a-7407-430d-9ae3-fe0f8654429d · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.988746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9dad1868-ed6d-4d57-9a8e-7f5e01236c04 · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.974615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9eea51be-9e48-4b7d-829c-f322ba75d2aa · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.960284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c7a53e91-7e5a-4d12-8c0e-5b4bb7ef168e · outbound

This paper cites The hydrogen identity for Laplacians.

Remarks on the Brouwer Conjecture The hydrogen identity for Laplacians

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:15:34.782252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e30791cb-cbf5-4074-b4ea-de77fae71efc · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.945941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 77fe86db-c886-4f51-9340-76203ff7b321 · outbound

This paper cites Green functions of Energized complexes.

Remarks on the Brouwer Conjecture Green functions of Energized complexes

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T22:15:34.601377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation facf085d-8634-456d-b31a-8ddc2ee10cbc · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.930931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8e423192-3bb1-420c-825e-a936ef3a8093 · outbound

This paper cites Zhang K.Wang, Z.

Remarks on the Brouwer Conjecture Zhang K.Wang, Z

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.916298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 7452832e-7f33-43f2-bcef-faba7598df66 · outbound

This paper cites Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs.

Remarks on the Brouwer Conjecture Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:15:34.746324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ea18151f-804b-4fb4-9509-6008cfa542e3 · outbound

This paper cites Sums of Laplacian eigenvalues and sums of degrees.

Remarks on the Brouwer Conjecture Sums of Laplacian eigenvalues and sums of degrees

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-05T22:15:34.621390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b8cd13d-854e-4f63-8c63-52fe0d1e1036 · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.902194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation b0d641ba-10b6-4972-bc28-8ac2dd7a0dd8 · outbound

This paper cites Li and J.

Remarks on the Brouwer Conjecture Li and J

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.888027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e1923480-ed9b-49f0-9996-aa4dea0dad07 · outbound

This paper cites On variants of the Grone-Merris conjecture.

Remarks on the Brouwer Conjecture On variants of the Grone-Merris conjecture

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.872514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 15d8d180-1a11-41e0-ad8c-f19097fdba1e · outbound

This paper cites Brouwer's conjecture holds asymptotically almost surely.

Remarks on the Brouwer Conjecture Brouwer's conjecture holds asymptotically almost surely

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-05T22:15:34.707483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 9e78f321-37a5-41ba-8f9a-9e50c33853ab · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.856988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 673cb762-89b6-419c-8540-8290befe4bc3 · outbound

This paper cites Spielman.

Remarks on the Brouwer Conjecture Spielman

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.842550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a7ff13b0-6a1f-4a4f-abbd-0e95b708fff0 · outbound

This paper cites Torres and V.

Remarks on the Brouwer Conjecture Torres and V

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.827727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4af574f4-befc-482e-ab8c-fe129f2d7d3c · outbound

This paper cites Trinajstic.

Remarks on the Brouwer Conjecture Trinajstic

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T22:15:34.812406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5f284900-78fd-47ce-bb23-a8d469df94bc · outbound

This paper cites an unresolved cited work.

Remarks on the Brouwer Conjecture Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-05T22:15:34.797585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

Observation 03775519-4a02-4b9b-a4ed-d7567a55812b · inbound

Remarks about Connection and Dirac matrices cites this paper.

Remarks about Connection and Dirac matrices Remarks on the Brouwer Conjecture

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T08:20:46.851965Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.