Pith. sign in

Paper Citation Record · LEDGER

Sums of Laplacian eigenvalues and sums of degrees

As of 16 August 2026, this Paper Citation Record lists 57 of 57 outbound references and 7 inbound Pith citation observations for arXiv:2508.04209.

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

pith.paper-citation-record.v1
2508.04209 v1

Coverage vector

measured 57 of 57 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T01:03:41.420335Z

measured 64 of 64 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:42:40.994871Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-10T07:16:52.875015Z

Reference resolution

57 of 57 outbound references displayed

  • verified exact1
  • verified fuzzy33
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6a51a3bd-c2c7-4f39-a893-638630177d07 · outbound

This paper cites A Conjectural Brouwer Inequality for Higher-Dimensional Laplacian Spectra.

Sums of Laplacian eigenvalues and sums of degrees A Conjectural Brouwer Inequality for Higher-Dimensional Laplacian Spectra

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-06T01:03:35.732157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T01:03:35.732157Z digest=sha256:fcd0b58caa293003d6c5f59d21ab90ff5a12885a0a764d6b071abb5763342362

Observation 4360e865-87fd-489e-895d-23c2f0eca00c · outbound

This paper cites Abebe and J.

Sums of Laplacian eigenvalues and sums of degrees Abebe and J

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:51.494857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:35.804730Z digest=sha256:0ce3261cdd95536bb1009222242dc4c4026a311fd94aadd61abc3dc50a6aadba

Observation 5ee8e6df-cae7-4e41-8234-1e8156345619 · outbound

This paper cites Aharoni, E.

Sums of Laplacian eigenvalues and sums of degrees Aharoni, E

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:51.315495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:35.945181Z digest=sha256:9440f3bc8ddd618803d0680ebb869fda51f0b046f487b9ea71f97f80b4f8e3e2

Observation 3dd00c52-0422-455e-bf71-f64edd887c35 · outbound

This paper cites Alon and V.

Sums of Laplacian eigenvalues and sums of degrees Alon and V

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:51.148650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.069266Z digest=sha256:f185f04f10345c165750278cdd927a5f4501e4186d67e55ca5766eeb36d82586

Observation 5f1f6228-8c08-4028-bee3-2e79e80a4460 · outbound

This paper cites Anari, K.

Sums of Laplacian eigenvalues and sums of degrees Anari, K

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:50.984952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.172226Z digest=sha256:206dd282245246462237738013655b191c9430547d71aa159ae458bd3a16c3f4

Observation 36833e22-a108-4a2f-97d1-593030bc4204 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:50.785861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.295851Z digest=sha256:ec289ad7468b6eadb2e9a7efd506ad3da4197ab4660d9fc8b38d9277e2e940c5

Observation 5a57a991-4abb-4f04-8405-f0b22a288ef9 · outbound

This paper cites Ashraf, G.

Sums of Laplacian eigenvalues and sums of degrees Ashraf, G

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:50.596031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.387418Z digest=sha256:c1ad368bcbcc950bdd168f9582a21c49b570b3ce1f9b9ebb834e05bc67dc1a87

Observation b2485646-93fc-46d1-91d3-dd7ed76d24d1 · outbound

This paper cites Bai, The Grone-Merris conjecture , Trans.

Sums of Laplacian eigenvalues and sums of degrees Bai, The Grone-Merris conjecture , Trans

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:50.408172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.492494Z digest=sha256:f66c9ac8d5daa6262593cc7ff048f2c69f972b339682fb802342fad55afe4a50

Observation be4f92bb-6e36-42c0-a233-1bcfee86c5d2 · outbound

This paper cites Ballmann and J.

Sums of Laplacian eigenvalues and sums of degrees Ballmann and J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:50.243957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.600534Z digest=sha256:d77667a7d83f2a955743c0845936fd07ce51b2d011cf1ede5dd2b6677128bcca

Observation 74c7f1a8-119f-454f-87b7-9556f95b2bf7 · outbound

This paper cites Berndsen, Three problems in algebraic combinatorics , Master’s Thesis, Eindhoven University of Technology, 2010.

Sums of Laplacian eigenvalues and sums of degrees Berndsen, Three problems in algebraic combinatorics , Master’s Thesis, Eindhoven University of Technology, 2010

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:50.021322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.681692Z digest=sha256:9df588d338222b96ec521ad28d52db8b93dfa8f8af1e927bf6ec19dd66d76e7f

Observation 2c9c5e4a-cd50-41a2-806f-fa0112fb179a · outbound

This paper cites Bollob´ as,Modern graph theory, Graduate Texts in Mathematics, vol.

Sums of Laplacian eigenvalues and sums of degrees Bollob´ as,Modern graph theory, Graduate Texts in Mathematics, vol

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:49.801612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.760496Z digest=sha256:e28ca4ea87712ea86d5c9004da726c12dd6d8e222fe0cedbc7e55d7f312f5a06

Observation 8537604a-8225-43f6-8038-1cb9726b0822 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:49.645010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.867014Z digest=sha256:a48b1ab87ba57981420732a6640e7888499232f7c85bab3680a7966f8ae3b112

Observation 3f16767c-d915-46bf-8f8b-b99b61274865 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:49.483641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:36.954234Z digest=sha256:569961089efca9efe7e3e68b57bdbad00a76d594160d5f572a944a163a035c52

Observation 47ea37de-2374-4ec3-b554-a7c725ad51a2 · outbound

This paper cites Caputo, T.

Sums of Laplacian eigenvalues and sums of degrees Caputo, T

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:49.329822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.076100Z digest=sha256:9a2f240c8d49968c95b88ccc47bd4c1745c85e8de68732e7b042a46973e0b79d

Observation 0f4f3063-89fe-4ebb-a1d0-bf7d7cfaa735 · outbound

This paper cites Chen, On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs, Linear Algebra Appl.

Sums of Laplacian eigenvalues and sums of degrees Chen, On Brouwer’s conjecture for the sum of k largest Laplacian eigenvalues of graphs, Linear Algebra Appl

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:49.132219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.174402Z digest=sha256:b49abefd956d2a613819cecc551f567010474708c2c571aa6921f7044ef7edae

Observation ac6013c7-1ece-4932-96df-133ab4ef55d7 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:48.897999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.336471Z digest=sha256:ce0b5d221752222d3ce9e236f405d34a1fb6c38d18e09e5e9d316ff06f390d51

Observation 5e0790f1-8188-453b-88f3-e04993041654 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:48.690767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.403238Z digest=sha256:dfa577127085757bd0a8ba93c2dfe0fa659cfe8b0657d76e0e629abcd682ed44

Observation 5d99a898-280b-4536-a47c-b35841170d17 · outbound

This paper cites More on the full Brouwer Laplacian spectrum conjecture.

Sums of Laplacian eigenvalues and sums of degrees More on the full Brouwer Laplacian spectrum conjecture

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-06T01:03:37.520279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T01:03:37.520279Z digest=sha256:b083159e5d98f1147390d74829c5165c8c406d2f6585fbfc04f1c26bba0ea93b

Observation 8fada80b-0b1d-4145-9f6a-55190a1c4d12 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:48.508715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.643124Z digest=sha256:2037758bb46b21531f6827ce542f2b3e3a7bf859c4238962663237d6c815c13f

Observation c733c11c-86f1-4ea9-b0f1-2dd13d7f61cf · outbound

This paper cites Du and B.

Sums of Laplacian eigenvalues and sums of degrees Du and B

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:48.290925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.749724Z digest=sha256:653494a4d0bc08e4f0952ee0862caa4f2f8ade758854e4764da0920c2d04ba80

Observation b235be92-e2c2-4f1a-b773-2e0102d1f78f · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:48.060531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.847244Z digest=sha256:af8e8ba81308de1ccfc026bb899b9a2c747a24b15d9e28f39730d360c19c95bd

Observation 9de38541-018b-4c8a-b64f-1d448d8ad739 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:47.902166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:37.964336Z digest=sha256:dd584bc2de44d871c8b6fd07e0361665cdabdf0609702867afc34f38c8e5d2ff

Observation 2ade8df5-8a12-4473-9402-2d08caa4dbe8 · outbound

This paper cites Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex , Comment.

Sums of Laplacian eigenvalues and sums of degrees Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex , Comment

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:47.752168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.069437Z digest=sha256:bed5b5f3bd9cd637b2f79631646dea22d13fd336e8271441d250b4d57cb2f4f6

Observation 624a50bf-e275-44e1-92f8-be687fc5c92d · outbound

This paper cites Fan, H.-F.

Sums of Laplacian eigenvalues and sums of degrees Fan, H.-F

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:47.538799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.161874Z digest=sha256:3f3c69fe0b75b9c7e46439d075bf97bcd1ada36f8802044adb530ca9c60171cc

Observation 5a8a9390-4055-47e6-8bcc-e5b681cf9a4c · outbound

This paper cites Fiedler, Algebraic connectivity of graphs , Czechoslovak Math.

Sums of Laplacian eigenvalues and sums of degrees Fiedler, Algebraic connectivity of graphs , Czechoslovak Math

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:47.392067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.248324Z digest=sha256:6d853194163728ccc0b27becb6f82535bb0db1c9ec2db6c94429bc970428631a

Observation 40415a65-894f-48b9-b15f-dd82b766c51c · outbound

This paper cites Fritscher, C.

Sums of Laplacian eigenvalues and sums of degrees Fritscher, C

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:47.229437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.344819Z digest=sha256:b124d2935499c1c7e8b351bf77e92cc5eff9ef7bfbb4855d5905be56a4f45cca

Observation 72ac6525-567d-40f7-b034-39226ba603e3 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:47.063607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.458346Z digest=sha256:5de95a46224c6dcb325e8bf02fd991dd00378bcc5e899c8d00062518def459aa

Observation 76943110-3bfc-4493-9b77-0bc8d4d67a67 · outbound

This paper cites Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann.

Sums of Laplacian eigenvalues and sums of degrees Garland, p-adic curvature and the cohomology of discrete subgroups of p-adic groups, Ann

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:46.893514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.518519Z digest=sha256:11999fbf1c6c96e3088a4f153c1d065250de5ab7f71756b9aabf6d99b183191a

Observation 05c199cd-1e28-4301-a133-25266f124e58 · outbound

This paper cites Grone and R.

Sums of Laplacian eigenvalues and sums of degrees Grone and R

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:46.732756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.621124Z digest=sha256:ee9902e3ef36e16047288b3f6a2fed3366450aeef0ffd7495dce5edfa24690de

Observation b791a583-6fc9-4902-be18-7f315c963ffb · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:46.602202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.699986Z digest=sha256:6eb6ddde9deb56ee0c476facd56b9b3a6ea278d93f6d0090fac50adff3d5a4bf

Observation 34653aba-d960-4d5c-8c77-fe4396ba1718 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:46.410114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.808557Z digest=sha256:5acc91bf99f8224acc9254d6676d66afa592324636ecbdd530ff6ef992bf74f2

Observation a740c018-44d5-4b8a-8453-62f74988a493 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:46.219504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:38.927015Z digest=sha256:845e38cb57b920330d7f49dd8b0567f96eff1bdb14b569bd4692f76453c89e64

Observation 4e724292-8f45-45f9-9cd1-19673fe18a8d · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:46.071099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.063451Z digest=sha256:b959b43e15dcd67165b1d372011720ee21be67aa2642798783ee80e9a07737ae

Observation 9b1c78d9-3249-4459-827a-2a271c6808ae · outbound

This paper cites Helmberg and V.

Sums of Laplacian eigenvalues and sums of degrees Helmberg and V

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:45.895284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.172513Z digest=sha256:bb9f2fab9666e9ef1c16855cd3e41c55b91e9175266714f84e6dcd438ce37c81

Observation 7a60631c-a773-4318-842f-f53002ee5dab · outbound

This paper cites Horak and J.

Sums of Laplacian eigenvalues and sums of degrees Horak and J

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:45.726855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.285285Z digest=sha256:7727e5ae2569b0d1eb56ac98344c346885ac2c45677754047f3723f196850736

Observation 47c04f50-54d5-4f38-8230-f5c46e39c093 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:45.593091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.386796Z digest=sha256:f8bc0c7db5b265833b5bf0ce71b594f011931ae04136d746b327296f46c5e277

Observation 04f7f273-0477-43ca-930f-e14e55bc02f5 · outbound

This paper cites Kahle, Sharp vanishing thresholds for cohomology of random flag complexes , Ann.

Sums of Laplacian eigenvalues and sums of degrees Kahle, Sharp vanishing thresholds for cohomology of random flag complexes , Ann

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:45.439370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.502731Z digest=sha256:751fe09f73d8cc2cecde3679fffaf403fb972bbeb4d6bd39bc72a958969bc934

Observation df985b07-7c18-42a7-9ab0-690cf9721d26 · outbound

This paper cites Kalai, Enumeration of Q-acyclic simplicial complexes , Israel J.

Sums of Laplacian eigenvalues and sums of degrees Kalai, Enumeration of Q-acyclic simplicial complexes , Israel J

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:45.255373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.565775Z digest=sha256:d4e91e57985fb4d361fd3df925975fd45dcf82695982c0e20ba7ef3e7bc6bad4

Observation ce152840-063d-47b3-9ef6-9ef3dc76be98 · outbound

This paper cites The Grone Merris Conjecture and a quadratic eigenvalue problem.

Sums of Laplacian eigenvalues and sums of degrees The Grone Merris Conjecture and a quadratic eigenvalue problem

Reference 39

Resolution
verified exact
local_arxiv, observed 2026-08-06T01:03:41.680320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.659053Z digest=sha256:dc12c33edb79e4114605baf5d6baa564229d87c17029ac796e5801179087127c

Observation 44755fc8-ec11-4882-9a74-ed585cbfeaaf · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:45.055402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.768778Z digest=sha256:3062b1abf75a3ffa57484607912001b3fe4b74a0d964979d13d6811e91fc3c65

Observation 8034c516-7c04-49af-b563-44f5a3cb8faa · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:44.878435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:39.881883Z digest=sha256:df0c5c684f0826e7a682deb124badbcd8a181c70d341d74213101a16db7bdfe4

Observation af3f8a04-f36d-472c-97e3-88413041297c · outbound

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

Sums of Laplacian eigenvalues and sums of degrees Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-06T01:03:40.003356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T01:03:40.003356Z digest=sha256:1b9f25f450bce167c4575d517af5509797968df64fce9a81017611aee25c629e

Observation b09cc373-116f-4b5f-9a6c-52bceb1d7181 · outbound

This paper cites Li and Y.-L.

Sums of Laplacian eigenvalues and sums of degrees Li and Y.-L

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:44.744067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.094330Z digest=sha256:fb3ef8fdc2129f168987a5a69c10bf3acb64087527ff8f998d369da5e9e9dda8

Observation 8544b182-6c39-4452-9a36-249fc3e5bfe6 · outbound

This paper cites Li and X.-D.

Sums of Laplacian eigenvalues and sums of degrees Li and X.-D

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:44.586847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.206673Z digest=sha256:370a9b67ec028512538df5ecd74d16825c1192edb8bd51ada4f191838c44b5f9

Observation 613096a5-e9cf-4427-83c3-1a05e2d31da0 · outbound

This paper cites Li and J.-M.

Sums of Laplacian eigenvalues and sums of degrees Li and J.-M

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:44.414095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.306496Z digest=sha256:3cd437df7e15967ce065931789f38b14e7dfc9a5ac5b41232088ff9acacd8854

Observation 5cf1e28f-a534-4bb0-90d4-45402876c856 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:44.217550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.420104Z digest=sha256:fc0be2df90a74b57239e43683f67fbf5dd86040372ddd15c3c9eb2f204d81e75

Observation 0e06424a-cf8c-4a1c-8383-18a1c0498be2 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:44.066943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.506880Z digest=sha256:a72a69c512d556aa9b09ec2497ab49d83ab5427e2e626d40bdb861637f2aba57

Observation fa3a6dd0-84b0-4701-9d1c-cd6a6b6b42c2 · outbound

This paper cites Merris, Laplacian matrices of graphs: a survey , Linear Algebra Appl.

Sums of Laplacian eigenvalues and sums of degrees Merris, Laplacian matrices of graphs: a survey , Linear Algebra Appl

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:43.914320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.607554Z digest=sha256:6f223a9aee36d8a662ad600b8f33036a600cb1b484aaf79cea21dea39dc0a9cc

Observation bcc25961-5f86-42dd-84e9-d9985db231c6 · outbound

This paper cites Mohar, Isoperimetric numbers of graphs, J.

Sums of Laplacian eigenvalues and sums of degrees Mohar, Isoperimetric numbers of graphs, J

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:43.631804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.680531Z digest=sha256:67a02e80b260d7408d577d0c720ba72e46eff4cfd4ffe71263826869b5d89547

Observation 60d3abdd-3eca-4158-939d-501cca550009 · outbound

This paper cites Oppenheim, Local spectral expansion approach to high dimensional expanders Part I: Descent of spectral gaps, Discrete Comput.

Sums of Laplacian eigenvalues and sums of degrees Oppenheim, Local spectral expansion approach to high dimensional expanders Part I: Descent of spectral gaps, Discrete Comput

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:43.360562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.775324Z digest=sha256:f0cf8431c7ca7f15f7d55ef9b23fe3b1a34135b163153e7903335477307cf48b

Observation 36de5a16-997c-4e97-ad80-5794ae490ca4 · outbound

This paper cites Pirzada, R.

Sums of Laplacian eigenvalues and sums of degrees Pirzada, R

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:43.122304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.851420Z digest=sha256:a495f6823b2ffa184b70f2eafde3f4f4939975db9566da4071f12dbd9d3f7325

Observation ae2fdba6-bf14-4c56-9ac8-c305a3e886bf · outbound

This paper cites Rocha, Brouwer’s conjecture holds asymptotically almost surely , Linear Algebra Appl.

Sums of Laplacian eigenvalues and sums of degrees Rocha, Brouwer’s conjecture holds asymptotically almost surely , Linear Algebra Appl

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:42.842947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:40.919132Z digest=sha256:d40ed4c7ccbfed4264b96405852c17121c045841ecb7eb061797417a55bb3e3a

Observation d2286019-20c5-4952-b32a-4f2f305b103b · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:42.606969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:41.009581Z digest=sha256:1b5ace28c33da932af8c414c52340bb70873a96af738733719163926c8eb2481

Observation 2bf92cf1-1373-439a-801b-48ac81670277 · outbound

This paper cites an unresolved cited work.

Sums of Laplacian eigenvalues and sums of degrees Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-08-06T01:03:42.457268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:41.114214Z digest=sha256:21a0e3494912bb0055c9e6d66fdf42fcc3c506e02293d6625727c7f2a39bbe85

Observation f35129c3-d596-48c8-b808-9850a9172bd2 · outbound

This paper cites Yang and L.

Sums of Laplacian eigenvalues and sums of degrees Yang and L

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:42.251760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:41.221913Z digest=sha256:941d7433cc9c0ecaead864d14aabd990ecadbec88308d99cd5c6b04408f26d37

Observation 11a681c7-aac9-415e-8ab1-e6fab45b57a4 · outbound

This paper cites Zhou, C.-X.

Sums of Laplacian eigenvalues and sums of degrees Zhou, C.-X

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:42.009059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:41.281259Z digest=sha256:23b472f8c37a6373cd71c4642a91f377f5950ecc875b4e3a41c08a96969bd9bf

Observation 105dcd09-d3c0-4a9d-9e81-b335b503b36f · outbound

This paper cites ˙Zuk, La propri´ et´ e (T) de Kazhdan pour les groupes agissant sur les poly` edres, C.

Sums of Laplacian eigenvalues and sums of degrees ˙Zuk, La propri´ et´ e (T) de Kazhdan pour les groupes agissant sur les poly` edres, C

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T01:03:41.876488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T01:03:41.420335Z digest=sha256:d2a874a3bf5e99f6723a49c6faca6ba7f49675ccc3a276270a3503235511a6b3

Pith citing papers

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

Remarks on the Brouwer Conjecture cites this paper.

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.

source=pdf_text observed=2026-08-05T22:15:34.621390Z digest=sha256:0c393a7e622eff9b530bc013ce5a5e12f04c875ba4f51e7a4ce56f78ba9f99df

Observation b5b7439f-220a-43d7-b2d8-3eab6160f97a · inbound

A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality cites this paper.

A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Sums of Laplacian eigenvalues and sums of degrees

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-07-09T20:16:29.585047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-07-09T19:58:17.125188Z digest=sha256:9623fb947d4d3a0edb80667f448e60cdc9397466b836345df57a21af2e350451

Observation 589d475f-bddd-4331-934f-7ab8c14ac6ff · inbound

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture cites this paper.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Sums of Laplacian eigenvalues and sums of degrees

Reference 14

Resolution
verified exact
local_arxiv, observed 2026-07-10T07:16:52.877802Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-07-10T07:15:01.722124Z digest=sha256:50d6146c9b295523389b6464024666f1a1f68a676d85d2435931d5907b195710

Observation 04d70e58-f487-48f2-aa39-c299867a98a1 · inbound

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture cites this paper.

Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture Sums of Laplacian eigenvalues and sums of degrees

Reference 17

Resolution
unresolved
no resolver link, observed 2026-07-14T15:33:15.240468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-14T15:33:15.240468Z digest=sha256:c2ab8185d3c3446d0b7547fff75dd31cf99fefe64c2b5dfe7b66fad2ac497eee

Observation e61bf069-fc4a-436a-a297-dbdeefd4a6af · inbound

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues cites this paper.

Characterizing the equality case in Brouwer's inequality for Laplacian eigenvalues Sums of Laplacian eigenvalues and sums of degrees

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-01T18:35:00.733449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T18:35:00.733449Z digest=sha256:9ac865af48dd16fcaec552d26e1bd03a762c717d46a7ec950368f6136e0478b2

Observation 63701420-f70d-4224-be08-f5f3a052f4cc · inbound

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality cites this paper.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Sums of Laplacian eigenvalues and sums of degrees

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-01T10:59:33.303022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T10:59:33.303022Z digest=sha256:9a0e8c3fe128bc748519c82a2313fcdcfb928c307252c213e971e8ea7325383c

Observation 5443493a-4e2d-484e-a217-d65393acbdf1 · inbound

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes cites this paper.

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes Sums of Laplacian eigenvalues and sums of degrees

Reference 19

Resolution
unresolved
no resolver link, observed 2026-08-15T15:42:40.994871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T15:42:40.994871Z digest=sha256:0d9f7d97cb77cee5513c70a4bf5aa3fdea84f9e197dd92e98587176752a4652e