Paper Citation Record · LEDGER

On the sum of the two largest eigenvalues of the curl-curl operator on graphs

As of 16 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 2 inbound Pith citation observations for arXiv:2606.26512.

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

pith.paper-citation-record.v1
2606.26512 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T04:50:10.127764Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:42:40.965591Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T15:42:41.173806Z

Reference resolution

26 of 26 outbound references displayed

verified exact0
verified fuzzy0
unresolved26
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 73822da3-71f0-463e-9663-462c41b1bb45 · outbound

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

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Bai, The Grone-Merris conjecture, Trans

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08c429fc-cfa9-492a-b385-b493c5844fd7 · outbound

This paper cites Cvetkovi´ c, P.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Cvetkovi´ c, P

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1b7bb50-1ee5-40cd-a78b-019508741e62 · outbound

This paper cites Desbrun, M.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Desbrun, M

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe760713-bed0-464f-b7ae-bf761b226adc · outbound

This paper cites an unresolved cited work.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 239ccded-c636-4a57-9ce0-423d26d12f0f · outbound

This paper cites an unresolved cited work.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 50723a2d-7b6a-4310-b899-99af84352287 · outbound

This paper cites an unresolved cited work.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 244b6c66-9d6c-4696-a389-ba08b714c61b · outbound

This paper cites Godsil, G.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Godsil, G

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9031f9f-b56c-4f6d-ac87-4d35c810aa42 · outbound

This paper cites Grone, R.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Grone, R

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f6858ac-4696-4e7b-b6a8-633b13cc420a · outbound

This paper cites Jiang, L.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Jiang, L

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4745e3a0-dd8d-4606-9038-eb9023f1438a · outbound

This paper cites Lim, Hodge Laplacians on graphs, SIAM Rev.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Lim, Hodge Laplacians on graphs, SIAM Rev

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a6c8d6b-1540-4e93-bd36-6a04d0d935c7 · outbound

This paper cites an unresolved cited work.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a0c0412-aecc-4785-9025-9abea991e159 · outbound

This paper cites an unresolved cited work.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 689c05f2-8eb6-4537-8eb8-95dfcf65a9f3 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eab65b3f-45a8-4a73-89d5-7124deec000e · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8611b56-2e90-4f7d-ba83-62a10d68932e · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84f04289-42cb-4e57-974b-7b1a1ab7032f · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e452c47-8958-4e5d-a578-41a1e99cb599 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2458ec4-808f-4d86-b63e-5e65481cf481 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b887947-51c0-4558-a237-2df62746d895 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34f34a27-6605-4a0b-9eca-dbda10662ca4 · outbound

This paper cites We claim that h(yx) ≥ 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs We claim that h(yx) ≥ 0

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c0c2a95-f8be-41a5-862a-d795152bc716 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5ea609d-e116-4aa8-a89a-4d0c4774d734 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 73a7c625-db95-43d5-9c7d-f65d38e2d727 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b88a42a8-7371-49a7-bf15-1528419813b8 · outbound

This paper cites 33 Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs 33 Suppose, to the contrary, that h(yx) < 0

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b9b2d761-4676-4214-871a-be76e27ea203 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a55372b-6553-418f-9772-f52cdaa72808 · outbound

This paper cites Suppose, to the contrary, that h(yx) < 0.

On the sum of the two largest eigenvalues of the curl-curl operator on graphs Suppose, to the contrary, that h(yx) < 0

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T04:50:10.127764Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 242c961c-ca34-4e60-9f84-ad63cb7e4fc0 · 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 On the sum of the two largest eigenvalues of the curl-curl operator on graphs

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.780530Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a34b32e-a4ae-4bf5-b4d8-ee1f52438baa · inbound

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

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes On the sum of the two largest eigenvalues of the curl-curl operator on graphs

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:42:41.177814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.