Paper Citation Record · LEDGER

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

As of 10 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation 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 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:59:32.780530Z

measured 0 of 1 external citation measurements

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

Source: cited_works

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.