Paper Citation Record · LEDGER

Strengthened upper bound on the third eigenvalue of graphs

As of 19 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 2 inbound Pith citation observations for arXiv:2501.07494.

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

pith.paper-citation-record.v1
2501.07494 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:44:57.031960Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T07:42:47.037325Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

13 of 13 outbound references displayed

verified exact0
verified fuzzy10
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation f7d305c4-b6d9-4135-afa4-c0c335adfeef · outbound

This paper cites Efficient testing of large graphs.

Strengthened upper bound on the third eigenvalue of graphs Efficient testing of large graphs

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T20:44:56.981293Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c70061b3-ae23-43ac-9a09-1db5183d5c78 · outbound

This paper cites Borgs, J.T.

Strengthened upper bound on the third eigenvalue of graphs Borgs, J.T

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.196875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e58faa81-07d2-4887-97f8-7a132497b0ff · outbound

This paper cites Chudnovsky, N.

Strengthened upper bound on the third eigenvalue of graphs Chudnovsky, N

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-10T20:44:56.990345Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfa168aa-d834-4ff0-8510-b2bfcff954b4 · outbound

This paper cites On a conjecture of V.

Strengthened upper bound on the third eigenvalue of graphs On a conjecture of V

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.176948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b7643b1d-b9ba-4f8a-9900-f6bfe50c1ca8 · outbound

This paper cites On the sum of two largest eigenvalues of a symmetric matrix.

Strengthened upper bound on the third eigenvalue of graphs On the sum of two largest eigenvalues of a symmetric matrix

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.164444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9d5b457e-c0ba-4dd3-8ebf-555bcf6fa8da · outbound

This paper cites Bounds of eigenvalues of graphs.

Strengthened upper bound on the third eigenvalue of graphs Bounds of eigenvalues of graphs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.152949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d5ce5472-0bd4-400c-a17b-b43d287be522 · outbound

This paper cites On graphs with large third eigenvalue, 2025.

Strengthened upper bound on the third eigenvalue of graphs On graphs with large third eigenvalue, 2025

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.141101Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5ad7b7a2-d899-4514-bd4e-6396048af175 · outbound

This paper cites Improved lower bounds on the extrema of eigenvalues of graphs.

Strengthened upper bound on the third eigenvalue of graphs Improved lower bounds on the extrema of eigenvalues of graphs

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.129465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6441bd7e-bf66-4895-aa8e-ad1d0b05e361 · outbound

This paper cites Linear combinations of graph eigenvalues.

Strengthened upper bound on the third eigenvalue of graphs Linear combinations of graph eigenvalues

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.116062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6e655d7c-7622-4577-b1d4-3b05130c7666 · outbound

This paper cites Eigenvalue problems of Nordhaus–Gaddum type.

Strengthened upper bound on the third eigenvalue of graphs Eigenvalue problems of Nordhaus–Gaddum type

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.103377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 572f625e-f8b6-4451-8606-d1595acacf79 · outbound

This paper cites Extrema of graph eigenvalues.

Strengthened upper bound on the third eigenvalue of graphs Extrema of graph eigenvalues

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.090038Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9e504141-5d5f-47d8-9436-c2d6896cfd54 · outbound

This paper cites an unresolved cited work.

Strengthened upper bound on the third eigenvalue of graphs Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-10T20:44:57.077354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d6bad5c-3018-42f7-b0f1-2a7eb802728f · outbound

This paper cites Proof of a conjecture of V.

Strengthened upper bound on the third eigenvalue of graphs Proof of a conjecture of V

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:44:57.064799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 86f4ed51-b304-48b8-bb79-31af436f6413 · inbound

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues cites this paper.

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues Strengthened upper bound on the third eigenvalue of graphs

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T22:08:15.348621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e24ec49d-ef84-421a-b655-f97d7172deb4 · inbound

Graph Eigenvalues and Projection Constants cites this paper.

Graph Eigenvalues and Projection Constants Strengthened upper bound on the third eigenvalue of graphs

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-04T07:43:20.449168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.