Paper Citation Record · LEDGER

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality

As of 16 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 1 inbound Pith citation observation for arXiv:2607.20051.

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

pith.paper-citation-record.v1
2607.20051 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:59:33.649152Z

measured 20 of 20 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:42:40.976230Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T15:42:41.156962Z

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy0
unresolved19
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c7329287-1d31-42bf-87a1-7b3fd7b52169 · outbound

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

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality A Conjectural Brouwer Inequality for Higher-Dimensional Laplacian Spectra

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.090089Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f552271f-9c09-4d48-bbde-c7a6fe62ed2b · outbound

This paper cites Abebe and J.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Abebe and J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.241445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0407db2-c841-4e04-9df1-0a07d21b00df · outbound

This paper cites Bai, The Grone–Merris conjecture,Transactions of the American Mathematical Society 363(2011), no.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Bai, The Grone–Merris conjecture,Transactions of the American Mathematical Society 363(2011), no

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.367979Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04292a7e-df14-4876-8ef4-c11230c12619 · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.466886Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a96a7b6-dcc7-4cbf-864b-faa48e718741 · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.604724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 329e7256-9ed6-435e-be19-c4e4c1507a96 · outbound

This paper cites Bhatia,Matrix Analysis, Graduate Texts in Mathematics, Vol.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Bhatia,Matrix Analysis, Graduate Texts in Mathematics, Vol

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.761891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acbf0af2-d3ef-41b6-bb54-842f5a988d33 · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:31.943547Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95527bf1-8ee4-4f7a-9bd8-6972fec4531d · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.123264Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5948f4d9-b381-480b-8470-9af7437d8177 · outbound

This paper cites Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex,Commentarii Mathematici Helvetici17(1944), 240–255.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex,Commentarii Mathematici Helvetici17(1944), 240–255

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.269969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c91a9601-b8b2-48dd-8d2b-0a1157266495 · outbound

This paper cites Fan, On a theorem of Weyl concerning eigenvalues of linear transformations I,Proceedings of the National Academy of Sciences of the United States of America35(1949), no.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Fan, On a theorem of Weyl concerning eigenvalues of linear transformations I,Proceedings of the National Academy of Sciences of the United States of America35(1949), no

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.398102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84110592-fdc7-4949-a24d-c2a6dde635e3 · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.547486Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e03af203-d78c-4e9e-9cc4-11d234fd2267 · outbound

This paper cites Grone and R.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Grone and R

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.663607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 242c961c-ca34-4e60-9f84-ad63cb7e4fc0 · outbound

This paper cites On the sum of the two largest eigenvalues of the curl-curl operator on graphs.

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 5703233f-3b66-49ae-9e0f-496761d944f4 · outbound

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

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality The Grone Merris Conjecture and a quadratic eigenvalue problem

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:32.894887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0201999c-5bc6-48d9-b78c-4770c0ff4506 · outbound

This paper cites an unresolved cited work.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:33.039083Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b63be31-7d41-4d8e-8148-2dc248277b14 · outbound

This paper cites Kirkland, Near threshold graphs,The Electronic Journal of Combinatorics16(2009), no.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Kirkland, Near threshold graphs,The Electronic Journal of Combinatorics16(2009), no

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:33.203080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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

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.

Observation cf8205c8-634b-40bf-9c6b-5a48339754fb · outbound

This paper cites Stephen, A majorization bound for the eigenvalues of some graph Laplacians,SIAM Journal on Discrete Mathematics21(2007), no.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Stephen, A majorization bound for the eigenvalues of some graph Laplacians,SIAM Journal on Discrete Mathematics21(2007), no

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:33.458396Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d8e7bd1-e7bb-43b0-b662-3c6c9f06c6c6 · outbound

This paper cites Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes.

The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T10:59:33.649152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 55c3b6cf-c7da-4ad5-a854-a12c2eecbce0 · inbound

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

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes The Duval--Reiner Conjecture: Counterexamples and the Second Partial-Sum Inequality

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:42:41.162684Z

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.