Paper Citation Record · LEDGER

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes

As of 10 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2606.21233.

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

pith.paper-citation-record.v1
2606.21233 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T14:17:57.337260Z

measured 13 of 13 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 2026-08-01T10:59:33.649152Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy0
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f600d1c4-4f33-4669-84ab-e5081512ca61 · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b46ffd6a-b42d-4398-bdfa-c31531132e2e · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 719f4dc8-a119-4ff7-adc1-827f0f8807b1 · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d286ea8b-e233-4c88-b3cf-72fbb336b137 · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78702cf2-e62c-4052-a321-0cbde9a8f2bc · outbound

This paper cites Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex, Commentarii Math- ematici Helvetici 17 (1944), 240–255.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex, Commentarii Math- ematici Helvetici 17 (1944), 240–255

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6846bb8a-e202-4d7e-8056-b4b21e42f04c · outbound

This paper cites Fan, H.-F.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Fan, H.-F

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66effe34-389f-4190-8787-c732c5f3334a · outbound

This paper cites Horak and J.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Horak and J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 92df800f-4549-49f1-bf35-043af80bd17e · outbound

This paper cites Horak and J.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Horak and J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a938032-2548-4959-889e-8c84a9e14f03 · outbound

This paper cites Merris, Laplacian matrices of graphs: a survey, Linear Algebra and its Applications , 197–198 (1994), 143–176.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Merris, Laplacian matrices of graphs: a survey, Linear Algebra and its Applications , 197–198 (1994), 143–176

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29fb911f-051a-4e66-83de-d72843a5afe4 · outbound

This paper cites Merris, Laplacian graph eigenvectors, Linear Algebra and its Applications , 278 (1998), 221–236.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Merris, Laplacian graph eigenvectors, Linear Algebra and its Applications , 278 (1998), 221–236

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54fb5ecc-5a09-40e9-ac2b-0f53c73fe222 · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd449843-ade7-4e86-93cb-6a56f8a2340b · outbound

This paper cites an unresolved cited work.

Upper Bounds for the Largest Laplacian Eigenvalue of Simplicial Complexes Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T14:17:57.337260Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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