Paper Citation Record · LEDGER

Maximizing higher eigenvalues in dimensions three and above

As of 8 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 5 inbound Pith citation observations for arXiv:2506.09328.

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

pith.paper-citation-record.v1
2506.09328 v3

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:01:08.425218Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T08:22:49.370384Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-01T12:25:43.351904Z

Reference resolution

20 of 20 outbound references displayed

verified exact0
verified fuzzy14
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5471d4de-5743-4b24-812e-3f2c1a4d2c66 · outbound

This paper cites More on convergence in unitary matrix spaces.

Maximizing higher eigenvalues in dimensions three and above More on convergence in unitary matrix spaces

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.802890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 189748a3-3d08-4274-9dd2-7ccdac056857 · outbound

This paper cites A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas.

Maximizing higher eigenvalues in dimensions three and above A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.752898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8ed44799-853c-4e50-9fa4-1c7ee679a698 · outbound

This paper cites On the singular set of stable- stationary harmonic maps.

Maximizing higher eigenvalues in dimensions three and above On the singular set of stable- stationary harmonic maps

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.743027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dee4952f-fc30-4f8a-941f-9021e8913bd3 · outbound

This paper cites Variational properties of the second eigenvalue of the conformal Laplacian.

Maximizing higher eigenvalues in dimensions three and above Variational properties of the second eigenvalue of the conformal Laplacian

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.772947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dbc0fefe-79aa-41f1-9ad7-5ea9f4e2d2de · outbound

This paper cites Extremal metrics for the Paneitz operator on closed four-manifolds.

Maximizing higher eigenvalues in dimensions three and above Extremal metrics for the Paneitz operator on closed four-manifolds

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.686000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c26a7c54-bae8-4b27-ade1-3a8126934b6d · outbound

This paper cites Geometric spectral optimization on surfaces.

Maximizing higher eigenvalues in dimensions three and above Geometric spectral optimization on surfaces

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:08.408837Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26d26744-68fe-4d65-b270-ffbdf365b276 · outbound

This paper cites Critical metrics of eigenvalue functionals via Clarke subdifferential.

Maximizing higher eigenvalues in dimensions three and above Critical metrics of eigenvalue functionals via Clarke subdifferential

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:08.412682Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4af46116-be2d-4a02-a381-009200cdcccc · outbound

This paper cites an unresolved cited work.

Maximizing higher eigenvalues in dimensions three and above Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:01:08.721847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ee5c043-e881-4fef-b072-92ff2da92db7 · outbound

This paper cites On the Existence of Metrics Which Maximize Laplace Eigenvalues on Surfaces.

Maximizing higher eigenvalues in dimensions three and above On the Existence of Metrics Which Maximize Laplace Eigenvalues on Surfaces

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.673174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ec33b671-6fda-45f2-b77b-09eeda26c382 · outbound

This paper cites Cambridge University Press, Cambridge, 1995, pp.

Maximizing higher eigenvalues in dimensions three and above Cambridge University Press, Cambridge, 1995, pp

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.793215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1c490ce3-6320-4226-ac95-33fb333aa2dd · outbound

This paper cites Quatre propri´ et´ es isop´ erim´ etriques de membranes sph´ eriques homog` enes.

Maximizing higher eigenvalues in dimensions three and above Quatre propri´ et´ es isop´ erim´ etriques de membranes sph´ eriques homog` enes

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.763008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation acc0fc17-7865-4736-95ce-bae001a22c5f · outbound

This paper cites Springer, Cham, 2023, pp.

Maximizing higher eigenvalues in dimensions three and above Springer, Cham, 2023, pp

Reference 117

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.661208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9ae3b80-9160-4b73-a656-37800bba05db · outbound

This paper cites American Mathematical Society, Providence, RI, 2005, pp.

Maximizing higher eigenvalues in dimensions three and above American Mathematical Society, Providence, RI, 2005, pp

Reference 121

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.650354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 61e5b8d7-d3a1-411d-869e-53e333f43b5e · outbound

This paper cites Dirac eigenvalue optimisation and harmonic maps to complex projective spaces.

Maximizing higher eigenvalues in dimensions three and above Dirac eigenvalue optimisation and harmonic maps to complex projective spaces

Reference 154

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.733190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ff14bda2-3d21-4de0-9e72-c6420b6a1c4e · outbound

This paper cites Immersions minimales, premi` ere valeur pro- pre du laplacien et volume conforme.

Maximizing higher eigenvalues in dimensions three and above Immersions minimales, premi` ere valeur pro- pre du laplacien et volume conforme

Reference 176

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.783406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2b8d7a3a-de26-4983-8c29-8ea47133661f · outbound

This paper cites Existence of harmonic maps and eigenvalue optimization in higher dimensions.

Maximizing higher eigenvalues in dimensions three and above Existence of harmonic maps and eigenvalue optimization in higher dimensions

Reference 239

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.710344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 77e87638-a980-455a-a66f-fe5c7fd92e45 · outbound

This paper cites Nonsmooth sequential analysis in Asplund spaces.

Maximizing higher eigenvalues in dimensions three and above Nonsmooth sequential analysis in Asplund spaces

Reference 330

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:01:08.697264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6af9739c-8387-47c7-9952-a6850d818084 · outbound

This paper cites Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces.

Maximizing higher eigenvalues in dimensions three and above Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:08.385069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7e6ee70-94ab-4fa8-a437-f3856d3ce462 · outbound

This paper cites A variational method for functionals depending on eigenvalues.

Maximizing higher eigenvalues in dimensions three and above A variational method for functionals depending on eigenvalues

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:08.404862Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8bc1ac4-5ec5-4982-be3d-1d2a09e44b88 · outbound

This paper cites an unresolved cited work.

Maximizing higher eigenvalues in dimensions three and above Unresolved cited work

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:08.421227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation af21d398-79ae-4d99-b050-cf0bccd37274 · inbound

Eigenvalue optimization in higher dimensions and $p$-harmonic maps cites this paper.

Eigenvalue optimization in higher dimensions and $p$-harmonic maps Maximizing higher eigenvalues in dimensions three and above

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T08:22:49.370384Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e4b3ba4-9a83-4c4e-aac5-f6598942ee28 · inbound

Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains cites this paper.

Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains Maximizing higher eigenvalues in dimensions three and above

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-31T01:08:31.464725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 86f65bce-1530-45e0-8dae-019cb39a02d0 · inbound

Eigenvalue optimization via a first-variation formula cites this paper.

Eigenvalue optimization via a first-variation formula Maximizing higher eigenvalues in dimensions three and above

Reference 73

Resolution: verified exact; arxiv_id, observed 2026-07-31T01:08:31.464725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e7668199-9c72-4b87-8dfd-438c5fc1e6ea · inbound

Eigenvalue optimization via a first-variation formula cites this paper.

Eigenvalue optimization via a first-variation formula Maximizing higher eigenvalues in dimensions three and above

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-02T09:39:59.423272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6fd2e9d-15f0-4296-8ebb-1546f469126d · inbound

Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map cites this paper.

Existence and Regularity of Extremal Metrics for the Conformal Dirichlet-to-Robin Map Maximizing higher eigenvalues in dimensions three and above

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-01T07:03:47.673911Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.