Paper Citation Record · LEDGER

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles

As of 16 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:1908.06483.

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

pith.paper-citation-record.v1
1908.06483 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:54:20.929870Z

measured 30 of 30 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

verified exact2
verified fuzzy26
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 54066294-ab08-4217-8071-258d17875481 · outbound

This paper cites Alves and P.R.S.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Alves and P.R.S

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.379747Z

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.

Observation ccd0732c-fbc5-479c-b88a-3d1c89b7e7df · outbound

This paper cites Antunes and P.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Antunes and P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.365745Z

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.

Observation 6ba40ccc-9127-4663-8bb1-534c014d47bc · outbound

This paper cites an unresolved cited work.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:54:21.351933Z

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.

Observation 89fc800f-70ff-4cb6-8259-db8a241d320e · outbound

This paper cites Ariturk and R.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Ariturk and R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.338769Z

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.

Observation c00333f2-b830-4e96-9641-b78f1864b996 · outbound

This paper cites Ashbaugh and R.D.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Ashbaugh and R.D

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.324241Z

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.

Observation 5df6e32d-7b6e-4241-bedc-28bfe01f2b55 · outbound

This paper cites Ashbaugh and R.S.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Ashbaugh and R.S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.311711Z

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.

Observation 53b0b6e6-457a-4554-a784-aeb2d2f9e802 · outbound

This paper cites van den Berg, D.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles van den Berg, D

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.298127Z

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.

Observation c60ad88f-79dd-422f-b844-d005b585bf2d · outbound

This paper cites van den Berg and K.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles van den Berg and K

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.284497Z

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.

Observation 63aab0e4-dfbf-4490-9b70-3814b0eaf6d5 · outbound

This paper cites Brown, E.B.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Brown, E.B

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.270647Z

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.

Observation c272a406-0411-45c9-8991-4c62a8cf5173 · outbound

This paper cites Bucur and P.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Bucur and P

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.257010Z

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.

Observation 1d8cca7f-60d8-472c-831d-24dc5028a324 · outbound

This paper cites Buoso, Analyticity and criticality results for the eigenvalues of the biharmonic operator.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Buoso, Analyticity and criticality results for the eigenvalues of the biharmonic operator

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.243372Z

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.

Observation 4b0a16b3-447f-4291-aa80-59c3d67651ff · outbound

This paper cites Buoso and P.D.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Buoso and P.D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.230261Z

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.

Observation 239a6071-9989-4d17-bf0a-4c84a939bd33 · outbound

This paper cites Burenkov, Sobolev spaces on domains, Teubner-Texte zur Mathematik, 137.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Burenkov, Sobolev spaces on domains, Teubner-Texte zur Mathematik, 137

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.217582Z

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.

Observation 585c4220-a214-487f-837a-d82132a48513 · outbound

This paper cites Coﬀman, On the structure of solutions ∆ 2u = λu which satisfy the clamped plate conditions on a right angle, SIAM J.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Coﬀman, On the structure of solutions ∆ 2u = λu which satisfy the clamped plate conditions on a right angle, SIAM J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.203474Z

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.

Observation 05d7147d-c0c9-4fcd-a839-e84f3177157a · outbound

This paper cites Colbois and A.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Colbois and A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.190558Z

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.

Observation 7a6cec2e-33df-4a72-9452-fe3577871e15 · outbound

This paper cites Freitas, Asymptotic behaviour of extremal averages of Laplacian eigenvalues, J.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Freitas, Asymptotic behaviour of extremal averages of Laplacian eigenvalues, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.177229Z

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.

Observation c17c1818-c440-44d9-a171-33bc62bc1fdf · outbound

This paper cites Extremal domains and P\'{o}lya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Extremal domains and P\'{o}lya-type inequalities for the Robin Laplacian on rectangles and unions of rectangles

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-14T12:54:20.994205Z

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.

Observation 8cbd6890-fc95-41b7-93bf-35f620a26b8b · outbound

This paper cites Gazzola, H.-C.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Gazzola, H.-C

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.163367Z

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.

Observation 8aaea48b-19f1-4905-bfb9-d1429d05f341 · outbound

This paper cites Gittins and S.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Gittins and S

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.150327Z

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.

Observation c32cd791-8ad1-4e19-8045-5a34d10ab517 · outbound

This paper cites Kozlov, V.A.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Kozlov, V.A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.136345Z

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.

Observation 38477904-217d-436d-bd74-e32492d180f2 · outbound

This paper cites an unresolved cited work.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T12:54:21.122753Z

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.

Observation 2af5651e-d507-4404-af5b-d86aff78dae3 · outbound

This paper cites Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domains

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-14T12:54:20.973314Z

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.

Observation df87d2f4-e5d9-42b0-b56e-8ea485ce5c5d · outbound

This paper cites Laugesen and S.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Laugesen and S

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.108860Z

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.

Observation 9c34933d-d716-4aa9-8258-27f383d4fad0 · outbound

This paper cites Marshall, Stretching convex domains to capture many lattice points, Int.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Marshall, Stretching convex domains to capture many lattice points, Int

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.094672Z

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.

Observation 0fab248f-4dc2-49dd-a0e3-0b1127ddea32 · outbound

This paper cites Marshall and S.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Marshall and S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.079808Z

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.

Observation bddae3f4-7a9f-4c0f-9616-d4f4360e0f20 · outbound

This paper cites Nadirashvili, Rayleighs conjecture on the principal frequency of the clamped plate, Arch.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Nadirashvili, Rayleighs conjecture on the principal frequency of the clamped plate, Arch

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.066209Z

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.

Observation 87f8c691-b1f2-4998-ad3b-c13aec2eb944 · outbound

This paper cites Owen, Asymptotic ﬁrst eigenvalue estimates for the biharmonic operator on a rectangle, J.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Owen, Asymptotic ﬁrst eigenvalue estimates for the biharmonic operator on a rectangle, J

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.051523Z

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.

Observation cd5148d5-b4e7-4884-8eac-06be5a5b903b · outbound

This paper cites Safarov and D.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Safarov and D

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.036592Z

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.

Observation 6df548e6-1174-4303-8824-bd6811c14dce · outbound

This paper cites Vasil’ev, Two-term asymptotic behavior of the spectrum of a boundary value problem in the case of a piecewise smooth boundary.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Vasil’ev, Two-term asymptotic behavior of the spectrum of a boundary value problem in the case of a piecewise smooth boundary

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.022550Z

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.

Observation 0afced9d-078f-493f-9fe1-e6ebcd12315b · outbound

This paper cites Wieners, Bounds for the N lowest eigenvalues of fourth-order boundary value problems, Computing 59 (1997), 29–41.

Extremal eigenvalues of the Dirichlet biharmonic operator on rectangles Wieners, Bounds for the N lowest eigenvalues of fourth-order boundary value problems, Computing 59 (1997), 29–41

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T12:54:21.008436Z

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.

Pith citing papers

No inbound Pith citation observations are available.