Paper Citation Record · LEDGER

Fundamental tones of clamped plates in nonpositively curved spaces

As of 23 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1909.02350.

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

pith.paper-citation-record.v1
1909.02350 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T04:59:49.896389Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

43 of 43 outbound references displayed

verified exact4
verified fuzzy36
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 667160b8-777c-4dfa-b9c9-bca85ffb4597 · outbound

This paper cites Ashbaugh, R.

Fundamental tones of clamped plates in nonpositively curved spaces Ashbaugh, R

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.573383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6ce9e30c-78f0-41a8-9c4d-a5ad7e9f8b9a · outbound

This paper cites Ashbaugh, R.S.

Fundamental tones of clamped plates in nonpositively curved spaces Ashbaugh, R.S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.559495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0b2ad4af-f4f8-4b97-8928-a0745c9a0d4d · outbound

This paper cites Bauer, E.

Fundamental tones of clamped plates in nonpositively curved spaces Bauer, E

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.545604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5b409fba-4d30-4863-8de6-019b5e377193 · outbound

This paper cites Bishop, R.J.

Fundamental tones of clamped plates in nonpositively curved spaces Bishop, R.J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.531236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9c0a7231-4e2f-4b18-b758-c30a4ee28fe6 · outbound

This paper cites Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen.Jber.

Fundamental tones of clamped plates in nonpositively curved spaces Bol, Isoperimetrische Ungleichungen f¨ ur Bereiche auf Fl¨ achen.Jber

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.516365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 37a33e43-77e7-4a59-b0f3-a9aef759c4c9 · outbound

This paper cites On Clamped Plates with Log-Convex Density.

Fundamental tones of clamped plates in nonpositively curved spaces On Clamped Plates with Log-Convex Density

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:59:50.003520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 612e6eb8-a763-44ae-a661-f5b728f69e5d · outbound

This paper cites Chasman, J.J.

Fundamental tones of clamped plates in nonpositively curved spaces Chasman, J.J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.501981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e236da4d-9edd-4209-bf54-613aaf70ae5d · outbound

This paper cites Chavel, Eigenvalues in Riemannian geometry.

Fundamental tones of clamped plates in nonpositively curved spaces Chavel, Eigenvalues in Riemannian geometry

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.488144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation abe9ace5-6896-4249-aaeb-a71da14331fc · outbound

This paper cites an unresolved cited work.

Fundamental tones of clamped plates in nonpositively curved spaces Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-14T04:59:50.474055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bb6c7f21-466f-4768-8046-b9e43df0b736 · outbound

This paper cites Cheng, T.

Fundamental tones of clamped plates in nonpositively curved spaces Cheng, T

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.460553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9ebb342d-80a3-44ee-9077-b97873e5770c · outbound

This paper cites Cheng, H.

Fundamental tones of clamped plates in nonpositively curved spaces Cheng, H

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.446917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a5ff33a0-aebe-4a46-ba91-e345d8f18a17 · outbound

This paper cites Cheng, H.

Fundamental tones of clamped plates in nonpositively curved spaces Cheng, H

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.433266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cbe58a52-bc57-4788-b24d-8ec1c408643d · outbound

This paper cites Cheng, H.

Fundamental tones of clamped plates in nonpositively curved spaces Cheng, H

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.418957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 35e45b21-fab9-4ae3-b202-9836ecc2b835 · outbound

This paper cites Croke, A sharp four-dimensional isoperimetric inequality.

Fundamental tones of clamped plates in nonpositively curved spaces Croke, A sharp four-dimensional isoperimetric inequality

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.404991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 95965e84-4591-4a38-9f4a-18915f626595 · outbound

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

Fundamental tones of clamped plates in nonpositively curved spaces Coﬀman, On the structure of solutions to ∆ 2u =λu which satisfy the clamped plate conditions on a right angle

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.390934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 134c767b-44ac-4e6b-954f-ed58603dab80 · outbound

This paper cites Coﬀman, R.J.

Fundamental tones of clamped plates in nonpositively curved spaces Coﬀman, R.J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.376418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0dc44351-42ec-4bd1-9a19-a7c43b9338f2 · outbound

This paper cites Cuyt, V.B.

Fundamental tones of clamped plates in nonpositively curved spaces Cuyt, V.B

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.362399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d93548c7-67f8-4556-8d00-56e60cd14e84 · outbound

This paper cites Dinghas, Einfacher Beweis der isoperimetrischen Eigenschaft der Kugel in Riemannschen R¨ aumen kon- stanter Kr¨ ummung.Math.

Fundamental tones of clamped plates in nonpositively curved spaces Dinghas, Einfacher Beweis der isoperimetrischen Eigenschaft der Kugel in Riemannschen R¨ aumen kon- stanter Kr¨ ummung.Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.347706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c435c5e6-1df2-4085-9fb1-614a3b6cf031 · outbound

This paper cites Duﬃn, Nodal lines of a vibrating plate.

Fundamental tones of clamped plates in nonpositively curved spaces Duﬃn, Nodal lines of a vibrating plate

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.333255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2fe06e0b-772a-4c9c-bd1b-b2dbf9e3ad84 · outbound

This paper cites Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds.

Fundamental tones of clamped plates in nonpositively curved spaces Total curvature and the isoperimetric inequality in Cartan-Hadamard manifolds

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:59:49.981711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d2fc4180-24ad-4d89-a758-cb5df9ab2040 · outbound

This paper cites Grunau, F.

Fundamental tones of clamped plates in nonpositively curved spaces Grunau, F

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.318675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d89730ab-c86d-4532-bfaf-1b60e6567b78 · outbound

This paper cites Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities.

Fundamental tones of clamped plates in nonpositively curved spaces Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.304197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 32a99577-6c8a-4d10-8115-69940ebb8146 · outbound

This paper cites Hille, Non-oscillation theorems.

Fundamental tones of clamped plates in nonpositively curved spaces Hille, Non-oscillation theorems

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.289818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1319e0da-5729-405e-a3c1-882749e77f07 · outbound

This paper cites Karp, private communication & manuscript in preparation.

Fundamental tones of clamped plates in nonpositively curved spaces Karp, private communication & manuscript in preparation

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.274882Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5923f418-9111-4894-933d-fc41a5672624 · outbound

This paper cites Karp, S.M.

Fundamental tones of clamped plates in nonpositively curved spaces Karp, S.M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.259949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ae754165-7c50-4f1d-8196-95a667f83316 · outbound

This paper cites Kleiner, An isoperimetric comparison theorem.

Fundamental tones of clamped plates in nonpositively curved spaces Kleiner, An isoperimetric comparison theorem

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.245691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3ebc469f-2ee7-40f4-9e5b-6ac064d90095 · outbound

This paper cites Klingenberg, Riemannian geometry.

Fundamental tones of clamped plates in nonpositively curved spaces Klingenberg, Riemannian geometry

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.231224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ec4ff047-ad8d-4b09-a470-8a156b23d9e0 · outbound

This paper cites The Cartan-Hadamard conjecture and The Little Prince.

Fundamental tones of clamped plates in nonpositively curved spaces The Cartan-Hadamard conjecture and The Little Prince

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:59:49.961197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9299c6cc-dda4-416f-b80c-46dc331aab40 · outbound

This paper cites New features of the first eigenvalue on negatively curved spaces.

Fundamental tones of clamped plates in nonpositively curved spaces New features of the first eigenvalue on negatively curved spaces

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-14T04:59:49.939244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 197f6802-a37f-427c-b3a6-c09c245839e7 · outbound

This paper cites McKean, An upper bound to the spectrum of ∆ on a manifold of negative curvature.

Fundamental tones of clamped plates in nonpositively curved spaces McKean, An upper bound to the spectrum of ∆ on a manifold of negative curvature

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.217500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9c4c5487-eb52-4d89-90a5-f04438c58115 · outbound

This paper cites Nadirashvili, New isoperimetric inequalities in mathematical physics.

Fundamental tones of clamped plates in nonpositively curved spaces Nadirashvili, New isoperimetric inequalities in mathematical physics

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.202192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation de766803-3e62-48ed-8e9f-946905888d9a · outbound

This paper cites Nadirashvili, Rayleigh’s conjecture on the principal frequency of the clamped plate.

Fundamental tones of clamped plates in nonpositively curved spaces Nadirashvili, Rayleigh’s conjecture on the principal frequency of the clamped plate

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.187449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b1e2f8ec-d3ba-4102-ada8-3308990a52b5 · outbound

This paper cites Olver, D.W.

Fundamental tones of clamped plates in nonpositively curved spaces Olver, D.W

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.172336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c7e419c0-0228-4023-a484-0c0aa2e82d61 · outbound

This paper cites Palais, The principle of symmetric criticality.

Fundamental tones of clamped plates in nonpositively curved spaces Palais, The principle of symmetric criticality

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.156628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fdbcd6c6-20ab-4109-a5a4-ff51f8f17b17 · outbound

This paper cites Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Diﬀerential Equations, CBMS Regional Conference Series in Mathematics Vol.

Fundamental tones of clamped plates in nonpositively curved spaces Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Diﬀerential Equations, CBMS Regional Conference Series in Mathematics Vol

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.142479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5aee9c7a-9d93-459b-88fb-1b60bc9444aa · outbound

This paper cites Rayleigh, The Theory of Sound.

Fundamental tones of clamped plates in nonpositively curved spaces Rayleigh, The Theory of Sound

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.127894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 341c9dc8-f33a-410a-95b3-2c4d9b075968 · outbound

This paper cites Robin, Fonctions sph´ eriques de Legendre et fonctions sph´ ero¨ ıdales.

Fundamental tones of clamped plates in nonpositively curved spaces Robin, Fonctions sph´ eriques de Legendre et fonctions sph´ ero¨ ıdales

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.098233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 03caf147-3bfc-4017-a655-b6e9dc146c9a · outbound

This paper cites Szeg˝ o, On membranes and plates.Proc.

Fundamental tones of clamped plates in nonpositively curved spaces Szeg˝ o, On membranes and plates.Proc

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.082696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 40124701-fc31-40e3-925f-2811916d6216 · outbound

This paper cites Sugie, K.

Fundamental tones of clamped plates in nonpositively curved spaces Sugie, K

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.067657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation fa6363d4-1fa7-4a47-934f-cc7403793d1f · outbound

This paper cites Talenti, On the ﬁrst eigenvalue of the clamped plate.

Fundamental tones of clamped plates in nonpositively curved spaces Talenti, On the ﬁrst eigenvalue of the clamped plate

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.052326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation babf5d0b-0bf7-4d73-b24a-9b7a72ea04ba · outbound

This paper cites Zhurina, L.

Fundamental tones of clamped plates in nonpositively curved spaces Zhurina, L

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T04:59:50.036334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9761788f-844e-4648-8a88-3a4add6eafac · outbound

This paper cites an unresolved cited work.

Fundamental tones of clamped plates in nonpositively curved spaces Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-14T04:59:50.020293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7a87b559-fd16-4a3b-8010-fb9573d1dcb6 · outbound

This paper cites an unresolved cited work.

Fundamental tones of clamped plates in nonpositively curved spaces Unresolved cited work

Reference 1926

Resolution: unresolved; raw_fallback, observed 2026-08-14T04:59:50.113050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.