Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:52:24.473010Z
Paper Citation Record · LEDGER
Optimal unions of scaled copies of domains and P\'olya's conjecture
As of 23 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:1908.08441.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
34 of 34 outbound references displayed
- verified exact4
- verified fuzzy24
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 09b9ca9c-ecad-4f06-b4da-3f24245ccac9 · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:25.007933Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a4296370-84d0-4538-9292-faf86938581d · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 2
- Resolution
- verified exact
- raw_fallback, observed 2026-08-14T11:52:24.674632Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a46a0086-6971-4dd4-bb45-d27f41a99cb1 · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:24.997070Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 29402865-9163-4dad-9cbf-3e2e320bc64a · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:24.987156Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4d1000bf-4615-4ce8-9d9c-483af3e1ad5a · outbound
This paper cites Berezin, Covariant and contravariant symbols of operators,Izv.
Optimal unions of scaled copies of domains and P\'olya's conjecture Berezin, Covariant and contravariant symbols of operators,Izv
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.976444Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5c5ac50e-5d55-4180-8f8c-b6aa34494e43 · outbound
This paper cites van den Berg, D.
Optimal unions of scaled copies of domains and P\'olya's conjecture van den Berg, D
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.965308Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e1bf170b-5589-4edd-a1b0-e6d101910d14 · outbound
This paper cites van den Berg and K.
Optimal unions of scaled copies of domains and P\'olya's conjecture van den Berg and K
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.954867Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 35fc07f1-e0fd-4d99-9d8a-8bfe430abe18 · outbound
This paper cites van den Berg and M.
Optimal unions of scaled copies of domains and P\'olya's conjecture van den Berg and M
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.944335Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6302bef4-754b-4069-a6ce-b5816c6460f9 · outbound
This paper cites Berger, The eigenvalues of the Laplacian with Dirichlet boundary condition inR2 are almost never minimized by disks,Ann.
Optimal unions of scaled copies of domains and P\'olya's conjecture Berger, The eigenvalues of the Laplacian with Dirichlet boundary condition inR2 are almost never minimized by disks,Ann
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.932991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ab59f303-ca46-496b-906d-94fe2484c0b2 · outbound
This paper cites Bogosel and E.
Optimal unions of scaled copies of domains and P\'olya's conjecture Bogosel and E
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.922290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 72539778-04e0-409e-b424-b3c3a9c0b7d3 · outbound
This paper cites Bucur and P.
Optimal unions of scaled copies of domains and P\'olya's conjecture Bucur and P
Reference 11
- Resolution
- verified exact
- doi, observed 2026-08-14T11:52:24.506055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e5ccf720-61cc-4ac8-a2c7-e236e485cb48 · outbound
This paper cites Bucur and A.
Optimal unions of scaled copies of domains and P\'olya's conjecture Bucur and A
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.910483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b945e9fd-b271-4a16-898f-32a2e6441e06 · outbound
This paper cites Canzani,Analysis on Manifolds via the Laplacian, Lecture notes, Harvard University (2013), 114 pp.
Optimal unions of scaled copies of domains and P\'olya's conjecture Canzani,Analysis on Manifolds via the Laplacian, Lecture notes, Harvard University (2013), 114 pp
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.899443Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 490e0cce-3f70-4bab-81ad-9c34c4149fc1 · outbound
This paper cites Colbois and A.
Optimal unions of scaled copies of domains and P\'olya's conjecture Colbois and A
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.889067Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 972dbaae-fcf1-4bb6-a00a-1f72915d06f6 · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:24.878596Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d631bcdb-c135-4c15-968a-a6fd28517068 · outbound
This paper cites Faber, Beweis, dass unter allen homogenen membranen von gleicher flüche und gleicher spannung die kreisfürmige den tiefsten grundton gibt, Sitz.
Optimal unions of scaled copies of domains and P\'olya's conjecture Faber, Beweis, dass unter allen homogenen membranen von gleicher flüche und gleicher spannung die kreisfürmige den tiefsten grundton gibt, Sitz
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.867561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0d4b7a72-3958-4931-bbc7-50b2511b8820 · outbound
This paper cites Freitas, Asymptotic behaviour of extremal averages of Laplacian eigenvalues.J.
Optimal unions of scaled copies of domains and P\'olya's conjecture Freitas, Asymptotic behaviour of extremal averages of Laplacian eigenvalues.J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.856623Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5496bd79-b83d-42ce-a396-9a457ee5aa83 · outbound
This paper cites Freitas, A remark on Pólya’s conjecture at low frequencies,Arch.
Optimal unions of scaled copies of domains and P\'olya's conjecture Freitas, A remark on Pólya’s conjecture at low frequencies,Arch
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.845326Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 338f523b-bf4c-4089-9d44-da6e93ba6b88 · outbound
This paper cites Freitas and J.B.
Optimal unions of scaled copies of domains and P\'olya's conjecture Freitas and J.B
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.834779Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 33301536-0a7a-4fb0-bf2a-4b59c9d5f606 · outbound
This paper cites Gittins and S.
Optimal unions of scaled copies of domains and P\'olya's conjecture Gittins and S
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.824499Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 361b8eea-8708-4bbe-9697-0f9ad3ef355e · outbound
This paper cites Kellner, On a theorem of Pólya,Amer.
Optimal unions of scaled copies of domains and P\'olya's conjecture Kellner, On a theorem of Pólya,Amer
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.812921Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation ef215075-255f-40db-a444-fa39c6b96cb2 · outbound
This paper cites Krahn, Über eine von Rayleigh formulierte minimaleigenschaft des kreises,Math.
Optimal unions of scaled copies of domains and P\'olya's conjecture Krahn, Über eine von Rayleigh formulierte minimaleigenschaft des kreises,Math
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.803239Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f9d191c1-d9de-4d20-b7e4-b4df971e7243 · outbound
This paper cites Krahn, Über Minimaleigenshaften der Kugel in drei und mehr Dimensionen, Acta Comm.
Optimal unions of scaled copies of domains and P\'olya's conjecture Krahn, Über Minimaleigenshaften der Kugel in drei und mehr Dimensionen, Acta Comm
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.793301Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 416a9d86-5679-4ade-99a3-908c6716ad9f · outbound
This paper cites Kröger, Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space,J.
Optimal unions of scaled copies of domains and P\'olya's conjecture Kröger, Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space,J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.777321Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation cb31761c-3151-4ca4-a5d5-437058747948 · outbound
This paper cites Larson, Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex do- mains, preprint arXiv:1611.0568 [math.SP] (2016).
Optimal unions of scaled copies of domains and P\'olya's conjecture Larson, Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex do- mains, preprint arXiv:1611.0568 [math.SP] (2016)
Reference 25
- Resolution
- verified exact
- raw_fallback, observed 2026-08-14T11:52:24.612456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation fe05f5eb-04e8-4916-9aa9-c3a15a676f15 · outbound
This paper cites Li and S.-T.
Optimal unions of scaled copies of domains and P\'olya's conjecture Li and S.-T
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.765556Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation caf82bb6-f28f-473d-9fa3-aa5ee3ee3521 · outbound
This paper cites Stretching convex domains to capture many lattice points.
Optimal unions of scaled copies of domains and P\'olya's conjecture Stretching convex domains to capture many lattice points
Reference 27
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:52:24.525843Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4318816e-0fca-4f7c-9462-609edf970a44 · outbound
This paper cites Oudet, Numerical minimization of eigenmodes of a membrane with respect to the domain,ESAIM Control Optim.
Optimal unions of scaled copies of domains and P\'olya's conjecture Oudet, Numerical minimization of eigenmodes of a membrane with respect to the domain,ESAIM Control Optim
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.755915Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3c78cfda-fc4b-48f6-b3c2-f0716e96ffaf · outbound
This paper cites Poliquin and G.
Optimal unions of scaled copies of domains and P\'olya's conjecture Poliquin and G
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.745945Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1c3d2b13-07c9-4b47-9ff0-3fa2b7cfe264 · outbound
This paper cites 1961 On the eigenvalues of vibrating membranes,Proc.
Optimal unions of scaled copies of domains and P\'olya's conjecture 1961 On the eigenvalues of vibrating membranes,Proc
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.734933Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2c0c53ab-46f3-4bf2-bd7c-9fd2d69c00c9 · outbound
This paper cites Safarov & D.
Optimal unions of scaled copies of domains and P\'olya's conjecture Safarov & D
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.722589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0466bed9-aedf-4df2-aa72-36f909686541 · outbound
This paper cites Urakawa, Lower bounds for the eigenvalues of the fixed vibrating membrane problems,Tôhoku Math.
Optimal unions of scaled copies of domains and P\'olya's conjecture Urakawa, Lower bounds for the eigenvalues of the fixed vibrating membrane problems,Tôhoku Math
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:52:24.711466Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 940bed84-58af-4bb8-9325-428bc98099dd · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:24.701207Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 03078dde-a432-4f3c-bb47-07049566b416 · outbound
This paper cites an unresolved cited work.
Optimal unions of scaled copies of domains and P\'olya's conjecture Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:52:24.684791Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.