Paper Citation Record · LEDGER

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$

As of 8 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2506.04341.

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

pith.paper-citation-record.v1
2506.04341 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:54:33.937471Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T09:32:43.371239Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T11:28:04.523079Z

Reference resolution

16 of 16 outbound references displayed

verified exact1
verified fuzzy12
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cbfac6cb-cc9d-44ba-9dd5-1bf474a5b019 · outbound

This paper cites B\' e rard and G.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ B\' e rard and G

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.202182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 45843a5d-30c7-4020-9e29-20bdf126e641 · outbound

This paper cites Luzzini, L.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Luzzini, L

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.191128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7bb90512-c1ad-4a4f-82eb-e9ca06bf321b · outbound

This paper cites Filonov, M.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Filonov, M

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.179823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c96e9924-9a2c-4788-9216-12b981d85414 · outbound

This paper cites Freitas, Upper and lower bounds for the first Dirichlet eigenvalue of a triangle, Proc.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Freitas, Upper and lower bounds for the first Dirichlet eigenvalue of a triangle, Proc

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.170335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0e51a252-7181-4841-aabf-d7a0c338ddad · outbound

This paper cites Freitas, J.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Freitas, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.156274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bebf340d-89a1-4b43-86d7-c4b814684e16 · outbound

This paper cites Freitas, J.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Freitas, J

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T10:54:33.901618Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation edde8dcb-cc87-42ea-8393-688156d2da4b · outbound

This paper cites Math.\ Phys.\ 64, 121503 (2023) DOI:10.1063/5.0161050.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Math.\ Phys.\ 64, 121503 (2023) DOI:10.1063/5.0161050

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T10:54:33.905243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2ef6703-a416-4fad-949f-685a5ec775ed · outbound

This paper cites P\'olya's conjecture for thin products.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ P\'olya's conjecture for thin products

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T10:54:33.910002Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf0056a7-6b28-41c2-a3d9-f4f87499723a · outbound

This paper cites Hersch, Bounds for eigenvalues of P\' o lya's ``plane covering domains'' by filling a torus or a cylinder, J.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Hersch, Bounds for eigenvalues of P\' o lya's ``plane covering domains'' by filling a torus or a cylinder, J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.145005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d228bc22-02d0-4771-b49a-14df39d71e6c · outbound

This paper cites Howards, M.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Howards, M

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-07T10:54:34.055385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a505f4f3-bf26-4eb6-9797-42965aebe4a8 · outbound

This paper cites Laptev, Dirichlet and Neumann eigenvalue problems on domains in Euclidean space.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Laptev, Dirichlet and Neumann eigenvalue problems on domains in Euclidean space

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.132704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d82286b2-e99e-4bd1-9e04-3146bb436b79 · outbound

This paper cites Li and S.-T.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Li and S.-T

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.120503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 51127873-f279-4271-8a5b-b8c44f5207c0 · outbound

This paper cites Pedrosa, The isoperimetric problem in spherical cylinders, Ann.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Pedrosa, The isoperimetric problem in spherical cylinders, Ann

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.109548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ca0806de-1ea2-41aa-ab2c-159de97197f2 · outbound

This paper cites P\' o lya, Mathematics and plausible reasoning: patterns of plausible inference, 2nd Edition, Princeton University Press (1968).

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ P\' o lya, Mathematics and plausible reasoning: patterns of plausible inference, 2nd Edition, Princeton University Press (1968)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.098821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0818ed94-7362-4066-ba01-51c02363e79e · outbound

This paper cites P\' o lya, On the eigenvalues of vibrating membranes.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ P\' o lya, On the eigenvalues of vibrating membranes

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.088070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f4724d82-c5ce-45e2-a3cb-e3cd0a241af0 · outbound

This paper cites Urakawa, Lower bounds for the eigenvalues of the fixed vibrating membrane problems, T\^ o hoku Math.

P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ Urakawa, Lower bounds for the eigenvalues of the fixed vibrating membrane problems, T\^ o hoku Math

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:54:34.077478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation f34f70a3-a331-4a49-bd65-a1e650d1aa67 · inbound

Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs cites this paper.

Krahn--Szeg\H{o} type inequalities and nodal domain methods on graphs P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-03T11:28:04.524575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.