Paper Citation Record · LEDGER

Frame bound, spectral gap and Plus space

As of 7 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2505.22136.

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

pith.paper-citation-record.v1
2505.22136 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:40:18.835852Z

measured 23 of 23 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 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

23 of 23 outbound references displayed

verified exact1
verified fuzzy17
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 662ece54-7895-4412-a15d-8cab997093a6 · outbound

This paper cites Ai, Z.-Y.

Frame bound, spectral gap and Plus space Ai, Z.-Y

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:23.073959Z

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 71209a32-cc71-463a-95da-f14ad8216bc0 · outbound

This paper cites Christensen, An introduction to frames and Riesz bases, Appl.

Frame bound, spectral gap and Plus space Christensen, An introduction to frames and Riesz bases, Appl

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.948130Z

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 f35cde30-d345-400e-b265-94734490c2a5 · outbound

This paper cites Dai, Spectra of Cantor measures, Math.

Frame bound, spectral gap and Plus space Dai, Spectra of Cantor measures, Math

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.831336Z

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 78c4aeec-69cf-4d72-8518-3a82b23ddc0e · outbound

This paper cites an unresolved cited work.

Frame bound, spectral gap and Plus space Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:22.681868Z

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 5c9c081d-ebaf-48a8-a683-78157a4f01b0 · outbound

This paper cites an unresolved cited work.

Frame bound, spectral gap and Plus space Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:22.555381Z

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 81b23d72-9c2d-4959-b88f-658cfe44adf8 · outbound

This paper cites Duffin,A.

Frame bound, spectral gap and Plus space Duffin,A

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.393422Z

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 aef45270-9b83-440c-abfb-dcbeb5007997 · outbound

This paper cites Fan, S.-L.

Frame bound, spectral gap and Plus space Fan, S.-L

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.230594Z

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 8fbfd2c7-70a6-4491-b31f-c4166edcbe06 · outbound

This paper cites Fuglede, Commuting self-adjoint partial differential operators and a group theoretic prob- lem, J.

Frame bound, spectral gap and Plus space Fuglede, Commuting self-adjoint partial differential operators and a group theoretic prob- lem, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:22.092319Z

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 61b84bd9-4553-4e44-935b-dafa5d69578e · outbound

This paper cites Heil, A Basis Theory Primer, Expanded Edition.

Frame bound, spectral gap and Plus space Heil, A Basis Theory Primer, Expanded Edition

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.948673Z

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 b52f07bb-e6ba-4472-b04c-930042f22f39 · outbound

This paper cites Iosevich, N.

Frame bound, spectral gap and Plus space Iosevich, N

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.802227Z

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 6b2f5774-cd13-4d04-a75e-4e5609f4a49e · outbound

This paper cites Iosevich, S.

Frame bound, spectral gap and Plus space Iosevich, S

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.633326Z

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 a8f66712-6bac-4eb7-a5d4-336a8b162883 · outbound

This paper cites Jorgensen, S.

Frame bound, spectral gap and Plus space Jorgensen, S

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:21.463285Z

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 f866516f-7e3a-42da-a0eb-bc60f4b84a0a · outbound

This paper cites an unresolved cited work.

Frame bound, spectral gap and Plus space Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:21.275097Z

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 1bca2f00-6db7-43e2-8541-19b09f3eef55 · outbound

This paper cites an unresolved cited work.

Frame bound, spectral gap and Plus space Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:21.133068Z

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 77a11f76-ebf7-4b9a-8dc8-922c65775f66 · outbound

This paper cites Spectrality of a measure consisting of two line segments.

Frame bound, spectral gap and Plus space Spectrality of a measure consisting of two line segments

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:40:19.068093Z

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 abf78cd6-520a-4fa3-9ffd-0e5e6844ae9c · outbound

This paper cites Laba, Fuglede’s conjecture for a union of two intervals, Proc.

Frame bound, spectral gap and Plus space Laba, Fuglede’s conjecture for a union of two intervals, Proc

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.842737Z

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 835c9c3c-6d4e-4e39-b9c3-e25d10a89ede · outbound

This paper cites an unresolved cited work.

Frame bound, spectral gap and Plus space Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:40:20.624064Z

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 02ba3fd2-6327-489c-ab78-481ece4c5c95 · outbound

This paper cites Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math.

Frame bound, spectral gap and Plus space Landau, Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.402136Z

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 cc3e0198-5694-4097-806c-06fbbdebcadf · outbound

This paper cites Lev and M.

Frame bound, spectral gap and Plus space Lev and M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.203079Z

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 af8c82b8-ec2e-46e8-8446-e3babb0e520f · outbound

This paper cites Matolcsi, Fuglede conjecture fails in dimension 4, Proc.

Frame bound, spectral gap and Plus space Matolcsi, Fuglede conjecture fails in dimension 4, Proc

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:20.071310Z

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 41000823-0bde-49a6-a2b5-6a6464c9a2b1 · outbound

This paper cites Lev, Fourier frames for singular measures and pure type phenomena, Proc.

Frame bound, spectral gap and Plus space Lev, Fourier frames for singular measures and pure type phenomena, Proc

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:19.858790Z

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 59aeec10-7316-4a26-b21e-354727ded7b2 · outbound

This paper cites Ortega-Cerd, K.

Frame bound, spectral gap and Plus space Ortega-Cerd, K

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:19.661653Z

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 5838f9af-c740-4ed0-910a-4de746f7d697 · outbound

This paper cites Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math.

Frame bound, spectral gap and Plus space Tao, Fuglede’s conjecture is false in 5 and higher dimensions, Math

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:40:19.400634Z

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

No inbound Pith citation observations are available.