Pith. sign in

Paper Citation Record · LEDGER

Hyperbolic Fourier series and the Klein-Gordon equation

As of 5 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2401.06871.

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

pith.paper-citation-record.v1
2401.06871 v3

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T04:09:03.986197Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T19:03:59.420829Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T02:28:24.338817Z

Reference resolution

28 of 28 outbound references displayed

  • verified exact1
  • verified fuzzy17
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

0
pith, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation b9b62f37-9a8c-42ac-8f13-1bd39d7f3672 · outbound

This paper cites V ., Complex analysis.

Hyperbolic Fourier series and the Klein-Gordon equation V ., Complex analysis

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.477714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:463e7d1d9f9438f8b92bb06e26d44df5c073d7b1994d8b687b340965c95aa35c

Observation 2c8bd066-576c-4296-b230-fb3e7a8ab909 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.481199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:6718b42bd9509d5951d381dcf6168a695b482bfd8788549a2bcb283c91d7dba9

Observation 8b1f8f5f-79a8-43b3-8822-8f70ac2cfb0b · outbound

This paper cites and Viazovska, M., Fourier uniqueness in even dimensions.

Hyperbolic Fourier series and the Klein-Gordon equation and Viazovska, M., Fourier uniqueness in even dimensions

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.459346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:88ec74bf6f7d32283df0b13bb1b33d30e1e82c73eb683481f7a621872515adcf

Observation 249df420-550a-465a-a418-9400a332d4ca · outbound

This paper cites Hyperbolic Fourier series.

Hyperbolic Fourier series and the Klein-Gordon equation Hyperbolic Fourier series

Reference 4

Resolution
verified exact
arxiv_id, observed 2026-05-24T04:13:53.905884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:640dac0dfcfb4945e39dc8be8950c447f4094c5158db7ade103cf2eb03f4e8e7

Observation fc17d5f0-f747-4afd-851f-2e9377a9098e · outbound

This paper cites and Seip K., Fourier interpolation with zeros of zeta and L- functions.

Hyperbolic Fourier series and the Klein-Gordon equation and Seip K., Fourier interpolation with zeros of zeta and L- functions

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.453047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:618173eb14592a1572796828b128ec42baa83759c8e47c0410ebbf65751efbbc

Observation ec04976b-8de4-45c2-8824-8ab0e17d44c7 · outbound

This paper cites Acta Math.

Hyperbolic Fourier series and the Klein-Gordon equation Acta Math

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.456029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:285aaffd992727d906dae0f958a8c39a8260376404c8ebf44986ec8b47164b7a

Observation 9b6786e0-67de-4a02-8a69-10718c2df3d0 · outbound

This paper cites R., The one-dimensional heat equation.

Hyperbolic Fourier series and the Klein-Gordon equation R., The one-dimensional heat equation

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.463719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:61d767e5a3bc7f176cce9d26eaa20bc2b34621ff631b3be964ef2bdc38a41d14

Observation e0d3f69e-36eb-4876-9e8c-c33af45bfbfa · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.439598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:91928f5cbba19340fd08c40a14aab327c3eac4de474da6a35f53903c476de3c6

Observation 72008fed-5d08-406f-ae3b-d55f5e398b3d · outbound

This paper cites Grundlehren der Mathematischen Wissenschaften [Fun- damental Principles of Mathematical Sciences], 281.

Hyperbolic Fourier series and the Klein-Gordon equation Grundlehren der Mathematischen Wissenschaften [Fun- damental Principles of Mathematical Sciences], 281

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.436218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a25fc915eb71aeb533529d981c168be6558e54b6d708d4eb3c4643f0903da5cb

Observation 23279676-58c8-405b-9c85-e2ad1af7a7a0 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.442977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:5b9f383dc67da4b5ce7dfd609c0a49335096860cdce434fc550aff989eea0481

Observation a0607ee9-45bc-4322-b3ff-3a65bd6ee320 · outbound

This paper cites D., Radchenko, D., Viazovska, M., The sphere packing problem in dimension 24.

Hyperbolic Fourier series and the Klein-Gordon equation D., Radchenko, D., Viazovska, M., The sphere packing problem in dimension 24

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.446573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:0d52e4a0364c8cb8cb535bd1fbb9f746a6b3c2266f328f09ccfd94ffb882b785

Observation db29bcff-1872-4ac7-82e1-824b98b4f02a · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.425209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:66573ccc9c13a184b3cdd656728e55826f77e4aeb153c7fa9a9a53f7383d9cf7

Observation e16b9f47-7503-4836-a30b-98b478e8259c · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.428725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:307eb42737daff5ccd418815387f58127105e395fe69e0ce4c42f1857df969a8

Observation 66ca6329-976e-45d4-929c-1a32b5f1ae69 · outbound

This paper cites In preparation.

Hyperbolic Fourier series and the Klein-Gordon equation In preparation

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.417597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:e362cccd0db8bb688a1a4e5649e91492a29da209e2cd28358ca14b4152b5705d

Observation 46f919a4-b231-43ca-b502-a55fe9c0687e · outbound

This paper cites and Montes-Rodriguez, A., Heisenberg uniqueness pairs and the Klein-Gordon equation.

Hyperbolic Fourier series and the Klein-Gordon equation and Montes-Rodriguez, A., Heisenberg uniqueness pairs and the Klein-Gordon equation

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.413709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:b663921285587f340ea6e502df80aa8e1415a3a39edb8cfb1509bfe5288496c5

Observation 1ca0af13-82d8-48cb-b64e-d6d4c7816bc8 · outbound

This paper cites and Montes-Rodr ´ıguez, A., The Klein-Gordon equation, the Hilbert transform and dynamics of Gauss-type maps.

Hyperbolic Fourier series and the Klein-Gordon equation and Montes-Rodr ´ıguez, A., The Klein-Gordon equation, the Hilbert transform and dynamics of Gauss-type maps

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.421938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:7e65061bce9d2e10f57507f9cf74d53705afeae96c99cc9ab46b43f56d4d6dcb

Observation 8f171594-dd99-4f11-b462-8448de9cff8f · outbound

This paper cites and Montes-Rodr ´ıguez, A.,The Klein-Gordon equation, the Hilbert transform, and Gauss-type maps: H ∞ approximation.

Hyperbolic Fourier series and the Klein-Gordon equation and Montes-Rodr ´ıguez, A.,The Klein-Gordon equation, the Hilbert transform, and Gauss-type maps: H ∞ approximation

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.432616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:30120b61f25fc586b534ed0e6a767fddcc20b97e334adfaf3522cf380da2163b

Observation 06b993c1-87dc-40ec-bfdd-f347ae4ffe76 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.449778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:866d50b356c45e61025c6c6d72dac3b7f7547f6b3c6061fd22238d3686b840a0

Observation fdb9277c-8bbc-4209-9b3c-be1ed597153a · outbound

This paper cites Acta Math.

Hyperbolic Fourier series and the Klein-Gordon equation Acta Math

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.467562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:d03469bf636c94d9c6f5d0ed3043c22fd14a9b322b8ae141b2383c2fafc21f54

Observation 83ed4b0c-c979-4104-8e6c-a2438ef84e6e · outbound

This paper cites Conditions fronti `eres, termes sources, coefficients incompl`etement connus [On the sentinels of distributed systems.

Hyperbolic Fourier series and the Klein-Gordon equation Conditions fronti `eres, termes sources, coefficients incompl`etement connus [On the sentinels of distributed systems

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.398741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:c564ba3fb85e8b545ddcc00d0b40998bf501d4c3adecdc46ad3aa07991bd2780

Observation a18bba10-1a43-4504-8f70-efa1e3b36356 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.406682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:ed52eb8ab4daca5691186f18de140b2ae63546ad61145f255e5682d165c30693

Observation 693d3437-b185-4c36-a71a-62ac092dbe6a · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.394459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a2eb406b127aa4d36c0305683847e86fc0bf2c52caa645dcb8fe95a7b3452d54

Observation 5bfef3c5-6ec0-4963-89f4-4f44f6123de5 · outbound

This paper cites P., Fourier uniqueness and interpolation in Euclidean space.

Hyperbolic Fourier series and the Klein-Gordon equation P., Fourier uniqueness and interpolation in Euclidean space

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.403095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:3c633b018fd6de894f13a28fffd253fbcb8706cb328cfd08934add2a6a4887a3

Observation 02a9b9f2-4226-4e2b-9fa0-d7802a18d1f9 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.410034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:9e72aa6fea1a6b0bfd2f67c2d5b6d529c7f2d24d051b6973d5f20487ae567394

Observation 10e4d79b-55d8-4389-9823-5f536c327eee · outbound

This paper cites J., Harmonic and analytic functions admitting a distribution boundary value.

Hyperbolic Fourier series and the Klein-Gordon equation J., Harmonic and analytic functions admitting a distribution boundary value

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.471163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:e32d78f88d85aaa549e2f98702268e0e047bdfb2e77046d90e68edc23cd0acb2

Observation 13190c9e-49e5-4a5d-b2f6-3cc12d621572 · outbound

This paper cites Reprinting of the 1959 original.

Hyperbolic Fourier series and the Klein-Gordon equation Reprinting of the 1959 original

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.485077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:e78fb7f463d2575810e291574b5d4fdf89cfd380b1e566e40d3b9c025e34237e

Observation 4cab945e-0ec2-4b4a-93cb-572d945fba67 · outbound

This paper cites an unresolved cited work.

Hyperbolic Fourier series and the Klein-Gordon equation Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-05-24T05:58:59.391078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:4cf57045bb54f6befee9f71812c3a5de2ff4565ea68441a34c6eb37b42cb87fd

Observation cc63ea6f-6c88-4fd1-a206-c1b30ad64b1f · outbound

This paper cites S., Methods of the theory of generalized functions.

Hyperbolic Fourier series and the Klein-Gordon equation S., Methods of the theory of generalized functions

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-05-24T05:58:59.387693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:bdc78f34f16ca82f84c48f3267aa07afd853ff1e20439882771495c559c95595

Pith citing papers

Observation 3453eba8-6722-4e76-95ab-5101d7e270c9 · inbound

Heisenberg Uniqueness Pairs for a Hyperbola Branch: Supercritical Nonuniqueness for Shifted Lattice Crosses cites this paper.

Heisenberg Uniqueness Pairs for a Hyperbola Branch: Supercritical Nonuniqueness for Shifted Lattice Crosses Hyperbolic Fourier series and the Klein-Gordon equation

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-01T19:08:23.657764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

source=pdf_text observed=2026-08-01T19:03:59.420829Z digest=sha256:244b26a96131ad69100e400194f050322f49d0320f65f4bf8f40fa577c3336d1