Pith. sign in

Paper Citation Record · LEDGER

Hyperbolic Fourier series and the Klein-Gordon equation

As of 3 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 2026-08-02T06:30:47.504484+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 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-02T00:16:10.520619Z

Reference resolution

28 of 28 outbound references displayed

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

External citation measurements

No source-named external measurement is stored.

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:51bc864b89ec051bc14b3471b6b32175c9a87c6cf5c1b038c3d82103b1cfa2d6

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:021d5ee60f5e421b48aa3c614c2a190749679464e804be401370d2df1e83c055

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:71dc7bb0c351311e20a29b64a9a7075f905c8495d82b48be0313783e106d4890

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a1e6f1e7b32942106e78e56e9b9c2a0c403507e9f07318c3cccc377d074c4317

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:7e915962281b226bda19c4356d1f67e7b574e26e885cb1f06509be8ff9b38195

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:331f4ed80b4259a7363e43f96a54e0edc6f89b54270321155733d5e29f92323d

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:e16d2047c76dd99444a2d6bfae72674910bd178f2b424a0288662a809ea82c12

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:ce83f8348403780bb9e2e08b9408051a0ca0f27701312fccb90d6d72b5f353b6

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:366240282827c3bdefedfdbea9dbcfe57d5753a2ae7a82b7c0e34acb1065e78d

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:fe6360732bdc53042d0230b193bf882f9458a5c99cffa896f6fcbdb0abfe3cf8

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:060c4e393a54647c861c9315b11b59f1040f4060fa79b87da11c2c7d31f5bc39

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:7e81bba2aacf87da9131a81eac95689b0b353caace4d26daadcbf834b59172cf

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:ee6aeaae8a2294040f1248d30bab497bd736fc8f542c1012fd47544d5ad379c8

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:e499d7f8eed55a9a87fe798c7ca106751847f21d6769deaeadcb4717b7445334

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:14e564232fa4f2b5bcfbc29f7ff1f91b8572ab701492384b95efc96ddaeec31f

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:f9d0cffb7adacc6536be9a1d39bda480b08c95405743adc987dbbb717966f102

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:4dfac4965e7ded6029715fe20d006486e5b01711beb3f205fe5c66b903de52a5

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a52a9a2d3e1b06d0716aa56cd01ef64a82f95b213f3114ff21183be8ad085c0d

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:b4774659b2c86363862dca692c010987ca82bfcd70cf3e674596ae01a2663a76

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:60d88cd71d75724b484d7c7e8782f5043192c3ca2f48321d461e5302ca282adc

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:271dc214d1d13737eeec861df444fbfcec5684613c60ffc73e4a8c91ba0cd123

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a1a08a14ea5fd785e4467332e55c2a761158edd5259be0b88031374bcfef9aaa

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:50c784c49785879ca2c187e2a353f7f519eba8532bb7145d310206d166934148

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:932a9039ca7699768165d633c05ee1846784d8d3767ed9e9207ae8bf869282aa

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:783f6c93ad85962b3c61fc759bd9bca9806705f07c5e3e93ae13a079f2ceb5ac

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:1f1e4bda700be3bf6696c023d8f0c118c3733b53ec93ad590e4fc77138cc3d87

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:a08fe4c208674ab9ee2caaaaa52ff05dafb8918bc4d1610c33fa5bbd4d76b658

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-05-24T04:09:03.986197Z digest=sha256:c69f73f64327feb33e56ce6744f735c33b3655bf24374e291952ca6924d312be

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 2026-08-02T06:30:47.504484+00:00.

source=pdf_text observed=2026-08-01T19:03:59.420829Z digest=sha256:87423dfa8fc90fbf54021b100ba1975d49d0fbbfdfacd02ca38948dceaf7c028