Pith. sign in

Paper Citation Record · LEDGER

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels

As of 9 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2506.22048.

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

pith.paper-citation-record.v1
2506.22048 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:25:00.323124Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

34 of 34 outbound references displayed

  • verified exact6
  • verified fuzzy12
  • unresolved14
  • parse uncertain0
  • malformed identifier2
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f8210225-0f0c-454b-957e-84b9c2295dec · outbound

This paper cites Ament and C.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Ament and C

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:05.180156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:57.828228Z digest=sha256:4a2b5641767f5e3825c2d3d4119f20b3e5c68776c0a00c95106be8c0240282bf

Observation 2f8cedfb-601c-4cd0-9f97-1cbe33412abd · outbound

This paper cites Benning and L.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Benning and L

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:05.021599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:57.903866Z digest=sha256:1e628a79bf4083ae5244de91b77c8731c19a4755ed34f936341aba7720998127

Observation 171bac08-5b66-4081-bc74-10988a10c4fa · outbound

This paper cites Berg and E.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Berg and E

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:04.847361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:57.979135Z digest=sha256:d55e8b755a07ddce40ad6d6caa7492ff7d4f53109b08f2a20e0bca05fbb1ea44

Observation 73de39a9-1b39-4aa5-9341-519c61818e48 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:04.711215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.159914Z digest=sha256:8a1681ded4c0630514372973d44b99c28ff41da25381251fc23df0d911733ec8

Observation 4025ae7c-145c-49cf-ac3f-2524f5e6cb4d · outbound

This paper cites Positive definite matrix must be Hermitian.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Positive definite matrix must be Hermitian

Reference 5

Resolution
verified exact
raw_fallback, observed 2026-08-06T22:25:01.279872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.342904Z digest=sha256:11ef1e8bf8474130140780de853c9b4491ac3a98f2ced18d5069aad722aa88bd

Observation 7f2b3acd-4f3b-4f7f-b759-67a8eb8cc6c3 · outbound

This paper cites Cho and L.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Cho and L

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:04.533884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.420771Z digest=sha256:64b6c5d1639af5b87991808ad3c72180488916c70a8300b7285be7d042f49548

Observation 2cfa7ec5-de8a-4502-a42b-f42436a55f82 · outbound

This paper cites de Roos, A.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels de Roos, A

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:04.365416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.502793Z digest=sha256:b92c02e154b8da2924d41fcc0406ddc252b4a6b51a4f83587540da2ce6c621a3

Observation 5fb18b48-9724-4a16-b558-a1be358903f3 · outbound

This paper cites Estrade, A.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Estrade, A

Reference 8

Resolution
malformed identifier
no resolver link, observed 2026-08-06T22:24:58.565630Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:58.565630Z digest=sha256:1987a8f4f54a98f0fee44c72521aa668edb80b880bca21284921c0f362803d53

Observation d479820c-198e-465f-a808-8c84eeb04e10 · outbound

This paper cites Galy-Fajou, D.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Galy-Fajou, D

Reference 9

Resolution
verified exact
doi, observed 2026-08-06T22:25:00.733772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.616178Z digest=sha256:cba0128446ca291ed0a95ea415d9d75d119546c8cd5ca0d6f46fb6f6cafcc44e

Observation bc4e30fe-3725-4f15-83ee-ac8175842aa7 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 10

Resolution
verified exact
doi, observed 2026-08-06T22:25:00.623233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.693171Z digest=sha256:b2a227309e3b33699922813d49f883ff578ec5d37eefe792938c1de6c71e23fe

Observation 35274eab-a3d5-4bb2-a9d7-48fb6241edb8 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:58.763270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:58.763270Z digest=sha256:7fd1b8ea5c0f4b0d67107944ece13eec791381b75492d39877d00f3a7444461d

Observation 69571f12-3062-4072-b52c-855e8b2f6f76 · outbound

This paper cites Jacot, F.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Jacot, F

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:04.224568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.856788Z digest=sha256:051c49f80ceaa56affefd175938f4350e98377087726a0b7eaf9effb11b37617

Observation 789dde90-f72b-4e92-b0cd-6cae720b9b2d · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:04.051938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.940598Z digest=sha256:fc669c5088d835dcfbd7a6cad6b46dbc8b082cd9d12b016b6894054ee06cb7cb

Observation d74e8155-9a5e-48d1-a13f-052db949b49e · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:03.806235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.038965Z digest=sha256:ceadd4df782c409ead765aab2279dc6fd1de0a0de6acf801e5bd73852375881d

Observation 32efe452-bfd8-4ad5-b136-c9f918ff785b · outbound

This paper cites Panchenko.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Panchenko

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:59.110091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:59.110091Z digest=sha256:0d30c08095632f8b4fa7e106d95cd7ac46157d73d8c06c73a5fc47d849dc0aea

Observation 3ad4c2ee-4239-4c13-a105-7e2b2294dacf · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 16

Resolution
verified exact
doi, observed 2026-08-06T22:25:00.476169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.167889Z digest=sha256:00d6677ce57cfbbebf195c938bc2abea7864d49af13a1cda49152a3471274fe9

Observation 202b0d7c-8a79-4f5c-9ef2-adf8235ec5f5 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:03.492575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.271753Z digest=sha256:5c3aa3b5b11e7571e44ab658bf2913d42d83cfdc22f690eebfd36698769ab25d

Observation 4089db0a-1b22-45ad-a254-1d2b5ee4f94c · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-06T22:24:59.362232Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:24:59.362232Z digest=sha256:9957aa58810b342b7af256d1e58e13a5b1bf59c4b6c53415c9610efde02ccf93

Observation 7a4153ea-c4a5-4b9f-8b4e-8623d807dadd · outbound

This paper cites Sasv´ ari.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Sasv´ ari

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:03.214929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.432715Z digest=sha256:9094a66aca341bb5d6e80dc67353a9a0fc08facb36c42debd7add6430a139814

Observation 6852095f-ad31-4588-b3ff-03c252187ed0 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:03.065383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.501916Z digest=sha256:2c7478ae37e082e8555de654f2b26b3d743e2e6e13f2aa9525f1a13613b6e7c7

Observation e1342713-b0f9-417b-9850-2a30044f10e3 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 21

Resolution
malformed identifier
raw_fallback, observed 2026-08-06T22:25:02.758542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.629792Z digest=sha256:0aa87c93018f947b7164b58d370c878226c141a6862c3bb3b436954012212a23

Observation 6f4ea64a-7bc5-4502-8729-58d08426a082 · outbound

This paper cites Sch¨ olkopf and A.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Sch¨ olkopf and A

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:02.578367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.710946Z digest=sha256:cdb87c738045f08742d094013a86963b95671ac2139072e37155e3c54cccfcf6

Observation 606fa371-3c59-4707-b79e-dc718b29d016 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:02.413463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.785263Z digest=sha256:77afb025c24d89deeb8b9e960025b2c469f744193f3622279bc5ed08b943c4d3

Observation 840f4636-36ad-4b8d-b95c-c97136425c1f · outbound

This paper cites Williams.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Williams

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:02.248525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.876661Z digest=sha256:b9ab6148688088e43fafac08782b0ac06c888f582231c2909676ff2c8969d57a

Observation f492397a-09be-4908-896c-605f093e80a7 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:01.886607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:25:00.014328Z digest=sha256:debfd857dac1d1b3e1c3da6d2b705d57b9904f52b482f984519513028e896b3d

Observation aa2d71d0-a3d4-454a-ae55-a8fc7e1f86b5 · outbound

This paper cites Tensor Programs II: Neural Tangent Kernel for Any Architecture.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Tensor Programs II: Neural Tangent Kernel for Any Architecture

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-06T22:25:00.068729Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T22:25:00.068729Z digest=sha256:804307726888f9a297e0aaa75d8fbe65f928c1f2159cd816a6c7c645c3326338

Observation 2316538f-0488-4525-9d58-28891af9b5dd · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:01.728777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:25:00.143329Z digest=sha256:7b7ebcddc860d290ea254559c8f3b3598c8b9dbe459ae4f2cba4ece2b88d6f1d

Observation 335785e7-15c4-4ffe-8937-94b065315bac · outbound

This paper cites (ii), (iii), (iv)⇒ (i).

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels (ii), (iii), (iv)⇒ (i)

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:01.568799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:25:00.213622Z digest=sha256:cd902e6172577061634ac6336ee1de03354fcecd0533ee6e8a49aa25eaf879ab

Observation d670fca7-092d-425d-9545-13fe26dab861 · outbound

This paper cites (i)⇒ (ii), (iii).

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels (i)⇒ (ii), (iii)

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:01.424197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:25:00.263867Z digest=sha256:81ed53f9961c988f347fdcb5634cb2e1f9bd89d5d8097c0551ebdf84d723a842

Observation 8c49f6ea-5d15-42fd-8775-4926901ef6a9 · outbound

This paper cites Remark A.4 (Universal kernels).

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Remark A.4 (Universal kernels)

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T22:25:01.303604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:25:00.323124Z digest=sha256:8a61d36571e8a4aca14857183680f70629df3bac46bb8fae04c1df2fb5113afe

Observation cb132722-e8bc-4684-95d9-3c1902a30985 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 940

Resolution
verified exact
doi, observed 2026-08-06T22:25:00.987385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.060485Z digest=sha256:9eed478b6777188cf5c62dc4a15505b8fe8dec3da891a30e8b621c1f6e3fd627

Observation 9199606b-b8ca-41e3-9f67-5fe6bec38709 · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 1807

Resolution
verified exact
doi, observed 2026-08-06T22:25:00.851846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:58.265575Z digest=sha256:78d36b7e93c8604c80fb41def79a26bd1f2253fd3521f762eb270eb983d29b3b

Observation 858173d1-48a4-4055-b6b3-b9db1ad7542b · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 1938

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:02.918646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.565633Z digest=sha256:0f9083da6f982e8f6c9680a3935ba36faa6de35d18a39560fbb4d80d67767eda

Observation 4a3eaf15-7541-442d-8e19-05f8672a8f5b · outbound

This paper cites an unresolved cited work.

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels Unresolved cited work

Reference 1996

Resolution
unresolved
raw_fallback, observed 2026-08-06T22:25:02.048968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-08-06T22:24:59.951702Z digest=sha256:41778b1930305399d29dd424d96cf404dbc198257faa4fbdc748ef4b6ef354ab

Pith citing papers

No inbound Pith citation observations are available.