Paper Citation Record · LEDGER

Schoenberg characterization of continuous non-stationary isotropic positive definite kernels

As of 18 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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

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 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.