Paper Citation Record · LEDGER

Fast kernel methods: Sobolev, physics-informed, and additive models

As of 9 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2509.02649.

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

pith.paper-citation-record.v1
2509.02649 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:56:11.942600Z

measured 15 of 15 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T12:20:57.284440Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

14 of 14 outbound references displayed

verified exact1
verified fuzzy11
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 46b5d870-8939-4d7c-8193-c3dd959766ce · outbound

This paper cites an unresolved cited work.

Fast kernel methods: Sobolev, physics-informed, and additive models Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:56:12.167784Z

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.

Observation d855ddcf-c2c9-412c-8b54-46426c80f78d · outbound

This paper cites an unresolved cited work.

Fast kernel methods: Sobolev, physics-informed, and additive models Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T11:56:12.158809Z

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.

Observation 4c76e21d-0803-4afe-869b-7499953ccb39 · outbound

This paper cites The second term E(∥ √ Σ( ˆΣ + λR)−1Φ∗ϵ/n∥2.

Fast kernel methods: Sobolev, physics-informed, and additive models The second term E(∥ √ Σ( ˆΣ + λR)−1Φ∗ϵ/n∥2

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.150149Z

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.

Observation 265a71d4-36ef-4819-9475-4ccda6b7ecd5 · outbound

This paper cites The last term E(∥ √ Σ( ˆΣ + λR)−1Φ∗δY/n∥2.

Fast kernel methods: Sobolev, physics-informed, and additive models The last term E(∥ √ Σ( ˆΣ + λR)−1Φ∗δY/n∥2

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.140373Z

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.

Observation f9b29030-4dd6-4cd1-9e2f-b960d171dbb9 · outbound

This paper cites In what follows, we will successively bound these three errors terms.

Fast kernel methods: Sobolev, physics-informed, and additive models In what follows, we will successively bound these three errors terms

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.130427Z

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.

Observation bb001cfd-8e8b-4f58-be4c-583efa1950f2 · outbound

This paper cites Observe that R1/2 = S for the Sobolev regression and R1/2 = I for the low-bias Sobolev regression.

Fast kernel methods: Sobolev, physics-informed, and additive models Observe that R1/2 = S for the Sobolev regression and R1/2 = I for the low-bias Sobolev regression

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.120666Z

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.

Observation 85c762c6-f5dc-4f5b-9c58-7ad71d9d8463 · outbound

This paper cites Approximation term.

Fast kernel methods: Sobolev, physics-informed, and additive models Approximation term

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.111372Z

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.

Observation 29527027-496c-4a95-a7ea-76c06668b181 · outbound

This paper cites Conclusion.

Fast kernel methods: Sobolev, physics-informed, and additive models Conclusion

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.102060Z

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.

Observation 07d208a1-a8a6-45dc-afb0-bf93811f107a · outbound

This paper cites Therefore, in the Sobolev regression, setting λ = O(n−2s/(2s+d)) such that λ ≥ n−1, and taking m = n1/(2s+d) leads to Sobolev mini- max rate.

Fast kernel methods: Sobolev, physics-informed, and additive models Therefore, in the Sobolev regression, setting λ = O(n−2s/(2s+d)) such that λ ≥ n−1, and taking m = n1/(2s+d) leads to Sobolev mini- max rate

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.091670Z

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.

Observation 0cc6d03d-0050-4596-af57-ea8535ccb2ff · outbound

This paper cites Similarly, the bias term is bounded by E(∥ √ Σ( ˆΣ + λ)−1λθ∥2.

Fast kernel methods: Sobolev, physics-informed, and additive models Similarly, the bias term is bounded by E(∥ √ Σ( ˆΣ + λ)−1λθ∥2

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.080599Z

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.

Observation ba2e70de-0b82-47af-874d-be8b2218bc30 · outbound

This paper cites As for the variance term, it is bounded by E(∥ √ Σ( ˆΣ + λ)−1Φ∗ε/n∥2.

Fast kernel methods: Sobolev, physics-informed, and additive models As for the variance term, it is bounded by E(∥ √ Σ( ˆΣ + λ)−1Φ∗ε/n∥2

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.069942Z

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.

Observation 76a7a587-355c-42d7-87a2-1168b63b19c5 · outbound

This paper cites Finally, the approximation term is bounded by E(∥ √ Σ( ˆΣ + λR)−1Φ∗δY/n∥2.

Fast kernel methods: Sobolev, physics-informed, and additive models Finally, the approximation term is bounded by E(∥ √ Σ( ˆΣ + λR)−1Φ∗δY/n∥2

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.058963Z

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.

Observation d0986c73-a76e-4dc8-94e3-f33d7e16d8db · outbound

This paper cites Putting everything together, we obtain E(∥fˆθ − f ⋆∥2 L2(PX )) ≤ inf θ∈Cd(2m+1) (2 + 6(1 + α2 λn )2)E(∥f ⋆ − fθ∥2 L2(PX )) + λ(1 + α2 λn )2∥θ∥2 2 + σ2 α2 n (1 + α2 λn ).

Fast kernel methods: Sobolev, physics-informed, and additive models Putting everything together, we obtain E(∥fˆθ − f ⋆∥2 L2(PX )) ≤ inf θ∈Cd(2m+1) (2 + 6(1 + α2 λn )2)E(∥f ⋆ − fθ∥2 L2(PX )) + λ(1 + α2 λn )2∥θ∥2 2 + σ2 α2 n (1 + α2 λn )

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T11:56:12.049013Z

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.

Observation 60f09492-9aca-4ebc-a481-a8e330e96118 · outbound

This paper cites Nathan Doum`eche, Francis Bach, ´Eloi Bedek, G´erard Biau, Claire Boyer, and Yannig Goude.

Fast kernel methods: Sobolev, physics-informed, and additive models Nathan Doum`eche, Francis Bach, ´Eloi Bedek, G´erard Biau, Claire Boyer, and Yannig Goude

Reference 2024

Resolution: verified exact; raw_fallback, observed 2026-08-05T11:56:12.037693Z

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.

Pith citing papers

Observation d5673e30-789b-438a-9034-997eee8ac92c · inbound

PIKS: Universal Physics-Informed Kernel Methods cites this paper.

PIKS: Universal Physics-Informed Kernel Methods Fast kernel methods: Sobolev, physics-informed, and additive models

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-07-30T12:20:57.284440Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.