Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T04:33:58.704351Z
Paper Citation Record · LEDGER
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages
As of 20 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2608.08893.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
27 of 27 outbound references displayed
- verified exact16
- verified fuzzy4
- unresolved7
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation e7c9efe6-4b36-4a15-a602-deab04dcedfa · outbound
This paper cites Christ,Convolution, curvature, and combinatorics: a case study, Internat.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Christ,Convolution, curvature, and combinatorics: a case study, Internat
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T04:33:59.064813Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 11f55e74-3be8-47de-a7d1-bbae61d0959b · outbound
This paper cites Sparse Bounds for the Discrete Cubic Hilbert Transform.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Sparse Bounds for the Discrete Cubic Hilbert Transform
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.972340Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7ea19530-04ad-4d48-98b7-fd392a72403a · outbound
This paper cites Sharp $l^p$-improving estimates for the discrete paraboloid.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Sharp $l^p$-improving estimates for the discrete paraboloid
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.960198Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 1c681acb-c187-4567-b79b-1fb585ee2544 · outbound
This paper cites Some subcritical estimates for the $\ell^p$-improving problem for discrete curves.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Some subcritical estimates for the $\ell^p$-improving problem for discrete curves
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.946961Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8b0fe188-f95b-4099-b0ed-108072a0b43d · outbound
This paper cites Averaging with the Divisor Function: $\ell^p$-improving and Sparse Bounds.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Averaging with the Divisor Function: $\ell^p$-improving and Sparse Bounds
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.933717Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 40171313-637f-445a-9016-1ed84a5e6ad8 · outbound
This paper cites Grosswald,Representations of integers as sums of squares, Springer-Verlag, New York, 1985.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Grosswald,Representations of integers as sums of squares, Springer-Verlag, New York, 1985
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T04:33:59.055644Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d79d724f-c9e2-42cc-9124-b30546b40bc4 · outbound
This paper cites Improving estimates for discrete polynomial averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Improving estimates for discrete polynomial averages
Reference 7
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.919017Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ce9d0b02-1ec3-4d3e-9f99-6a815dadc84a · outbound
This paper cites Averages Along the Primes: Improving and Sparse Bounds.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Averages Along the Primes: Improving and Sparse Bounds
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.901691Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e9d4efd2-deb8-42c6-b89a-0772de1bc48c · outbound
This paper cites Averages along the Square Integers: $\ell^p$ improving and Sparse Inequalities.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Averages along the Square Integers: $\ell^p$ improving and Sparse Inequalities
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.887561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3d6607c6-e245-4238-bd0c-66b130753b52 · outbound
This paper cites an unresolved cited work.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T04:33:59.044506Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b72ee151-385e-4745-b9d9-c7def2e70238 · outbound
This paper cites an unresolved cited work.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T04:33:59.032247Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d4e58a55-a780-43d5-83cb-5217e71941ff · outbound
This paper cites Restriction of toral eigenfunctions to totally geodesic submanifolds.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Restriction of toral eigenfunctions to totally geodesic submanifolds
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.874991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 7b5c237e-7975-45db-97d0-435d5a450cb9 · outbound
This paper cites The discrete spherical averages over a family of sparse sequences.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages The discrete spherical averages over a family of sparse sequences
Reference 13
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.862291Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d7425879-01ff-4dfe-8717-82cd53e745ce · outbound
This paper cites $\ell^p$-improving for discrete spherical averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages $\ell^p$-improving for discrete spherical averages
Reference 14
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.849111Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 71451692-c2c9-4163-9b27-ee0c5faffd45 · outbound
This paper cites an unresolved cited work.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T04:33:59.022415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 70ca12c9-bcc8-408b-86d8-80d34bc0d3c0 · outbound
This paper cites an unresolved cited work.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T04:33:59.010126Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bbb93223-de68-4304-800f-1f845cb3afae · outbound
This paper cites $\ell^p(\mathbb{Z}^d)$-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages $\ell^p(\mathbb{Z}^d)$-Improving Properties and Sparse Bounds for Discrete Spherical Maximal Averages
Reference 17
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.833368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2d09cb6d-133a-4d34-afc1-6f017fdf1a1d · outbound
This paper cites $\ell^p$-improving inequalities for Discrete Spherical Averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages $\ell^p$-improving inequalities for Discrete Spherical Averages
Reference 18
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.818701Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2d76ef94-912f-48c9-8712-ff520ecab0da · outbound
This paper cites Lacunary Discrete Spherical Maximal Functions.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Lacunary Discrete Spherical Maximal Functions
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T04:33:58.673934Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 844477e4-b115-4590-b061-09cd5649ae53 · outbound
This paper cites Sparse Bounds for the Discrete Spherical Maximal Function.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Sparse Bounds for the Discrete Spherical Maximal Function
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.791559Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9b75ff4a-9476-457b-beb6-efe10be05e4f · outbound
This paper cites Endpoint $ \ell ^{r}$ improving estimates for Prime averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Endpoint $ \ell ^{r}$ improving estimates for Prime averages
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.777520Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4c98db7f-cc93-4ed8-92d3-20b6ea5a9ad0 · outbound
This paper cites Magyar, Lp-bounds for spherical maximal operators on Zn, Rev.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Magyar, Lp-bounds for spherical maximal operators on Zn, Rev
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T04:33:59.000835Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b6bfbfac-d441-4b8c-a056-51a515c7e07e · outbound
This paper cites Discrete analogues in harmonic analysis: Spherical averages.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Discrete analogues in harmonic analysis: Spherical averages
Reference 23
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.762684Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3b02acb0-af62-4aef-83f8-c7416762ed53 · outbound
This paper cites Additive energies on spheres.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Additive energies on spheres
Reference 24
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T04:33:58.748182Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 66c8ea2b-bd61-4cf5-9555-ce99d5c4c3bd · outbound
This paper cites Non-linear metric perturbation enhancement of primordial gravitational waves.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Non-linear metric perturbation enhancement of primordial gravitational waves
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T04:33:58.697234Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4e861838-5072-4135-9b24-c27548c1517c · outbound
This paper cites Schlag,On continuum incidence problems related to harmonic analysis, J.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Schlag,On continuum incidence problems related to harmonic analysis, J
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T04:33:58.991903Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 13e9d35b-a6b9-4e7d-9fd1-f8dded8029a8 · outbound
This paper cites an unresolved cited work.
Sharp $\ell^p$-Improving Estimates for Fixed-Radius Discrete Spherical Averages Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T04:33:58.982516Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.