Paper Citation Record · LEDGER

Generalized Hardy's identity for the astroid-type p-circle lattice point problem

As of 8 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:2506.03331.

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

pith.paper-citation-record.v1
2506.03331 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:24:25.210149Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T01:45:40.759526Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T01:48:28.654195Z

Reference resolution

17 of 17 outbound references displayed

verified exact3
verified fuzzy5
unresolved7
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 65ea1cc7-0eda-40a5-ae22-929714336265 · outbound

This paper cites Aomoto, K.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Aomoto, K

Reference 1

Resolution: verified exact; doi, observed 2026-08-07T11:24:25.885019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3157d7cd-53ba-4b41-a671-2d0be2e5aaac · outbound

This paper cites Gauss, De nexu inter multitudinem classium, in quas formae binariae secundi gradus distribuuntur, earumque determinantem, In: Schering, E., ed., Werke, Vol.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Gauss, De nexu inter multitudinem classium, in quas formae binariae secundi gradus distribuuntur, earumque determinantem, In: Schering, E., ed., Werke, Vol

Reference 2

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T11:24:27.212726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f9548c9b-d77b-4863-96d9-9f159b396e7c · outbound

This paper cites Hankel, Die Cylinderfunctionen erster und zweiter Art, Math.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Hankel, Die Cylinderfunctionen erster und zweiter Art, Math

Reference 3

Resolution: verified exact; doi, observed 2026-08-07T11:24:25.670928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dad43b79-8e2d-4246-8fbf-f5bf4572552a · outbound

This paper cites Hardy, On the expression of a number as the sum of two squares, Q.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Hardy, On the expression of a number as the sum of two squares, Q

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:24:27.043903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 03010e26-d4a8-4906-a459-7fcf9d887bbc · outbound

This paper cites Hardy, E.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Hardy, E

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.291852Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 227260b6-c091-4cbd-9ccd-9d7c107b4607 · outbound

This paper cites Huxley, Exponential sums and lattice points.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Huxley, Exponential sums and lattice points

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.387101Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b50c5885-6587-40c9-ab40-b62d276923c0 · outbound

This paper cites Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.488637Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d16aad3-14cb-4c78-9f41-646bdd007749 · outbound

This paper cites Kilbas, H.M.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Kilbas, H.M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:24:26.835359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6072c364-db99-4cc2-8bd9-adaa7d9ffca7 · outbound

This paper cites Series expansions by generalized Bessel functions for functions related to the lattice point problems for the p-circle.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Series expansions by generalized Bessel functions for functions related to the lattice point problems for the p-circle

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.607296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation effd9562-b6f1-418d-b76a-89aa46d5437f · outbound

This paper cites Asymptotic evaluations of generalized Bessel function of order zero related to the p-circle lattice point problem.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Asymptotic evaluations of generalized Bessel function of order zero related to the p-circle lattice point problem

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:24:25.445013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 98b06f11-6455-4073-9260-995347233fc2 · outbound

This paper cites Kr¨ atzel, Lattice Points, Kluwer Academic Publication, (1988).

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Kr¨ atzel, Lattice Points, Kluwer Academic Publication, (1988)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:24:26.677501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 44388762-782e-4c9b-abeb-c9e7db4c50c2 · outbound

This paper cites Kuba, On sums of two k-th powers of numbers in residue classes II, Abh.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Kuba, On sums of two k-th powers of numbers in residue classes II, Abh

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.843885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3139a41f-5b58-4d28-8363-de5126147ba6 · outbound

This paper cites Kuratsubo, E.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Kuratsubo, E

Reference 13

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T11:24:26.102444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6ede50ad-90ff-4d93-97bb-933b76a8da70 · outbound

This paper cites Laugesen, S.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Laugesen, S

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:24.998250Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30f0f86c-b2f2-4cf8-8449-8fce434bd683 · outbound

This paper cites Laugesen, S.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Laugesen, S

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T11:24:25.088099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 835a5111-36cf-4967-951e-2305b54b6811 · outbound

This paper cites Stein, G.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Stein, G

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:24:26.498498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 43d68221-9acd-46c6-92f9-b4422f689e8f · outbound

This paper cites Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge Univ.

Generalized Hardy's identity for the astroid-type p-circle lattice point problem Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge Univ

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:24:26.304484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 32cf36b5-4562-4518-bdb6-1591c4ccf909 · inbound

Analytic Study of $p$-Bessel Functions: Fractional Calculus, Integral Representations, and Complex Extensions cites this paper.

Analytic Study of $p$-Bessel Functions: Fractional Calculus, Integral Representations, and Complex Extensions Generalized Hardy's identity for the astroid-type p-circle lattice point problem

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-15T01:48:28.655970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.