Paper Citation Record · LEDGER

Close points on a modular hyperbola

As of 8 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2506.04087.

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

pith.paper-citation-record.v1
2506.04087 v1

Coverage vector

measured 9 of 9 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:05:37.820367Z

measured 9 of 9 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 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

9 of 9 outbound references displayed

verified exact0
verified fuzzy9
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 51c33330-a0ca-422b-8973-c0b448f523de · outbound

This paper cites Banks, M.Z.

Close points on a modular hyperbola Banks, M.Z

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:39.500351Z

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 c625ac49-7eae-41c4-8a7c-1a84dbd48f4d · outbound

This paper cites Chan, Shortest distance in modular hyperbola and least quadratic non-residue, Mathematika 62 (2016), 860--865.

Close points on a modular hyperbola Chan, Shortest distance in modular hyperbola and least quadratic non-residue, Mathematika 62 (2016), 860--865

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:39.329885Z

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 bbb6cde6-102d-4bca-a334-f4adf95c3b29 · outbound

This paper cites Chang, On a question of Davenport and Lewis and new character sum bounds in finite fields, Duke Math.

Close points on a modular hyperbola Chang, On a question of Davenport and Lewis and new character sum bounds in finite fields, Duke Math

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:39.119301Z

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 1de42c5c-5cd1-4f8e-aa23-b2486ec48bd5 · outbound

This paper cites Granville and K.

Close points on a modular hyperbola Granville and K

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.933271Z

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 7e4b088a-338d-49c0-80da-6bf00a990b1b · outbound

This paper cites Iwaniec and E.

Close points on a modular hyperbola Iwaniec and E

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.757295Z

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 b8b8a4f1-804d-474c-8255-13abd717e20d · outbound

This paper cites Karatsuba, Distribution of values of Dirichlet characters on additive sequences, Soviet Math.

Close points on a modular hyperbola Karatsuba, Distribution of values of Dirichlet characters on additive sequences, Soviet Math

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.573833Z

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 ab1acbf5-de45-47dc-9e1a-3c933fbdd0dd · outbound

This paper cites Kerr, I.E.

Close points on a modular hyperbola Kerr, I.E

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.389710Z

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 4026d864-db9e-435d-bad1-0ca689104ac0 · outbound

This paper cites Graham and C.J.

Close points on a modular hyperbola Graham and C.J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.177807Z

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 2c0f9bc1-abc2-4da5-b77b-c2173dfa8d09 · outbound

This paper cites Shparlinski, Modular hyperbolas, Japan J.

Close points on a modular hyperbola Shparlinski, Modular hyperbolas, Japan J

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:05:38.032045Z

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

No inbound Pith citation observations are available.