Paper Citation Record · LEDGER

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals

As of 11 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2412.19866.

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

pith.paper-citation-record.v1
2412.19866 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:44:12.023451Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

12 of 12 outbound references displayed

verified exact0
verified fuzzy7
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 967c639f-2a3d-49ac-8041-7d9fed4d55db · outbound

This paper cites 4, 430–479.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals 4, 430–479

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.311264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c559c8d8-b3d1-44b3-9468-f64c21e4cd79 · outbound

This paper cites Comtet, Sur les coeﬃcients de l’inverse de la s´ erie formelle ∑ n!xn, C.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Comtet, Sur les coeﬃcients de l’inverse de la s´ erie formelle ∑ n!xn, C

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.296398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9df4de4d-9cae-4412-b2a7-81f5cd51c01d · outbound

This paper cites an unresolved cited work.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T00:44:12.281093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c873b94d-86f0-4e78-bf0b-db0286cb0023 · outbound

This paper cites an unresolved cited work.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T00:44:11.984948Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3a57877-43d5-4c2f-98e7-f54c7a20da28 · outbound

This paper cites an unresolved cited work.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T00:44:12.257561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 92a4e5d8-194f-4077-82b9-90f4b6f1803c · outbound

This paper cites Gao, Sergey Kitaev, and Philip B.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Gao, Sergey Kitaev, and Philip B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.241707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 4fb20921-b097-4916-8364-eb29a176a9eb · outbound

This paper cites an unresolved cited work.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T00:44:12.225240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2897015f-afc3-4128-811b-acfe53633e4a · outbound

This paper cites Hunter, Asymptotic Analysis and Singular Perturbation Theory , 2004.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Hunter, Asymptotic Analysis and Singular Perturbation Theory , 2004

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.209400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 02f28f3e-277a-4382-b216-c5ef1f8d8bf6 · outbound

This paper cites 8, 871–889, available at https://doi.org/10.1080/00029890.1969.12000359.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals 8, 871–889, available at https://doi.org/10.1080/00029890.1969.12000359

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T00:44:12.009560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab5a1c12-c4ab-4df0-a56b-87c6fb5ee1de · outbound

This paper cites Entry A003319 in The On-Line Encyclopedia of Integer Sequences, https://oeis.org/A003319.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Entry A003319 in The On-Line Encyclopedia of Integer Sequences, https://oeis.org/A003319

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.193711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d6d5164e-e959-41b3-80b7-5bdc36c83e5e · outbound

This paper cites Panaitopol, A formula for π (x) applied to a result of Koninck-Ivi´ c, Nieuw Arch.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals Panaitopol, A formula for π (x) applied to a result of Koninck-Ivi´ c, Nieuw Arch

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.177847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6e241a90-0947-401b-a16d-1d068c2d3757 · outbound

This paper cites 3, 143–148.

Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals 3, 143–148

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:44:12.161326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

No inbound Pith citation observations are available.