Paper Citation Record · LEDGER

The n-th prime exponentially

As of 20 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2504.14458.

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

pith.paper-citation-record.v1
2504.14458 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:57:22.859731Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:14:31.226926Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:14:32.692988Z

Reference resolution

10 of 10 outbound references displayed

verified exact3
verified fuzzy1
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7324d4ec-2246-42d4-a651-841890857551 · outbound

This paper cites Updating the error term in the prime number theorem.

The n-th prime exponentially Updating the error term in the prime number theorem

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:57:23.186874Z

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 57489b31-80fa-498b-8f4f-e43267cb87b6 · outbound

This paper cites Some explicit estimates for the error term in the prime numb er theorem.

The n-th prime exponentially Some explicit estimates for the error term in the prime numb er theorem

Reference 2

Resolution: metadata mismatch; raw_fallback, observed 2026-08-16T11:57:23.166352Z

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 a22046a1-ac43-4244-9be5-2926131e3846 · outbound

This paper cites Sharper bounds for the error term in the Prime Number Theorem.

The n-th prime exponentially Sharper bounds for the error term in the Prime Number Theorem

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T11:57:22.826153Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce0fdb27-b311-4079-be1a-5e61a8b548bf · outbound

This paper cites Eﬀective de la Vall´ e Poussin style bounds on the ﬁrst Chebys hev function.

The n-th prime exponentially Eﬀective de la Vall´ e Poussin style bounds on the ﬁrst Chebys hev function

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T11:57:22.830871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b76a6619-6042-4789-9a0f-3929f8098f81 · outbound

This paper cites Recherches analytiques sur la th´ eorie des nombres premie rs.

The n-th prime exponentially Recherches analytiques sur la th´ eorie des nombres premie rs

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:57:23.202300Z

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 9d25bbc3-cd76-4146-98fc-b984abe22374 · outbound

This paper cites On The Interval Containing At Least One Prime Number.

The n-th prime exponentially On The Interval Containing At Least One Prime Number

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T11:57:22.840935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e26d5f05-b288-4ada-9ada-89832c8242fd · outbound

This paper cites The n-th Prime is Greater than n log n.

The n-th prime exponentially The n-th Prime is Greater than n log n

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T11:57:22.845435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e0ad901-a445-423a-b3aa-556d28cc0f72 · outbound

This paper cites Explicit bounds for some functions of prim e numbers.

The n-th prime exponentially Explicit bounds for some functions of prim e numbers

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T11:57:22.850507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fa3a75c-3c4d-4989-9432-0d5180101401 · outbound

This paper cites The n-th prime asymptotically.

The n-th prime exponentially The n-th prime asymptotically

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:57:22.942584Z

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 54c2cc97-a0f4-4653-b319-b6f790a542e7 · outbound

This paper cites Effective exponential bounds on the prime gaps.

The n-th prime exponentially Effective exponential bounds on the prime gaps

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:57:22.921480Z

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

Observation ac6b203f-bae0-495b-acd8-bdaaf62ca0c2 · inbound

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ cites this paper.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ The n-th prime exponentially

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.696652Z

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.