Paper Citation Record · LEDGER

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$

As of 11 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2507.14410.

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

pith.paper-citation-record.v1
2507.14410 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:14:31.593835Z

measured 19 of 19 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

19 of 19 outbound references displayed

verified exact11
verified fuzzy3
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a25283dc-bfdb-4cb1-b173-7e849f0cf8c0 · outbound

This paper cites Autour de la fonction qui compte le nombre de nombres premiers.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Autour de la fonction qui compte le nombre de nombres premiers

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:14:32.897315Z

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 8eccdcb5-aa23-4462-a96a-3d0469c38031 · outbound

This paper cites Bornes effectives pour certaines fonctions concernant les nombres premiers.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Bornes effectives pour certaines fonctions concernant les nombres premiers

Reference 2

Resolution: verified exact; raw_fallback, observed 2026-08-06T16:14:32.867637Z

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 6042de3f-a696-46aa-bd7e-7421bf08fac6 · outbound

This paper cites The kth prime is greater than k(ln k + ln lnk − 1) for k ≥ 2.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ The kth prime is greater than k(ln k + ln lnk − 1) for k ≥ 2

Reference 3

Resolution: verified exact; doi, observed 2026-08-06T16:14:31.849575Z

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 666e2904-0641-4f17-ad68-a3334d0d1ca5 · outbound

This paper cites On the arithmetic average of the first $n$ primes.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ On the arithmetic average of the first $n$ primes

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.795081Z

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 d8e009b7-1b13-42fc-80b3-7ce59eab60ef · outbound

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

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ The n-th Prime is Greater than n log n

Reference 5

Resolution: verified exact; doi, observed 2026-08-06T16:14:31.729408Z

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 8fa13433-a26e-487a-8cbc-325f657f9779 · outbound

This paper cites Approximate formulas for some functions of prime numbers.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Approximate formulas for some functions of prime numbers

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T16:14:30.813962Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6efafd0-2c9b-4eb6-937f-48dc73573d67 · outbound

This paper cites Explicit estimates of some functions over primes.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Explicit estimates of some functions over primes

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T16:14:30.864365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18d36095-bac4-4779-825c-7cdaf5598962 · outbound

This paper cites Estimates of Some Functions Over Primes without R.H..

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Estimates of Some Functions Over Primes without R.H.

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T16:14:30.941028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94208892-b363-4809-a9e7-8906f7830cac · outbound

This paper cites New estimates for some functions defined over primes.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ New estimates for some functions defined over primes

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.721373Z

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 db0bf787-d54d-4f4c-aef6-558ab2111f4f · outbound

This paper cites New estimates for the $n$th prime number.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ New estimates for the $n$th prime number

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.710076Z

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 9a4b0c60-ef9c-4c35-9b26-9b352e631a46 · outbound

This paper cites The little book of big primes.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ The little book of big primes

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:14:32.887930Z

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 bcdd94ce-1f66-41bb-aa7b-5679efa7bca2 · outbound

This paper cites Unsolved problems in number theory.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Unsolved problems in number theory

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:14:32.878027Z

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 ac6b203f-bae0-495b-acd8-bdaaf62ca0c2 · outbound

This paper cites The n-th prime exponentially.

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 2026-08-11T06:34:44.6726+00:00.

Observation 261b982f-1ee0-4639-8529-cacec79028cd · outbound

This paper cites Effective de la Valle Poussin style bounds on the first Chebyshev function.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Effective de la Valle Poussin style bounds on the first Chebyshev function

Reference 14

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:14:32.684703Z

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 95d6ff03-e3e9-4a61-b872-486816549246 · outbound

This paper cites Effective exponential bounds on the prime gaps.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Effective exponential bounds on the prime gaps

Reference 15

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:14:32.610815Z

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 c422bd7a-2ba4-4e9d-818a-2dfaa387e151 · outbound

This paper cites On the first sign change of $\theta(x) - x$.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ On the first sign change of $\theta(x) - x$

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.473804Z

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 c49a6b92-2e70-4521-af5b-e2c3111978a9 · outbound

This paper cites Variants on Andrica's conjecture with and without the Riemann hypothesis.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Variants on Andrica's conjecture with and without the Riemann hypothesis

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.356635Z

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 6e8b59ee-9b24-4bd1-b1fb-d5f61c13f132 · outbound

This paper cites Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Verifying the Firoozbakht, Nicholson, and Farhadian conjectures up to the 81st maximal prime gap

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:14:32.182200Z

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 923a57ae-5a24-4d4a-8083-923abc0196e5 · outbound

This paper cites Strong Version of Andrica’s Conjecture.

Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$ Strong Version of Andrica’s Conjecture

Reference 19

Resolution: verified exact; raw_fallback, observed 2026-08-06T16:14:32.092990Z

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.