Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:14:31.593835Z
Paper Citation Record · LEDGER
Behaviour of the sequence $\vartheta_n = \vartheta(p_n)$
As of 18 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
No inbound Pith citation observations are available.