Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T12:12:55.647674Z
Paper Citation Record · LEDGER
On arithmetic terms expressing the prime-counting function and the n-th prime
As of 15 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2412.14594.
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 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T05:08:12.032994Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T03:57:38.344078Z
Reference resolution
23 of 23 outbound references displayed
- verified exact4
- verified fuzzy6
- unresolved13
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 06b9f486-7f26-4124-bdf4-224ac21e4698 · outbound
This paper cites Grzegorczyk.
On arithmetic terms expressing the prime-counting function and the n-th prime Grzegorczyk
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:56.107624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9f8d15fb-8538-4543-80c8-c114f2fd653a · outbound
This paper cites On the impossibility of discovering a formula for primes using AI.
On arithmetic terms expressing the prime-counting function and the n-th prime On the impossibility of discovering a formula for primes using AI
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T12:12:55.537220Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f81653ba-3bff-473b-be6a-093eb8d003c9 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 3
- Resolution
- verified exact
- doi, observed 2026-08-11T12:12:55.717753Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b95993d7-ce1e-49cc-94ac-0950af03385d · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.091883Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4defe6ae-bff1-4c4d-b3d7-fe84710fb385 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 5
- Resolution
- verified exact
- raw_fallback, observed 2026-08-11T12:12:55.840773Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 43cf5399-1f13-47c3-8e85-ae4c8cc50ed3 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.077159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2251f2f2-17f1-4663-b8ec-4584602f3330 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.062663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d416c563-e36d-439e-b1c1-585ead425cd0 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.048251Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 22187fad-4985-4846-af44-1ff2fd17938e · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.033084Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 82460da2-36a4-4dca-854e-d6dced962fd1 · outbound
This paper cites Robinson.
On arithmetic terms expressing the prime-counting function and the n-th prime Robinson
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:56.017503Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation da47a5ec-06eb-440a-8b47-87e333a01d00 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:56.001413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5b3c013b-329f-479e-9729-4b7684ef12e2 · outbound
This paper cites du Sautoy.
On arithmetic terms expressing the prime-counting function and the n-th prime du Sautoy
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:55.984862Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c5a1eb56-548b-411c-a2e9-45e1b298678d · outbound
This paper cites Prunescu and J.
On arithmetic terms expressing the prime-counting function and the n-th prime Prunescu and J
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:55.968273Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d8d35e7e-7c36-4576-bccf-6eecb4f15248 · outbound
This paper cites Prunescu and L.
On arithmetic terms expressing the prime-counting function and the n-th prime Prunescu and L
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:55.951772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 91c16114-5b76-4eb1-a90b-94b9d325b899 · outbound
This paper cites On the representation of number-theoretic functions by arithmetic terms.
On arithmetic terms expressing the prime-counting function and the n-th prime On the representation of number-theoretic functions by arithmetic terms
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T12:12:55.619052Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 808c5467-8bb5-4855-88da-2d0352f6026d · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:55.935477Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4803645b-fbab-4b35-8c77-3242e8c983fc · outbound
This paper cites Mazzanti.
On arithmetic terms expressing the prime-counting function and the n-th prime Mazzanti
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T12:12:55.920265Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 470889a4-06b1-4f4c-9558-697d837e2edf · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:55.905244Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7e2155bb-048d-4230-81e1-06585f396e31 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:55.889784Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a2b94d84-6df0-4b7d-ad1b-eda0cf07ac99 · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 20
- Resolution
- verified exact
- doi, observed 2026-08-11T12:12:55.685994Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a86f6fcb-57d1-4a59-96b8-39fe3f3704da · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T12:12:55.874129Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2a8dde6f-cdf1-431d-afa6-08e110dc9bfb · outbound
This paper cites an unresolved cited work.
On arithmetic terms expressing the prime-counting function and the n-th prime Unresolved cited work
Reference 1975
- Resolution
- verified exact
- doi, observed 2026-08-11T12:12:55.702611Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b04a4ac5-869c-4153-977d-f52ba75bae71 · outbound
This paper cites Arithmetic-term representations for the greatest common divisor.
On arithmetic terms expressing the prime-counting function and the n-th prime Arithmetic-term representations for the greatest common divisor
Reference 2024
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T12:12:55.608878Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 2417fa73-e4b0-4839-9697-831f2a33c846 · inbound
Undecidability, Chaos and Universality in Arithmetic Terms cites this paper.
Undecidability, Chaos and Universality in Arithmetic Terms On arithmetic terms expressing the prime-counting function and the n-th prime
Reference 24
- Resolution
- verified exact
- arxiv_id, observed 2026-07-03T03:57:38.345331Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fca6b1b6-f5c1-4ce6-bcfc-859a101a5d52 · inbound
Prime-Interval Algebras cites this paper.
Prime-Interval Algebras On arithmetic terms expressing the prime-counting function and the n-th prime
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T05:08:12.032994Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.