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Paper Citation Record · LEDGER

The strange story of an almost unknown prime number counter: The Rafael Barrett formula

As of 13 August 2026, this Paper Citation Record lists 7 of 7 outbound references and 0 inbound Pith citation observations for arXiv:2509.19324.

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

pith.paper-citation-record.v1
2509.19324 v7

Coverage vector

measured 7 of 7 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T17:41:00.484022Z

measured 7 of 7 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

7 of 7 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved7
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 23337485-eb9b-4548-890b-a88fdd5cb98c · outbound

This paper cites Paraguayan Sorrow: Writings of Rafael Barrett, Monthly Review Press.

The strange story of an almost unknown prime number counter: The Rafael Barrett formula Paraguayan Sorrow: Writings of Rafael Barrett, Monthly Review Press

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.460811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.460811Z digest=sha256:47db64d1a1286570e505cf2a3d88b385d2e66379974c0e58695cc42b84759691

Observation 743c5a24-89af-4aa5-9ff6-4582ead970c9 · outbound

This paper cites Mirando Vivir, (1912).

The strange story of an almost unknown prime number counter: The Rafael Barrett formula Mirando Vivir, (1912)

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.465011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.465011Z digest=sha256:8c858c4cd2cc51103df79869a9f8d884f5369b41be3ea0a4ae5b9176a3751e40

Observation 04c80fd5-066c-4f21-abf4-8739f82a5893 · outbound

This paper cites an unresolved cited work.

The strange story of an almost unknown prime number counter: The Rafael Barrett formula Unresolved cited work

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.468629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.468629Z digest=sha256:40f61c542f8cb26b94ca0319735e628965ea41fc3dd2a8f3332b540fcf3cc169

Observation c8cae313-fdca-45dc-b998-10d3401586dd · outbound

This paper cites an unresolved cited work.

The strange story of an almost unknown prime number counter: The Rafael Barrett formula Unresolved cited work

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.471945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.471945Z digest=sha256:20e439c1fb798d11d34862e4dc4e57bc88a50abfd3a928b4f611ab7298673659

Observation 318bc665-4900-40d1-b975-950a01d27bfa · outbound

This paper cites an unresolved cited work.

The strange story of an almost unknown prime number counter: The Rafael Barrett formula Unresolved cited work

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.475268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.475268Z digest=sha256:75015770a2b26f3e1d0e54b26657b89934027726b3e7e9d7384856c5f711d06c

Observation a5b2abbb-3c0e-45bf-998b-25d0c72f431d · outbound

This paper cites absorbed.

The strange story of an almost unknown prime number counter: The Rafael Barrett formula absorbed

Reference 6

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.480434Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.480434Z digest=sha256:28e477b909802352542fec232f1902da6018f52ac4db0a2119bb1f440a81d115

Observation 62efb543-ad8c-4e56-813e-8e0e85f54b76 · outbound

This paper cites We write it as follows: (k 1)! 1 1 [(k 1)! 1] 1 k k k     .

The strange story of an almost unknown prime number counter: The Rafael Barrett formula We write it as follows: (k 1)! 1 1 [(k 1)! 1] 1 k k k     

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-04T17:41:00.484022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T17:41:00.484022Z digest=sha256:bb4cd5c9fe31114a0669336fe914cb7c7f9bc7d5bd71ad674be6ac3dd9a0953c

Pith citing papers

No inbound Pith citation observations are available.