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Paper Citation Record · LEDGER

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

As of 12 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 2026-08-12T06:34:41.77262+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:f921e23fa0e600322824ebb19855c2066ad2799a01ace49891a2cf0bb3dbb7e8

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=sha256:2c5a3949997500238d686efc23435d30868623ddc82a3c4c1b61df1e2420e07b

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:f01f643f5cc44099dcd0d6661ce455f7d76da6440a478510d2d616412d49fa4d

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=sha256:9dc26fd95f44630e29822c75a084dcbfde3685f1b685ac59644802676d013e84

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=sha256:10979b25d5038399493d850636d919ef0c7279bb962216f8b9147dc512f2f939

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:cfcdb9c3bd163463b80104b09557b000a2efa9e17be45daba5527ba593552bc4

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=sha256:5fa927137eacf08cefe257d1f16aff67d8cefd57843494f5b2c035d6b8f0a360

Pith citing papers

No inbound Pith citation observations are available.