Paper Citation Record · LEDGER

A Rigorous Error Bound for the TG Kernel in Prime Counting

As of 21 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2506.22634.

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

pith.paper-citation-record.v1
2506.22634 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:07:33.022300Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

12 of 12 outbound references displayed

verified exact0
verified fuzzy8
unresolved3
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6e360ce0-24c2-4ded-8458-43b1f2c0027b · outbound

This paper cites Riemann, ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse , Monatsber.

A Rigorous Error Bound for the TG Kernel in Prime Counting Riemann, ¨Uber die Anzahl der Primzahlen unter einer gegebenen Gr¨ osse , Monatsber

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:36.047208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 69f3e317-6675-4b3c-b1f7-229a94a2f53a · outbound

This paper cites von Mangoldt, Zu Riemanns Abhandlung ’ ¨Uber...’, J.

A Rigorous Error Bound for the TG Kernel in Prime Counting von Mangoldt, Zu Riemanns Abhandlung ’ ¨Uber...’, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:35.750068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 198f3b4e-7fe4-4076-b621-ac7625af6696 · outbound

This paper cites Chebyshev, M´ emoire sur les nombres premiers, Acad.

A Rigorous Error Bound for the TG Kernel in Prime Counting Chebyshev, M´ emoire sur les nombres premiers, Acad

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:35.507453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e1c505cf-97c5-468a-b882-c4447d165b6b · outbound

This paper cites Riesz, Quelques cons´ equences de la formule explicite de M.

A Rigorous Error Bound for the TG Kernel in Prime Counting Riesz, Quelques cons´ equences de la formule explicite de M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:35.274942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4105f0f6-6e58-4fb5-9619-048eda0343aa · outbound

This paper cites Weil, Sur les ’formules explicites’ de la th´ eorie des nombres,Comm.

A Rigorous Error Bound for the TG Kernel in Prime Counting Weil, Sur les ’formules explicites’ de la th´ eorie des nombres,Comm

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:34.993070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a85199c6-8fb5-4e7f-a3c7-727a5141e29e · outbound

This paper cites Landau, Handbuch der Lehre von der Verteilung der Primzahlen , 2 vols., Teubner, 1909–1911.

A Rigorous Error Bound for the TG Kernel in Prime Counting Landau, Handbuch der Lehre von der Verteilung der Primzahlen , 2 vols., Teubner, 1909–1911

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:34.706517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5d1774b7-dde7-4bfc-a74b-502c6db51ad3 · outbound

This paper cites an unresolved cited work.

A Rigorous Error Bound for the TG Kernel in Prime Counting Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:34.374745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 18ec2d0c-db19-4c17-962e-af88d892cf52 · outbound

This paper cites an unresolved cited work.

A Rigorous Error Bound for the TG Kernel in Prime Counting Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:34.097768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2e6437cc-95c3-43e8-8c47-383e82ae7618 · outbound

This paper cites Davenport, Multiplicative Number Theory, 1st ed., Springer, 1952.

A Rigorous Error Bound for the TG Kernel in Prime Counting Davenport, Multiplicative Number Theory, 1st ed., Springer, 1952

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:33.893741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f2a6bd74-0718-4ddc-aac0-dbd99d902bda · outbound

This paper cites Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J.

A Rigorous Error Bound for the TG Kernel in Prime Counting Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:07:33.655795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation adeff3ea-8ffc-4f53-af97-60e62b9afed9 · outbound

This paper cites an unresolved cited work.

A Rigorous Error Bound for the TG Kernel in Prime Counting Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:07:33.384782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7e8aca80-fd7c-446d-bf3d-5120efc4baae · outbound

This paper cites Alpay, Formal Proof: Faruk Alpay ≡ Φ∞, Preprints, 2025.

A Rigorous Error Bound for the TG Kernel in Prime Counting Alpay, Formal Proof: Faruk Alpay ≡ Φ∞, Preprints, 2025

Reference 12

Resolution: malformed identifier; no resolver link, observed 2026-08-06T22:07:33.022300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.