Paper Citation Record · LEDGER

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $

As of 12 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2501.04488.

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

pith.paper-citation-record.v1
2501.04488 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:44:07.086227Z

measured 17 of 17 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

17 of 17 outbound references displayed

verified exact0
verified fuzzy16
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 556e0170-c765-4a15-afe1-8a4192145a60 · outbound

This paper cites Abramowitz, I.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Abramowitz, I

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.294988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c14d1fdc-40ce-4412-a709-3f025c238f87 · outbound

This paper cites Backlund, Über die Nullstellen der Riemannschen Zetafunktion, Acta.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Backlund, Über die Nullstellen der Riemannschen Zetafunktion, Acta

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.282705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 65289f8a-fd54-4c96-9ff1-73bfa3456527 · outbound

This paper cites Bays and R.H.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Bays and R.H

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.273951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation b8dae446-9fc8-4a8c-b197-24abb3d011af · outbound

This paper cites Büthe, An analytic method for boundingψ (x), Math.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Büthe, An analytic method for boundingψ (x), Math

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.264893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 53f69ae6-9898-494d-9cd1-d8eabd7e926d · outbound

This paper cites Chao and R.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Chao and R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.254906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a1478dfa-8861-4bff-987c-eeb75c5676dd · outbound

This paper cites 1 (2018), 227-251.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ 1 (2018), 227-251

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.244448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5f9a1d4d-e7b3-4873-bc40-8320517d66c7 · outbound

This paper cites an unresolved cited work.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-10T21:44:07.234195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f66776f9-c940-4580-84ce-5ae86e06e309 · outbound

This paper cites Ingham, The distribution of prime numbers , Cambridge Math.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Ingham, The distribution of prime numbers , Cambridge Math

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.223830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ace16e2d-7372-4538-9d15-42f06362d97e · outbound

This paper cites Lebedev, Special functions and their applications , Dover (1972).

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Lebedev, Special functions and their applications , Dover (1972)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.213195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e22591a5-a39e-4ebc-a703-f5159aa956ff · outbound

This paper cites Lehman, On the difference π (x)− li (x), Acta Arithmetica XI (1966), 397-410.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Lehman, On the difference π (x)− li (x), Acta Arithmetica XI (1966), 397-410

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.202245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 04b7557a-1fbf-4435-ad5e-a28b4e28a5a7 · outbound

This paper cites Littlewood, Sur la distribution des nombres premiers, C.R.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Littlewood, Sur la distribution des nombres premiers, C.R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.191194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cd4889ab-abca-4349-aec6-c8bf7e18614a · outbound

This paper cites Plymen, The Great Prime Number Race , Student Mathematical Li- brary, Vol 92, AMS (2020).

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Plymen, The Great Prime Number Race , Student Mathematical Li- brary, Vol 92, AMS (2020)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.178039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3a303b0c-0c46-4c75-aaca-3ab2310cd64c · outbound

This paper cites Saouter and P.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Saouter and P

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.163880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ebac5bfe-266c-428d-91b7-6553041ddb99 · outbound

This paper cites Saouter, T.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Saouter, T

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.151704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8b9979d3-62ec-4d32-81ad-a9d64c77dd05 · outbound

This paper cites Skewes, On the differenceπ (x)−li (x), J.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Skewes, On the differenceπ (x)−li (x), J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.140242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7fe184f5-771a-4295-815d-979df44abb0e · outbound

This paper cites Skewes, On the differenceπ (x)−li (x), Proc.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ Skewes, On the differenceπ (x)−li (x), Proc

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.128606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bd8131ef-a3da-4916-8b1f-968979fa7305 · outbound

This paper cites te Riele, On the sign of the differenceπ (x)−li (x), Math.

New bounds in R.S. Lehman's estimates for the difference $\pi\left( x\right) -li\left( x\right) $ te Riele, On the sign of the differenceπ (x)−li (x), Math

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T21:44:07.117199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.