Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T13:52:00.596188Z
Paper Citation Record · LEDGER
Chebyshev's bias without linear independence
As of 12 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2512.23302.
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 2026-08-11T06:34:44.6726+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
17 of 17 outbound references displayed
- verified exact5
- verified fuzzy0
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 84571932-b608-46c4-a698-5c7953dbcf4f · outbound
This paper cites Aoki and S.-y.
Chebyshev's bias without linear independence Aoki and S.-y
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.514566Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1558eef6-1536-4b2c-bcfb-2b5b36b33351 · outbound
This paper cites de la Bret` eche and D.
Chebyshev's bias without linear independence de la Bret` eche and D
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.520257Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e948a52-cb5e-4605-bb37-08775bc4e711 · outbound
This paper cites de la Bret` eche, D.
Chebyshev's bias without linear independence de la Bret` eche, D
Reference 3
- Resolution
- verified exact
- doi, observed 2026-08-03T13:54:00.379239Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation ea758436-df2d-44ea-be5d-71b1662aaa57 · outbound
This paper cites Chebyshev, Lettre de M.
Chebyshev's bias without linear independence Chebyshev, Lettre de M
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.530529Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 56b6f31c-3bbd-4bf3-8bfa-9db8241edaac · outbound
This paper cites Conrad, Partial Euler products on the critical line , Canad.
Chebyshev's bias without linear independence Conrad, Partial Euler products on the critical line , Canad
Reference 5
- Resolution
- verified exact
- doi, observed 2026-08-03T13:54:00.225601Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 2fa3a5d5-f672-40b7-b9e7-e295efedb84c · outbound
This paper cites Devin, Chebyshev’s bias for analytic L-functions, Math.
Chebyshev's bias without linear independence Devin, Chebyshev’s bias for analytic L-functions, Math
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.542111Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 32b9e8ad-cff5-4bb2-aaea-fc6577be92c3 · outbound
This paper cites Fiorilli and F.
Chebyshev's bias without linear independence Fiorilli and F
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.547468Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f162fd8a-8928-48e9-a5fc-089052be3bea · outbound
This paper cites Hooley, On the Barban-Davenport-Halberstam theorem.
Chebyshev's bias without linear independence Hooley, On the Barban-Davenport-Halberstam theorem
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.554724Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5c194911-31ce-4992-b845-d6c96120a476 · outbound
This paper cites Kaczorowski, On the distribution of primes (mod 4), Analysis 15 (1995), no.
Chebyshev's bias without linear independence Kaczorowski, On the distribution of primes (mod 4), Analysis 15 (1995), no
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.559627Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8a5def61-0136-4fb1-86b0-940a3a6c241a · outbound
This paper cites Koyama and N.
Chebyshev's bias without linear independence Koyama and N
Reference 10
- Resolution
- verified exact
- doi, observed 2026-08-03T13:54:00.096985Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 6d8f73f5-4a25-4c0a-aa05-407dd860bb7b · outbound
This paper cites an unresolved cited work.
Chebyshev's bias without linear independence Unresolved cited work
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.569112Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation da84e0ea-bb5c-4f4e-9aef-fa6845e3f749 · outbound
This paper cites an unresolved cited work.
Chebyshev's bias without linear independence Unresolved cited work
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.573426Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 76b4d97f-23ec-4473-af83-a2e41ec5fb5f · outbound
This paper cites an unresolved cited work.
Chebyshev's bias without linear independence Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.578003Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3a0a8b77-8557-4c44-a457-6e47fa2c3bb9 · outbound
This paper cites Puchta, On large oscillations of the remainder of the prime number th eorems, Acta Math.
Chebyshev's bias without linear independence Puchta, On large oscillations of the remainder of the prime number th eorems, Acta Math
Reference 14
- Resolution
- verified exact
- doi, observed 2026-08-03T13:53:59.927826Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 54c05722-3d1d-4d1b-9519-bb21f7a2a053 · outbound
This paper cites Rubinstein and P.
Chebyshev's bias without linear independence Rubinstein and P
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.587144Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f59cfbb6-5a4e-4949-897c-43944d9439de · outbound
This paper cites Sheth, Euler products at the centre and applications to Chebyshev’ s bias , Math.
Chebyshev's bias without linear independence Sheth, Euler products at the centre and applications to Chebyshev’ s bias , Math
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T13:52:00.592188Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0e16e8ab-94f2-49ec-a965-f67e0fc6999c · outbound
This paper cites Suzuki, On variants of Chebyshev’s conjecture , Ramanujan J.
Chebyshev's bias without linear independence Suzuki, On variants of Chebyshev’s conjecture , Ramanujan J
Reference 17
- Resolution
- verified exact
- doi, observed 2026-08-03T13:53:59.812896Z
Source-reported events for the cited work
correction dated 2025-12-19. Source: crossref record 10.1007/s11139-025-01289-y->10.1007/s11139-025-01238-9:correction, observed 2026-07-11T02:58:06.126977+00:00. This notice travels one citation hop only.
Pith citing papers
No inbound Pith citation observations are available.