Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T15:00:37.396217Z
Paper Citation Record · LEDGER
Bounds for sets of remainders
As of 11 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2508.20853.
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
10 of 10 outbound references displayed
- verified exact3
- verified fuzzy2
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch1
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 50012651-c136-4353-a319-3ee83868541a · outbound
This paper cites On the length of Pierce expansions.
Bounds for sets of remainders On the length of Pierce expansions
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T15:00:37.788172Z
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 d8a1d624-9514-47f2-95bf-0e49877548f1 · outbound
This paper cites Erd˝ os and J.
Bounds for sets of remainders Erd˝ os and J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:00:37.830440Z
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 c8ba7045-aee5-4b56-99dc-05dda1bc9179 · outbound
This paper cites Hoseana and R.
Bounds for sets of remainders Hoseana and R
Reference 3
- Resolution
- metadata mismatch
- raw_fallback, observed 2026-08-05T15:00:37.775140Z
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 df40e7a2-ec22-4c99-87a9-02e7a965fa1f · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 4
- Resolution
- verified exact
- raw_fallback, observed 2026-08-05T15:00:37.702890Z
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 3382ff15-9fcd-4df6-97ce-14ccab75e761 · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:00:37.819648Z
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 a44f0a82-0f32-4de0-b064-aced4eb8f540 · outbound
This paper cites The On-Line Encyclopedia of Integer Sequences, 2025.
Bounds for sets of remainders The On-Line Encyclopedia of Integer Sequences, 2025
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T15:00:37.809589Z
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 6a195032-9b99-4f40-93c3-7563851aecc6 · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T15:00:37.387081Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 451aedec-4901-4a04-b7cb-60a765e97fd3 · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T15:00:37.390395Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1e7e61e1-bfbe-4155-9da8-ae56234f2c81 · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T15:00:37.798593Z
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 ff330850-8953-44a3-a929-fbbc4caca2b4 · outbound
This paper cites an unresolved cited work.
Bounds for sets of remainders Unresolved cited work
Reference 10
- Resolution
- verified exact
- doi, observed 2026-08-05T15:00:37.426669Z
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.
Pith citing papers
No inbound Pith citation observations are available.