Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:57:23.337428Z
Paper Citation Record · LEDGER
Every real number is a sum of two real numbers with diverging partial quotients
As of 13 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 1 inbound Pith citation observation for arXiv:2507.04521.
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 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-27T17:38:49.983205Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-02T23:57:28.791336Z
Reference resolution
8 of 8 outbound references displayed
- verified exact1
- verified fuzzy5
- unresolved2
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1f18bdaa-cf51-4f05-b500-45187a56d35c · outbound
This paper cites an unresolved cited work.
Every real number is a sum of two real numbers with diverging partial quotients Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:57:24.693365Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4c54881f-7b64-4435-9ddc-132cbe3b589c · outbound
This paper cites Representations of real numbers as sums and products of Liouville numbers.
Every real number is a sum of two real numbers with diverging partial quotients Representations of real numbers as sums and products of Liouville numbers
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:57:24.553967Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 39a9abdb-5acb-457d-94e9-ee6141968bf9 · outbound
This paper cites an unresolved cited work.
Every real number is a sum of two real numbers with diverging partial quotients Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:57:24.369935Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c556ec2c-6859-4a31-b824-4255a1becd68 · outbound
This paper cites On the sum and product of continued fractions.Annals of Mathematics, 48(4):966–993, 1947.
Every real number is a sum of two real numbers with diverging partial quotients On the sum and product of continued fractions.Annals of Mathematics, 48(4):966–993, 1947
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:57:24.230573Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e8bdcb0e-17fb-439c-b7d2-0799ecc862e5 · outbound
This paper cites Continued fractions.
Every real number is a sum of two real numbers with diverging partial quotients Continued fractions
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:57:24.097789Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1f44fbed-421f-44ea-ada4-8ab50ebaa2ca · outbound
This paper cites Rockett and Peter Sz¨ usz.Continued fractions.
Every real number is a sum of two real numbers with diverging partial quotients Rockett and Peter Sz¨ usz.Continued fractions
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:57:23.943733Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 876ec701-cd5a-4f79-a118-bb826bb74c6a · outbound
This paper cites Schmidt.Diophantine approximation, volume 785 ofLecture Notes in Mathe- matics.
Every real number is a sum of two real numbers with diverging partial quotients Schmidt.Diophantine approximation, volume 785 ofLecture Notes in Mathe- matics
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:57:23.772433Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c2fa8c29-a79f-4cc0-8701-5bad79b4cf10 · outbound
This paper cites On a Conjecture of Cusick on a sum of Cantor sets.
Every real number is a sum of two real numbers with diverging partial quotients On a Conjecture of Cusick on a sum of Cantor sets
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T19:57:23.584899Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation d51b030e-fda1-4e12-ae96-58e96e64c54f · inbound
The Dirichlet spectrum with respect to $L_1$ norm is $\left[\frac12,1\right]$ cites this paper.
The Dirichlet spectrum with respect to $L_1$ norm is $\left[\frac12,1\right]$ Every real number is a sum of two real numbers with diverging partial quotients
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T23:57:28.792576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.