Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T07:09:39.151897Z
Paper Citation Record · LEDGER
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham
As of 20 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 4 inbound Pith citation observations for arXiv:2601.21442.
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 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-13T12:18:10.165894Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T18:17:33.766357Z
Reference resolution
22 of 22 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved22
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b9f9725f-9161-47f8-a90d-45d6ef0e90a0 · outbound
This paper cites an unresolved cited work.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Unresolved cited work
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.044133Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1e48840d-d725-4131-a69f-333c05db3e2c · outbound
This paper cites Cantor, ¨Uber die einfachen zahlensysteme, Zeitschrift f¨ ur Mathematik und Physik14 (1869), 121–128.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Cantor, ¨Uber die einfachen zahlensysteme, Zeitschrift f¨ ur Mathematik und Physik14 (1869), 121–128
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.050170Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3c220adf-8ac8-45de-be62-f8efdd4f1c36 · outbound
This paper cites de Stainville,M´ elanges d’analyse alg´ ebrique et de g´ eom´ etrie, Courcier, Paris, 1815.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham de Stainville,M´ elanges d’analyse alg´ ebrique et de g´ eom´ etrie, Courcier, Paris, 1815
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.055376Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation caef5d78-207d-44ff-8834-18080478d1f1 · outbound
This paper cites Erd˝ os,Some problems and results on the irrationality of the sum of infinite series, J.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os,Some problems and results on the irrationality of the sum of infinite series, J
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.060774Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 60af746b-b375-4b6e-94ab-40e3ef8c0333 · outbound
This paper cites Erd˝ os,On the irrationality of certain series: problems and results, New advances in tran- scendence theory (Durham, 1986), Cambridge Univ.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os,On the irrationality of certain series: problems and results, New advances in tran- scendence theory (Durham, 1986), Cambridge Univ
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.065851Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9ff9b1d4-84e2-4ffc-9d6a-65f243e7c61f · outbound
This paper cites Erd˝ os and R.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os and R
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.071656Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6a4a5de3-3025-4dbd-85b4-411b330688b9 · outbound
This paper cites Erd˝ os and E.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os and E
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.077293Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a0cce574-f632-4470-992c-ff9cdde78c58 · outbound
This paper cites Erd˝ os and E.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os and E
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.082034Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0d85bb48-e2b1-4576-ad76-8df0b9fa18e2 · outbound
This paper cites Erd˝ os and E.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Erd˝ os and E
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.086930Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3b5bd0c2-9bca-451f-8da7-de8d0d151caa · outbound
This paper cites an unresolved cited work.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Unresolved cited work
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.091488Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9efa6a9e-b07a-4ead-ae4b-bbc09aa7fdf9 · outbound
This paper cites an unresolved cited work.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Unresolved cited work
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.095776Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cf73b1f1-04fb-422c-b279-45a6cf11ddac · outbound
This paper cites Hanˇ cl,Expression of real numbers with the help of infinite series, Acta Arith.59(1991), no.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl,Expression of real numbers with the help of infinite series, Acta Arith.59(1991), no
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.101338Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 325a7048-f11a-4fbf-98b5-9a0d6f1d5cee · outbound
This paper cites Hanˇ cl and F.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl and F
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.109919Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f4d993c1-be1b-4843-9cf5-acbe177e9bd2 · outbound
This paper cites Hanˇ cl and R.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl and R
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.115179Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation dcc8f153-0035-4b78-9ca7-9b8ba31ad536 · outbound
This paper cites Hanˇ cl and S.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl and S
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.119776Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a1a8891c-947e-4e75-a23c-c5803c2a1787 · outbound
This paper cites Hanˇ cl and R.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl and R
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.124067Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc475ec1-faef-4509-a330-9c8daf997daa · outbound
This paper cites Hanˇ cl and R.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Hanˇ cl and R
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.128545Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0a839744-9e5e-4602-b2f6-5205ada7e545 · outbound
This paper cites Kovaˇ c and T.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Kovaˇ c and T
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.132657Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b05ad04b-2337-476d-82cc-e7f91f5dea5b · outbound
This paper cites Mahler,Lectures on transcendental numbers, Lecture Notes in Mathematics, vol.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Mahler,Lectures on transcendental numbers, Lecture Notes in Mathematics, vol
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.136858Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4c32cd40-6b3a-4596-803d-e06a1060093b · outbound
This paper cites Nishioka,Mahler functions and transcendence, Lecture Notes in Mathematics, vol.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Nishioka,Mahler functions and transcendence, Lecture Notes in Mathematics, vol
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.141382Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 82bf1dae-5c03-4f0c-b07f-c3edf6d548df · outbound
This paper cites Oppenheim,Criteria for irrationality of certain classes of numbers, Amer.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Oppenheim,Criteria for irrationality of certain classes of numbers, Amer
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.146585Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3675aaa6-7b67-47fc-a239-87c2686c784a · outbound
This paper cites Tijdeman and P.
Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham Tijdeman and P
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:09:39.151897Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation e61d4f7d-d746-4dd3-a1b4-da51735741a2 · inbound
Automated Conjecture Resolution with Formal Verification cites this paper.
Automated Conjecture Resolution with Formal Verification Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-07-09T02:19:50.716561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f2f04ffa-a3f7-4895-8b29-df61ec3f2ac4 · inbound
Automated Conjecture Resolution with Formal Verification cites this paper.
Automated Conjecture Resolution with Formal Verification Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-07-13T12:18:10.165894Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 789a715a-8f55-4913-a769-fb1fea937968 · inbound
LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization cites this paper.
LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-07-09T02:19:50.716561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e3428f18-54fb-4545-b7df-cb17b671a18f · inbound
From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier cites this paper.
From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier Irrationality of rapidly converging series: a problem of Erd\H{o}s and Graham
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T18:17:33.767569Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.