Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:47:58.905817Z
Paper Citation Record · LEDGER
Large prime gaps and probabilistic models
As of 19 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:1908.08613.
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 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-25T05:17:02.131156Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-25T05:20:25.135022Z
Reference resolution
38 of 38 outbound references displayed
- verified exact1
- verified fuzzy22
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 4753f353-7f32-4daf-b6f6-bfdd316499fc · outbound
This paper cites Azuma, Weighted sums of certain dependent random variables , Tˆ ohoku Math.
Large prime gaps and probabilistic models Azuma, Weighted sums of certain dependent random variables , Tˆ ohoku Math
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.330655Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b2055a2a-0e9c-4687-b52a-77ceb8793469 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.320302Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 075760e3-bd49-4423-9f52-7c7312062758 · outbound
This paper cites Bennett, Probability inequalities for the sum of independent random variables, J.
Large prime gaps and probabilistic models Bennett, Probability inequalities for the sum of independent random variables, J
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.310383Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 1381552e-fff1-497e-87e9-a78d04677b64 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.300305Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation fa9fddaf-fadb-4a4d-aa00-bea11c4309ae · outbound
This paper cites Cram´ er,On the order of magnitude of the difference between consecutive prime num- bers, Arkiv f¨ or Mat.
Large prime gaps and probabilistic models Cram´ er,On the order of magnitude of the difference between consecutive prime num- bers, Arkiv f¨ or Mat
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.290007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b350eceb-e35e-4f92-a9bd-6c5288a2f6a8 · outbound
This paper cites Cram´ er,Some theorems concerning prime numbers, Acta Arith.
Large prime gaps and probabilistic models Cram´ er,Some theorems concerning prime numbers, Acta Arith
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.278446Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ed7e3886-b516-4c47-8680-080fde171f25 · outbound
This paper cites Davenport, Multiplicative number theory (3rd edition).
Large prime gaps and probabilistic models Davenport, Multiplicative number theory (3rd edition)
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.268007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c94504e4-ff26-4808-af13-67c9f16e8e14 · outbound
This paper cites Elsholtz, Upper bounds for prime k-tuples of size logN and oscillations , Arch.
Large prime gaps and probabilistic models Elsholtz, Upper bounds for prime k-tuples of size logN and oscillations , Arch
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.257841Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 94a3daf1-3487-4e67-81ea-eaec8f39e201 · outbound
This paper cites Erd˝ os and I.
Large prime gaps and probabilistic models Erd˝ os and I
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.247784Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f65ba451-f974-4dc4-a570-80a5e5c06d66 · outbound
This paper cites Ford, Large prime gaps and progressions with few primes , preprint.
Large prime gaps and probabilistic models Ford, Large prime gaps and progressions with few primes , preprint
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.237660Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c788aef3-9873-495d-b49a-17231dc46e31 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.227276Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2050ffea-7bb7-4db5-85b2-17b7bf9fbbf9 · outbound
This paper cites Friedlander and H.
Large prime gaps and probabilistic models Friedlander and H
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.217023Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 94354d4d-927c-4ed1-9aae-05ebd3616b22 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.206739Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5f371189-a98f-47d0-a341-e7c39231b14e · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.197114Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2f9591f8-58a0-487c-a247-c9fba0b0fb16 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.188104Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bb4ac661-43c5-4341-a450-be8d3b38b023 · outbound
This paper cites Granville, Harald Cram´ er and the distribution of prime numbers, Harald Cram´ er Sym- posium (Stockholm, 1993).
Large prime gaps and probabilistic models Granville, Harald Cram´ er and the distribution of prime numbers, Harald Cram´ er Sym- posium (Stockholm, 1993)
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.177886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 851d631b-36b6-4673-ac6b-e1fcc80e8da4 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.167786Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 4a23abd8-be0c-400b-9195-1bf4f0683eab · outbound
This paper cites Hensley and I.
Large prime gaps and probabilistic models Hensley and I
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.157153Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 866f4073-7a80-4ae3-afca-14bfc9285911 · outbound
This paper cites Iwaniec, On the error term in the linear sieve , Acta Arith.
Large prime gaps and probabilistic models Iwaniec, On the error term in the linear sieve , Acta Arith
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.147183Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 37323308-6ebf-4e04-9832-a5ab753d2ac8 · outbound
This paper cites Iwaniec, Conversations on the exceptional character , in the book Analytic number theory, lectures given at the C.I.M.E.
Large prime gaps and probabilistic models Iwaniec, Conversations on the exceptional character , in the book Analytic number theory, lectures given at the C.I.M.E
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.136729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 92482849-c0c9-400f-b977-c602c1a7998e · outbound
This paper cites Koukoulopoulos, The distribution of prime numbers.
Large prime gaps and probabilistic models Koukoulopoulos, The distribution of prime numbers
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.126833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation e4882d81-0d06-4786-8472-fee60768176c · outbound
This paper cites Leikauf and J.
Large prime gaps and probabilistic models Leikauf and J
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.117551Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation cc40834a-46cd-4a84-90e4-d05b17284c8f · outbound
This paper cites Maier, Primes in short intervals , Michigan Math.
Large prime gaps and probabilistic models Maier, Primes in short intervals , Michigan Math
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.107053Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 45063591-bda0-4e9c-8fc5-cc497e10d4a1 · outbound
This paper cites Positive proportion of short intervals containing a prescribed number of primes.
Large prime gaps and probabilistic models Positive proportion of short intervals containing a prescribed number of primes
Reference 24
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:47:58.941481Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b31c5031-89a6-46bf-81f0-95694b4a63c1 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.096923Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d6feffc1-0e75-42e9-8d8d-2c83422137bb · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.086673Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9edb14d8-6e3d-4707-b266-c6b16ba21e48 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.076602Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5c971e4e-6488-4135-a0b8-f7b28bee86c0 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.066754Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 26906bfa-f813-47b2-9616-a43a0fbe2dee · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.056224Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b2301934-9481-47bc-8359-ee3029649a3a · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.045947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0f1ad655-8bbf-424a-b3ca-55bc997d089f · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.035811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7f5b9944-8756-4b08-9faf-6e422588e3b6 · outbound
This paper cites an unresolved cited work.
Large prime gaps and probabilistic models Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:47:59.024866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 989ea821-dda1-4c85-9237-6d530cf99854 · outbound
This paper cites Pintz, Cram´ er vs.
Large prime gaps and probabilistic models Pintz, Cram´ er vs
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.013926Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bfb1c2d3-c556-49e8-81ad-50f32d008b3f · outbound
This paper cites P´ olya,Heuristic reasoning in the theory of numbers , Amer.
Large prime gaps and probabilistic models P´ olya,Heuristic reasoning in the theory of numbers , Amer
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:59.002019Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 467dc10c-071c-4619-a32c-ee214d97777b · outbound
This paper cites Selberg, On the normal density of primes in small intervals, and the difference between consecutive primes, Arch.
Large prime gaps and probabilistic models Selberg, On the normal density of primes in small intervals, and the difference between consecutive primes, Arch
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:58.990366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b73ea522-e500-4f0f-8501-c27b110e4ac1 · outbound
This paper cites Selberg, Remarks on sieves , Proc.
Large prime gaps and probabilistic models Selberg, Remarks on sieves , Proc
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:58.979733Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c47f7e4b-3700-4892-862a-3dc22828db2e · outbound
This paper cites Shanks, On maximal gaps between successive primes.
Large prime gaps and probabilistic models Shanks, On maximal gaps between successive primes
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:58.966453Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a1309ce6-3eab-44af-95b9-668789950fd6 · outbound
This paper cites Soundararajan, The distribution of prime numbers , in the book Equidistribution in number theory, an introduction , 59–83.
Large prime gaps and probabilistic models Soundararajan, The distribution of prime numbers , in the book Equidistribution in number theory, an introduction , 59–83
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:47:58.954790Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
Observation ca2c7174-af5b-476c-9be4-1b5fb1826978 · inbound
The Poisson Tail Conjecture for Primes in Short Intervals cites this paper.
The Poisson Tail Conjecture for Primes in Short Intervals Large prime gaps and probabilistic models
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-25T05:20:25.138489Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.