Paper Citation Record · LEDGER

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity

As of 11 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2607.04166.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2607.04166 v3

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T08:47:18.091985Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

verified exact0
verified fuzzy0
unresolved29
parse uncertain0
malformed identifier1
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External citation measurements

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Outbound references

Observation d36d4be5-3f53-40ba-b7a5-af39089c002d · outbound

This paper cites Bounded gaps between primes in short intervals.Preprint, pages 1–29,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Bounded gaps between primes in short intervals.Preprint, pages 1–29,

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:16.884989Z

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Observation d3b3d6d7-5999-4ade-bc51-46b7e36f5137 · outbound

This paper cites Effective estimates for some functions defined over primes.Integers, 24:227–251, 2024.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Effective estimates for some functions defined over primes.Integers, 24:227–251, 2024

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.144953Z

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Observation 413a71d1-5fe5-4b69-9e6f-6bc399bcd233 · outbound

This paper cites an unresolved cited work.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.175788Z

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Observation d21ef985-cab4-43bd-934f-5f5acbc24b52 · outbound

This paper cites Scrambled Linear Pseudorandom Number Generators.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Scrambled Linear Pseudorandom Number Generators

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.338363Z

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Observation 8f175c40-6e30-40aa-b0c6-f7ee27e1e3c2 · outbound

This paper cites A random analogue of Gilbreath’s conjecture.Mathematische Annalen, 388:2611—-2625,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity A random analogue of Gilbreath’s conjecture.Mathematische Annalen, 388:2611—-2625,

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.565100Z

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Observation 03acca3b-b3e0-4259-b656-9a3a3dd13001 · outbound

This paper cites Gilbreath's conjecture: a Cram\'er random model and a deterministic analysis.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Gilbreath's conjecture: a Cram\'er random model and a deterministic analysis

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.684019Z

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Observation 953c418f-c430-459d-99ba-547295d75ebb · outbound

This paper cites Generation of multivariate discrete data with generalized Poisson, negative binomial and binomial marginal distributions.Preprint, pages 1–19, 2026.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Generation of multivariate discrete data with generalized Poisson, negative binomial and binomial marginal distributions.Preprint, pages 1–19, 2026

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.775647Z

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Observation 437f8c5e-0ed6-411c-b56b-7b1ab13cd536 · outbound

This paper cites Random sieves and generalized leader- election.Austrian Journal of Statistics, 52:13–25, 2023.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Random sieves and generalized leader- election.Austrian Journal of Statistics, 52:13–25, 2023

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.936405Z

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Observation 555031f2-4572-4a49-953c-6d69cd7edce4 · outbound

This paper cites Explicit estimates of some functions over primes.The Ramanujan Journal, 45:227–251,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Explicit estimates of some functions over primes.The Ramanujan Journal, 45:227–251,

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:17.992242Z

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Observation 9e5d2a0b-d0a0-4aff-a4e8-c91702e8b021 · outbound

This paper cites Large gaps between consecutive prime numbers.Annals of Mathematics, 183:935–974,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Large gaps between consecutive prime numbers.Annals of Mathematics, 183:935–974,

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.037631Z

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Observation 2c29606b-1477-492f-9945-7fd8bcd228de · outbound

This paper cites Springer, 2023.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Springer, 2023

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.040803Z

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Observation 791f8273-0116-4677-8f34-3e8336597099 · outbound

This paper cites Goldston, J´ anos Pintz, and Cem Y.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Goldston, J´ anos Pintz, and Cem Y

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.043591Z

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Observation 00ee82c4-b923-4b24-9df3-485101c9f3da · outbound

This paper cites Harald Cram´ er and the distribution of prime numbers.Scandinavian Actuarial Journal, 1:12–28, 1995.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Harald Cram´ er and the distribution of prime numbers.Scandinavian Actuarial Journal, 1:12–28, 1995

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.047011Z

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Observation 2124d3ef-a604-4d9f-a9ca-eb1f8456a365 · outbound

This paper cites MLT, 2023.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity MLT, 2023

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.049783Z

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Observation b3bbb14c-69ad-40fd-abef-5194dc8bb1aa · outbound

This paper cites MLT, 2026.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity MLT, 2026

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.053204Z

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Observation e49f98c5-ef99-4026-badc-8e629989419b · outbound

This paper cites LLMs Without Deep Neural Networks: New Architecture, Benefits and Case Study.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity LLMs Without Deep Neural Networks: New Architecture, Benefits and Case Study

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.055950Z

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Observation 728f3627-87c2-4d97-b31e-a7c7d3c8fff1 · outbound

This paper cites Cycles and patterns in the sieve of Eratosthenes.Preprint, pages 1–18, 2019.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Cycles and patterns in the sieve of Eratosthenes.Preprint, pages 1–18, 2019

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.059143Z

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Observation cd1fe494-9a52-494f-ae94-0b9ac9450cbe · outbound

This paper cites an unresolved cited work.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.061802Z

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Observation 6cf26c22-97e6-4b45-9211-d289dc1a6dd1 · outbound

This paper cites The Poisson Tail Conjecture for Primes in Short Intervals.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity The Poisson Tail Conjecture for Primes in Short Intervals

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.064737Z

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Observation 0c156361-a1d7-4da4-85b7-d43fba755434 · outbound

This paper cites Statistical distributions of prime number gaps.Journal of Advances in Mathematics and Computer Science, 39:36–61, 2024.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Statistical distributions of prime number gaps.Journal of Advances in Mathematics and Computer Science, 39:36–61, 2024

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.067226Z

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Observation beb8d1e8-3bf5-46b0-afb2-36578e49f85d · outbound

This paper cites Chains of large gaps between consecutive primes.Advances in Mathematics, 39:257–269,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Chains of large gaps between consecutive primes.Advances in Mathematics, 39:257–269,

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.069727Z

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Observation 6bff2cf7-0ade-493d-8b5a-d5d7f71a2553 · outbound

This paper cites Small gaps between primes.Annals of Mathematics, 181:383–413, 2015.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Small gaps between primes.Annals of Mathematics, 181:383–413, 2015

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.072739Z

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Observation 795dfc97-0d99-446e-a2ce-2685f9e71283 · outbound

This paper cites Holes in Valid-Extension Sets of Finite Gilbreath Sequences.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Holes in Valid-Extension Sets of Finite Gilbreath Sequences

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.075198Z

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Observation 6e9d9f78-be40-46bc-b56b-1293043331e9 · outbound

This paper cites On the distribution of gaps between consecutive primes.The Ramanujan Journal, 45:1–22,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity On the distribution of gaps between consecutive primes.The Ramanujan Journal, 45:1–22,

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.078204Z

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Observation 55fe9031-4f8b-432d-98c4-941fbe0a7b92 · outbound

This paper cites arXiv:2510:06688 [Link].

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity arXiv:2510:06688 [Link]

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.081119Z

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Observation 25e517b1-49be-4351-a948-0097a8d366eb · outbound

This paper cites Large gaps between consecutive prime numbers.Terence Tao’s Blog, 2014.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Large gaps between consecutive prime numbers.Terence Tao’s Blog, 2014

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.083816Z

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Observation dd9542dd-fd34-4456-99e7-20152063ae46 · outbound

This paper cites On the maximal gap between primes.Preprint, pages 1–8, 2025.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity On the maximal gap between primes.Preprint, pages 1–8, 2025

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.086541Z

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Observation bda925b0-d280-4acb-b8e1-cbff5b48c9e9 · outbound

This paper cites On differences between consecutive numbers coprime to primorials.Preprint, pages 1–14,.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity On differences between consecutive numbers coprime to primorials.Preprint, pages 1–14,

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:18.089213Z

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Observation 63c7639f-477b-4d21-a1c5-3003c32791db · outbound

This paper cites Bounded gaps between primes in short intervals.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity Bounded gaps between primes in short intervals

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-02T08:47:16.986946Z

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Observation 01b0c0fc-b732-49a2-9ca0-675b89111090 · outbound

This paper cites --- Part 1: gil.check\n.

Piercing Gilbreath's Conjecture: From Deep Number Theory Insights to Fintech and Cybersecurity --- Part 1: gil.check\n

Reference 2020

Resolution: malformed identifier; no resolver link, observed 2026-08-02T08:47:18.091985Z

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Pith citing papers

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