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Paper Citation Record · LEDGER

Goldbach's Problem in short intervals for numbers with a missing digit

As of 22 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 0 inbound Pith citation observations for arXiv:2412.19975.

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

pith.paper-citation-record.v1
2412.19975 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:55:56.753284Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

17 of 17 outbound references displayed

  • verified exact0
  • verified fuzzy17
  • unresolved0
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5632002a-e9ef-4a92-b55c-69eb90cfc43d · outbound

This paper cites Banks, Alessandro Conflitti, and Igor E.

Goldbach's Problem in short intervals for numbers with a missing digit Banks, Alessandro Conflitti, and Igor E

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:57.028869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.678642Z digest=sha256:1ffaa5a8c9572794e1035ee476edbe2c07acef77b6b116f512d6663505b1edc7

Observation 380bd6f7-9a94-4b02-a6a2-b40223b0751f · outbound

This paper cites Digitally restricted sets and the go ldbach conjecture: An exceptional set result, 2024.

Goldbach's Problem in short intervals for numbers with a missing digit Digitally restricted sets and the go ldbach conjecture: An exceptional set result, 2024

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:57.014047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.683639Z digest=sha256:742442b75f00b256adc6b3ad6e0fa97f88b13c4600a295ef9f47a72b73e0b8e7

Observation ab1bfcb6-5c88-42fa-b89c-e3e9749f1aea · outbound

This paper cites Nombres presque p remiers dont l’écriture en base r ne comporte pas certains chiffres.

Goldbach's Problem in short intervals for numbers with a missing digit Nombres presque p remiers dont l’écriture en base r ne comporte pas certains chiffres

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.999876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.688533Z digest=sha256:558ed7b51f40831dd0c02be9f74899a90c2fd5b1db5efd3c08133a9da37d3ce5

Observation e4fb5330-fc84-408f-b9e3-e0a238ea2dda · outbound

This paper cites Ensembles de den sitĂŠ nulle contenant des entiers possĂŠdant au plus deux facteurs premiers.

Goldbach's Problem in short intervals for numbers with a missing digit Ensembles de den sitĂŠ nulle contenant des entiers possĂŠdant au plus deux facteurs premiers

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.985385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.693160Z digest=sha256:fd1064a47f2247bd628dcb60ee7af9196a2b36fbc56d945f83f75aa7be203d43

Observation f254b76f-0ccb-49ea-a059-99d34540ba1b · outbound

This paper cites On ar ithmetic properties of integers with missing digits.

Goldbach's Problem in short intervals for numbers with a missing digit On ar ithmetic properties of integers with missing digits

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.971353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.697826Z digest=sha256:d5fe3d952320b521dbd03c6923069579eb0b3a0e1c7d3a8173b01febe1001532

Observation 35e416c2-556e-4182-b65d-72f1cb9bfab6 · outbound

This paper cites On ar ithmetic properties of integers with missing digits.

Goldbach's Problem in short intervals for numbers with a missing digit On ar ithmetic properties of integers with missing digits

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.957552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.703072Z digest=sha256:777dbfad87df0306003226900a621356fcef8a41291ce442c37485e8d416fe9d

Observation 46cb747c-6128-42b7-9bac-2e00404dc1c9 · outbound

This paper cites Prime-detecting sieves, volume 33 of London Mathematical Society Monographs Series.

Goldbach's Problem in short intervals for numbers with a missing digit Prime-detecting sieves, volume 33 of London Mathematical Society Monographs Series

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.943770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.708486Z digest=sha256:e3d20117b3126cf4c31dbec6c12e931c90a9612890edc2393c27aabe5e608280

Observation 378e7435-142d-4aa1-9725-88ea64682068 · outbound

This paper cites On Linnik’s constant.

Goldbach's Problem in short intervals for numbers with a missing digit On Linnik’s constant

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.928617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.712959Z digest=sha256:3c6d6ed6f184422d74c148077d9c3d94d61e70829ff79252795bb0b700b11dfc

Observation 7b53e7ed-4904-4424-83bb-71be32d88b2d · outbound

This paper cites The divisor function over integers with a mi ssing digit, 2024.

Goldbach's Problem in short intervals for numbers with a missing digit The divisor function over integers with a mi ssing digit, 2024

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.914132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.717601Z digest=sha256:2dc59cb5c4bf862153c16047e91781656e8259a1e2d7a050daf7c782c0a4791b

Observation 67886927-eff7-401f-bd41-4a7838349461 · outbound

This paper cites Arithmetic properties of integers wi th missing digits: distribution in residue classes.

Goldbach's Problem in short intervals for numbers with a missing digit Arithmetic properties of integers wi th missing digits: distribution in residue classes

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.899652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.722037Z digest=sha256:790f94f8c9387908f0e89390bb77d742aee5596ae3afe55af47f08828e982afe

Observation a960d15b-823a-4b7d-9579-ca3e70120649 · outbound

This paper cites Higher uniformity of arithmetic functions in short interva ls ii.

Goldbach's Problem in short intervals for numbers with a missing digit Higher uniformity of arithmetic functions in short interva ls ii

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.884825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.726619Z digest=sha256:9f70dd60c62d09c8527306166fe611c88985971a38c8fabf85293ea6437bcb1b

Observation 2fc771cf-ddd2-4e04-9cfa-443c4355c25a · outbound

This paper cites Discorrelation bet ween primes in short intervals and polynomial phases.

Goldbach's Problem in short intervals for numbers with a missing digit Discorrelation bet ween primes in short intervals and polynomial phases

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.869346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.730936Z digest=sha256:ba4bfc54d8c0b96b4fbe2352fdd3d4647dbae92064b6b8b4ba2ea1557eb3b1b9

Observation 6e88de2c-83d8-48d8-92b3-6b5e0c5058ec · outbound

This paper cites Higher uniformity of arithmetic functions in short intervals I.

Goldbach's Problem in short intervals for numbers with a missing digit Higher uniformity of arithmetic functions in short intervals I

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.853055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.735365Z digest=sha256:8a0dca9f5b92953c2ff66d292bb48390560ce64abc2b7bc6748c467ba8238fb6

Observation 82436443-11f3-4946-b6d0-6d2581ab33c3 · outbound

This paper cites Primes with restricted digits.

Goldbach's Problem in short intervals for numbers with a missing digit Primes with restricted digits

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.838858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.740027Z digest=sha256:8712c2257b818e5c2fe6432aa8bf77c664526d1de48305d54a1da997531c2dc2

Observation 9be9da9f-ba69-4735-857f-3ba28964defa · outbound

This paper cites Primes with a missing digit: distribu tion in arithmetic progressions and an application in sieve theory.

Goldbach's Problem in short intervals for numbers with a missing digit Primes with a missing digit: distribu tion in arithmetic progressions and an application in sieve theory

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.824141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.744621Z digest=sha256:97cf967a3fd9ebe20967651451c57770882c7e1d99cf72b15f88d045afe10b7b

Observation 087ae738-fcc4-49df-bd61-42043b5fda14 · outbound

This paper cites Perelli and J.

Goldbach's Problem in short intervals for numbers with a missing digit Perelli and J

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.805429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.748994Z digest=sha256:188c8b579eb4058985cea6cf6b3b4032e41de01e2f0062ee329fe6e7be187012

Observation 77fd58c7-7686-454e-9821-187c93c1b802 · outbound

This paper cites Higher order Fourier analysis , volume 142 of Graduate Studies in Mathematics.

Goldbach's Problem in short intervals for numbers with a missing digit Higher order Fourier analysis , volume 142 of Graduate Studies in Mathematics

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:55:56.790222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-10T23:55:56.753284Z digest=sha256:67cf5704235bd1c666573f2255d42a64bb773d334ee7863e415b856e435f442f

Pith citing papers

No inbound Pith citation observations are available.