Paper Citation Record · LEDGER

Mean value theorems with smooth numbers

As of 13 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2506.22192.

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

pith.paper-citation-record.v1
2506.22192 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:25:33.035610Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

21 of 21 outbound references displayed

verified exact2
verified fuzzy14
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e751408-7fa4-422d-80b7-23af9b8c9f4c · outbound

This paper cites Aistleitner, G.

Mean value theorems with smooth numbers Aistleitner, G

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:36.704120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 877c0cbd-83b3-4883-afbf-90ed58ab2c85 · outbound

This paper cites an unresolved cited work.

Mean value theorems with smooth numbers Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:25:36.507538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8befbf10-4059-4538-9535-d4f063cfbed2 · outbound

This paper cites an unresolved cited work.

Mean value theorems with smooth numbers Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:25:36.362250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cf9ec87f-ab20-4439-b6ca-0502ff5cdc11 · outbound

This paper cites Blomer and J.

Mean value theorems with smooth numbers Blomer and J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:36.236128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3217402a-1804-41fa-8317-f50d6e8bda83 · outbound

This paper cites an unresolved cited work.

Mean value theorems with smooth numbers Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:25:36.075980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 67b8bd57-84d7-4e16-82c6-194234b6dbac · outbound

This paper cites Bourgain, M.

Mean value theorems with smooth numbers Bourgain, M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.941029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0ddec4bd-e950-475b-96e6-4ea4d3827d81 · outbound

This paper cites Br¨ udern and T.

Mean value theorems with smooth numbers Br¨ udern and T

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.800933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f0acccb0-7280-44a9-944d-c798800743c8 · outbound

This paper cites an unresolved cited work.

Mean value theorems with smooth numbers Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:25:35.661540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 746013e0-a124-4670-8dd8-1442d9d0bacc · outbound

This paper cites de la Bret` eche, ‘Sommes d’exponentielles et entiers sans grand facteur pre- mier’, Proc.

Mean value theorems with smooth numbers de la Bret` eche, ‘Sommes d’exponentielles et entiers sans grand facteur pre- mier’, Proc

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.507180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 001366dd-a71d-4b0b-8215-a0ddd901a7ab · outbound

This paper cites de la Bret` eche and A.

Mean value theorems with smooth numbers de la Bret` eche and A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.356618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e2a58117-dfd5-49c5-8ef0-0f59a7d7e0c0 · outbound

This paper cites de la Bret` eche and and G.

Mean value theorems with smooth numbers de la Bret` eche and and G

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.203069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 30ff0090-f9f6-4ce3-af03-bc93c90c8a41 · outbound

This paper cites Drappeau, ‘Sommes friables d’exponentielles et applications’, Canad.

Mean value theorems with smooth numbers Drappeau, ‘Sommes friables d’exponentielles et applications’, Canad

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:35.056335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c7a1f890-0efb-4ebd-9644-e990efaca4de · outbound

This paper cites Drappeau and X.

Mean value theorems with smooth numbers Drappeau and X

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:34.904662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c2d9cd59-f2aa-42b6-9e56-cc94c5f528c7 · outbound

This paper cites Exponential sums over integers without large prime divisors.

Mean value theorems with smooth numbers Exponential sums over integers without large prime divisors

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:25:33.493224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3fe71e3b-4d2c-47e0-9ec1-ecc483dce8a2 · outbound

This paper cites Fouvry and G.

Mean value theorems with smooth numbers Fouvry and G

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:34.737412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5a3fee4c-e2e1-4e1c-9b91-beee7579050c · outbound

This paper cites Granville, ‘On positive integers ď x with prime factors ď t log x’, Number Theory and Applications (Banff, AB, 1988) , NATO Adv.

Mean value theorems with smooth numbers Granville, ‘On positive integers ď x with prime factors ď t log x’, Number Theory and Applications (Banff, AB, 1988) , NATO Adv

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:34.518175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9a4827c2-d0aa-4cf3-ae50-0dc5a29d48c9 · outbound

This paper cites Granville, ‘Smooth numbers: Computational number theory and beyond’, Proc.

Mean value theorems with smooth numbers Granville, ‘Smooth numbers: Computational number theory and beyond’, Proc

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:34.342846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8ad3f28b-2d37-4a86-9872-3e97f41224d7 · outbound

This paper cites an unresolved cited work.

Mean value theorems with smooth numbers Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:25:34.098205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d67a8268-a8e2-409e-9d13-2deb922ca2d5 · outbound

This paper cites Hildebrand and G.

Mean value theorems with smooth numbers Hildebrand and G

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:33.907673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation fac8112c-038d-48d6-a278-5898df16dac9 · outbound

This paper cites Smooth numbers are orthogonal to nilsequences.

Mean value theorems with smooth numbers Smooth numbers are orthogonal to nilsequences

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-06T22:25:33.279166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 240d123f-cfb6-4d85-8287-0f6187bbf086 · outbound

This paper cites Mohammadi, A.

Mean value theorems with smooth numbers Mohammadi, A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:25:33.714126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.