Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-02T23:38:42.249200Z
Paper Citation Record · LEDGER
Binomial coefficients with divisors avoiding an interval
As of 23 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2605.21221.
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 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
41 of 41 outbound references displayed
- verified exact1
- verified fuzzy18
- unresolved22
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5a26bf9a-5038-49c3-b184-3d61605bd74d · outbound
This paper cites Banks, K.
Binomial coefficients with divisors avoiding an interval Banks, K
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.086535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bdf26310-0da6-4a75-ba79-51e0baeb21ed · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.063778Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5e259261-a69b-43ce-bd8b-609a7ca772a5 · outbound
This paper cites Bourgain and M.
Binomial coefficients with divisors avoiding an interval Bourgain and M
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.065789Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 585edcba-356b-4e00-91a6-d51d35dd1327 · outbound
This paper cites Davenport.Multiplicative number theory, volume 74 ofGraduate Texts in Mathematics.
Binomial coefficients with divisors avoiding an interval Davenport.Multiplicative number theory, volume 74 ofGraduate Texts in Mathematics
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.055025Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f08a12ab-f071-42b1-9da9-6025c7bb6158 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.081213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation acdaf0a6-29ca-4ce2-b4ee-86b9916baf94 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.076576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7a888a02-995e-4156-af2f-6ca7478c278b · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.050668Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 181380f3-96d6-4393-a2e3-c119d93b5c16 · outbound
This paper cites Erd˝ os and R.
Binomial coefficients with divisors avoiding an interval Erd˝ os and R
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.048442Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation c75f4a68-49da-41a2-9e7d-25924dbefc74 · outbound
This paper cites Erd˝ os and R.
Binomial coefficients with divisors avoiding an interval Erd˝ os and R
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.052388Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation e64f4562-8e65-48d9-a112-ebf0cdd0a818 · outbound
This paper cites Erd˝ os and G.
Binomial coefficients with divisors avoiding an interval Erd˝ os and G
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.069477Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7a2fc8e2-7c56-489d-8961-d4c21e475bda · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.042550Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9993c089-c135-4f55-a15f-79b467e12701 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.044334Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1a862e2a-692e-4b82-8356-d71845bc77f7 · outbound
This paper cites Friedlander and H.
Binomial coefficients with divisors avoiding an interval Friedlander and H
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.037996Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 63d6d3e6-2203-44e8-8348-907ccd1d5e66 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.039902Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation b628099f-bec1-48d5-88ea-7ea7ed45c4ef · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.046174Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d5292d8d-8671-40b4-b57c-c0a3275dc342 · outbound
This paper cites Granville.
Binomial coefficients with divisors avoiding an interval Granville
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.056858Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation feba80f8-a55d-40d7-be3d-8d384f8e166a · outbound
This paper cites Granville and O.
Binomial coefficients with divisors avoiding an interval Granville and O
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.058572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8c547a87-b10a-4f52-bc9b-57b32a425b8c · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.061207Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 6fd09427-a53a-466b-8d27-4472db6138e3 · outbound
This paper cites Harborth.
Binomial coefficients with divisors avoiding an interval Harborth
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.067658Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 97828c28-3e13-44fb-992d-a5f4af74b45b · outbound
This paper cites Refinements for primes in short arithmetic progressions.
Binomial coefficients with divisors avoiding an interval Refinements for primes in short arithmetic progressions
Reference 20
- Resolution
- verified exact
- local_arxiv, observed 2026-07-02T23:47:27.264821Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2259e80d-305b-4b77-813f-f0491ecbd7ec · outbound
This paper cites Harman.Prime-detecting sieves, volume 33 ofLondon Mathematical Society Monographs Series.
Binomial coefficients with divisors avoiding an interval Harman.Prime-detecting sieves, volume 33 ofLondon Mathematical Society Monographs Series
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.121500Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f76e3ce6-7ab3-404e-b0dc-cf6ca8b8a0c4 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.117627Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4474ddc3-7afb-414c-92f8-1701c1b9a623 · outbound
This paper cites Hildebrand and G.
Binomial coefficients with divisors avoiding an interval Hildebrand and G
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.110838Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1d70057e-d16a-4396-94ab-a8dcc6e60bd1 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.114881Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 585ac4a0-f7af-40f2-92e0-75c02eb307d1 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.108866Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 10c24755-f24f-456e-a2ae-008f16292468 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.104323Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 142465fd-a647-472c-859c-0f0b9f31fa8b · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.106241Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bb8b3a00-43b7-42d6-9a37-3a8dbda07bed · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.099800Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 16802574-189d-4166-ad07-27fe54791c67 · outbound
This paper cites Iwaniec.Lectures on the Riemann zeta function, volume 62 ofUniversity Lecture Series.
Binomial coefficients with divisors avoiding an interval Iwaniec.Lectures on the Riemann zeta function, volume 62 ofUniversity Lecture Series
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.102290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4426d649-6697-4c2b-ac08-a0e3b8ab5238 · outbound
This paper cites Iwaniec and E.
Binomial coefficients with divisors avoiding an interval Iwaniec and E
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.113095Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 11491642-0b4e-46f8-bc4e-11f902578ce7 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.078684Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f059683b-c25f-42ea-96c0-fa865075f2f5 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.090517Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a5e3851e-352b-41fb-a75e-a61fca193fcb · outbound
This paper cites Matom¨ aki, M.
Binomial coefficients with divisors avoiding an interval Matom¨ aki, M
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.088545Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8defdc8b-8e77-4510-be14-efd0c6310a93 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 34
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.092390Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5018f956-1791-4ac4-8ecc-e0df400ad00d · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.094226Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 595885c0-39cd-4bfa-a8e3-955fd9c4e0fe · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.097869Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 70e10a6d-0859-401f-bed0-e74ff7c70b95 · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.096167Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1a322b8a-084e-4207-9fe2-4919104f8eba · outbound
This paper cites an unresolved cited work.
Binomial coefficients with divisors avoiding an interval Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-07-05T17:41:18.119340Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 165379fa-3508-4d45-8c78-1ca4761afa90 · outbound
This paper cites S´ ark¨ ozy.
Binomial coefficients with divisors avoiding an interval S´ ark¨ ozy
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.083640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5600f502-2d17-4320-8699-1e7055e6f77e · outbound
This paper cites Schinzel.
Binomial coefficients with divisors avoiding an interval Schinzel
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.071729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0c64369f-836d-4233-b745-bd20abce4b02 · outbound
This paper cites Velammal.
Binomial coefficients with divisors avoiding an interval Velammal
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-05T17:41:18.073816Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.