Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T10:51:59.555255Z
Paper Citation Record · LEDGER
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
As of 12 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2501.16779.
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 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-28T08:32:26.456964Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-02T05:06:40.075721Z
Reference resolution
31 of 31 outbound references displayed
- verified exact0
- verified fuzzy9
- unresolved22
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 6fee56e7-ddf6-486b-85a1-3e34b614e485 · outbound
This paper cites Bourgain.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:52:00.031430Z
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 c69538d3-25b0-494c-9609-9204132ccae4 · outbound
This paper cites Bourgain.
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:52:00.015460Z
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 c0fd6c21-abf8-400c-adb6-2f42d872fcf6 · outbound
This paper cites Bourgain.
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.999588Z
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 6c3ed643-e3c4-411c-8b7b-42ac9dab9bd2 · outbound
This paper cites Bourgain.
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.985939Z
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 f0432646-a7db-46fd-9c45-30102ea047c6 · outbound
This paper cites Bourgain.
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.971621Z
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 77f64a74-8db8-4abb-b7fa-a30fd871f4c4 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.956871Z
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 b2c732c7-7406-4bcf-97df-93a0edfadb6f · outbound
This paper cites Cladek and T.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Cladek and T
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.942488Z
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 46bfa4ff-1636-4351-a1d9-801bba5035a4 · outbound
This paper cites New large value estimates for Dirichlet polynomials.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach New large value estimates for Dirichlet polynomials
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T10:51:59.449528Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cbb7916f-18cf-43c7-a923-fadb496d61db · outbound
This paper cites Hal\' a sz and P.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Hal\' a sz and P
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.927111Z
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 3b70c1c6-530b-4cb5-ae62-6ed95ba15a35 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.912335Z
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 68a849b8-6714-480c-a4d0-0ff671366c51 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.897152Z
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 8f14e37d-70f8-4382-97eb-81c24ce574ce · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.882270Z
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 4dbb1250-4afa-4829-a662-678a6ed3d5ef · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.867424Z
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 f6e78d2a-971b-4516-9fa5-635470c7aa53 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.852743Z
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 c407127a-8eb6-4e21-b9b6-5fbedb499aab · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.838429Z
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 3b929e4f-1c4e-4174-aecc-c759dc2bd464 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.824535Z
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 18018425-c154-47f5-968f-7b8983b9a171 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.809622Z
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 46357d84-d4ec-40cf-adf8-fafc51c9ac79 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.796382Z
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 6235b37e-4da6-483b-b0e9-a8613510e06c · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.782977Z
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 813dc249-d72e-4d74-84de-4545f797bced · outbound
This paper cites Iwaniec and E.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Iwaniec and E
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.768898Z
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 47d128ee-a79a-473b-b325-a5914e8a1a2f · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.754954Z
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 5f0baee4-e725-406a-965e-fa0b21fa370f · outbound
This paper cites A note on zero density results implying large value estimates for Dirichlet polynomials.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach A note on zero density results implying large value estimates for Dirichlet polynomials
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T10:51:59.513404Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 299fc0a8-c78e-4f05-8129-4311ef7824ba · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.740303Z
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 85c1d576-0db0-4061-9a6d-4169ac0709b9 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.725850Z
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 23f9388c-a30e-4626-86af-c19da40de8e2 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.711294Z
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 edff5d43-a4cd-4636-8877-9fba8d4b7ad6 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.695633Z
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 62328495-9eb2-4506-8615-32629f0f7938 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.681258Z
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 017d1fb1-ca75-4675-bd5d-58f67a5b3f7c · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.667006Z
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 6415fc36-e67d-4502-9c16-0baede4acce9 · outbound
This paper cites Tao and V.
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T10:51:59.650640Z
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 bd7043df-3d07-4d01-9c4a-fc225dac2bf5 · outbound
This paper cites Toward optimal exponent pairs.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Toward optimal exponent pairs
Reference 30
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T10:51:59.550360Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e2ca56fb-6ba0-487d-97ab-1330873cfdb2 · outbound
This paper cites an unresolved cited work.
New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T10:51:59.635213Z
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
Observation 45a6a296-8810-42c7-926b-76834712f3bc · inbound
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ cites this paper.
Pair correlation of $\alpha n^{\theta}$ for random $\theta$ New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach
Reference 33
- Resolution
- verified exact
- arxiv_id, observed 2026-07-02T05:06:40.077483Z
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.