Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-10T00:40:37.969330Z
Paper Citation Record · LEDGER
Entropy lower bounds and sum-product phenomena
As of 10 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2604.20233.
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 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T14:55:05.012043Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
29 of 29 outbound references displayed
- verified exact5
- verified fuzzy24
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 7f014c36-1ea0-43bd-853a-4c1ed7696186 · outbound
This paper cites Growth estimates in positive characteristic via collisions.
Entropy lower bounds and sum-product phenomena Growth estimates in positive characteristic via collisions
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.212286Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1ced7992-78e9-49c3-a7a6-8c0a9434436b · outbound
This paper cites Extracting randomness using few independent sources.
Entropy lower bounds and sum-product phenomena Extracting randomness using few independent sources
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.220527Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation b381a8cb-916f-4530-a3be-b42be5a86874 · outbound
This paper cites An improved sum-product bound for quaternions.
Entropy lower bounds and sum-product phenomena An improved sum-product bound for quaternions
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.207471Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 81c834ab-c1b8-41c2-9a1e-eac3418f6e48 · outbound
This paper cites Control and its applications in additive combinatorics.
Entropy lower bounds and sum-product phenomena Control and its applications in additive combinatorics
Reference 4
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T13:46:03.575641Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ca528028-12b8-4be6-b055-0b350aad1681 · outbound
This paper cites Recherches sur les nombres.
Entropy lower bounds and sum-product phenomena Recherches sur les nombres
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.217380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f6337866-5b08-4b68-bde1-1fbdaccb2379 · outbound
This paper cites Elements of Information Theory (New York: John Wiley and Sons, 2nd edition, 2006).
Entropy lower bounds and sum-product phenomena Elements of Information Theory (New York: John Wiley and Sons, 2nd edition, 2006)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.186048Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation f6d82d3b-1291-4c94-ae74-f374a546bab2 · outbound
This paper cites On the addition of residue classes.
Entropy lower bounds and sum-product phenomena On the addition of residue classes
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.174770Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 142a5003-0713-4e2a-b3cb-b36c78efaada · outbound
This paper cites A short proof of Rudnev's point-plane incidence bound.
Entropy lower bounds and sum-product phenomena A short proof of Rudnev's point-plane incidence bound
Reference 8
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T13:46:03.677743Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1d134952-51cc-49ad-a84c-73ae5b06c06c · outbound
This paper cites Marton's Conjecture in abelian groups with bounded torsion.
Entropy lower bounds and sum-product phenomena Marton's Conjecture in abelian groups with bounded torsion
Reference 9
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T13:46:03.635992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0b41e6e9-2610-4323-8892-cf67bde38f55 · outbound
This paper cites On a conjecture of Marton.
Entropy lower bounds and sum-product phenomena On a conjecture of Marton
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.167080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation fa8b17ea-6c4f-48b8-aac6-73b3898b6f98 · outbound
This paper cites Entropy and the discrete central limit theorem.
Entropy lower bounds and sum-product phenomena Entropy and the discrete central limit theorem
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.190751Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6ec7c561-49aa-4e15-a47c-c85b5842eb5b · outbound
This paper cites Sumsets and entropy revisited.
Entropy lower bounds and sum-product phenomena Sumsets and entropy revisited
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.161675Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ebd6defd-4cc4-4476-b0e0-692e55a32d17 · outbound
This paper cites On an entropic analogue of additive energy.
Entropy lower bounds and sum-product phenomena On an entropic analogue of additive energy
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-05-27T15:06:19.979776Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 68c9a086-9969-4f76-9c11-39e5f91e7dd5 · outbound
This paper cites A new entropy power inequality for integer-valued random variables.
Entropy lower bounds and sum-product phenomena A new entropy power inequality for integer-valued random variables
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.170570Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation b64353a3-8a0c-4b28-a6cb-adfdab151839 · outbound
This paper cites Sumset and inverse sumset inequalities for differential entropy and mutual information.
Entropy lower bounds and sum-product phenomena Sumset and inverse sumset inequalities for differential entropy and mutual information
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.153029Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 420b92dd-39dc-494e-b358-1ed13055dfb9 · outbound
This paper cites Exponential sum estimates over prime fields.
Entropy lower bounds and sum-product phenomena Exponential sum estimates over prime fields
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.158185Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 80e703cf-7aa7-442b-8d81-51b1c1e1b276 · outbound
This paper cites S zemerédi– T rotter-type theorems in dimension 3.
Entropy lower bounds and sum-product phenomena S zemerédi– T rotter-type theorems in dimension 3
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.149430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation c1cca4f0-ee82-49bc-b52b-8c33ced865d8 · outbound
This paper cites Entropic additive energy and entropy inequalities for sums and products.
Entropy lower bounds and sum-product phenomena Entropic additive energy and entropy inequalities for sums and products
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.177950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation abe95c0a-00c6-4e06-aed0-0afb5dc5bf48 · outbound
This paper cites An improved sum-product estimate for general finite fields.
Entropy lower bounds and sum-product phenomena An improved sum-product estimate for general finite fields
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.193763Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation a47244ec-6216-41b5-b660-8a602c5c85bc · outbound
This paper cites Discretised sum-product theorems by Shannon-type inequalities.
Entropy lower bounds and sum-product phenomena Discretised sum-product theorems by Shannon-type inequalities
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.201391Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5b3a3866-f4d0-4501-bc31-edf58ebe7fe3 · outbound
This paper cites ``Sum-product in finite fields via entropy.'' Blog post at https://pohoatza.wordpress.com/2026/01/12/sum-product-in-finite -fields-via-entropy , January 12 (2026).
Entropy lower bounds and sum-product phenomena ``Sum-product in finite fields via entropy.'' Blog post at https://pohoatza.wordpress.com/2026/01/12/sum-product-in-finite -fields-via-entropy , January 12 (2026)
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.141564Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 714576f3-5f13-40d6-aab0-60cea7852c97 · outbound
This paper cites Raghavan,Improved Bounds for the Freiman-Ruzsa Theorem.
Entropy lower bounds and sum-product phenomena Raghavan,Improved Bounds for the Freiman-Ruzsa Theorem
Reference 22
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T13:46:03.641963Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation df0b7ddf-72fc-4202-b7c4-67fa06bd2579 · outbound
This paper cites On the M inkowski distances and products of sum sets.
Entropy lower bounds and sum-product phenomena On the M inkowski distances and products of sum sets
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.137017Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 6ee0e7e7-be06-49ba-adb1-686652ff3470 · outbound
This paper cites Sumsets and entropy.
Entropy lower bounds and sum-product phenomena Sumsets and entropy
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.182566Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 63a0d57a-f351-4e8e-8c2e-05f68916482a · outbound
This paper cites A mathematical theory of communication.
Entropy lower bounds and sum-product phenomena A mathematical theory of communication
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.133345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation eb40d3fb-a28a-4bae-9802-0bd4c67c20b2 · outbound
This paper cites Some inequalities satisfied by the quantities of information of F isher and S hannon.
Entropy lower bounds and sum-product phenomena Some inequalities satisfied by the quantities of information of F isher and S hannon
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.123263Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ed5efdc3-eb2e-4c31-b5f1-3418d12c1968 · outbound
This paper cites Sumset and inverse sumset theory for S hannon entropy.
Entropy lower bounds and sum-product phenomena Sumset and inverse sumset theory for S hannon entropy
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.144950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation c1f5b123-8001-4966-a9e3-7c1bad5c4867 · outbound
This paper cites John-type theorems for generalized arithmetic progressions and iterated sumsets.
Entropy lower bounds and sum-product phenomena John-type theorems for generalized arithmetic progressions and iterated sumsets
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.128610Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 0d35d617-43e0-4a39-9c76-94c888c66007 · outbound
This paper cites Pseudorandomness.
Entropy lower bounds and sum-product phenomena Pseudorandomness
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T10:52:53.198207Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Pith citing papers
Observation c83b36f6-b798-4fc7-96c7-618d7a2b2673 · inbound
The Entropic Sum-Product Phenomenon cites this paper.
The Entropic Sum-Product Phenomenon Entropy lower bounds and sum-product phenomena
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T14:55:05.012043Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.