frontiers / frontier

Additive combinatorics: Sidon sets and N(h,k) bounds

id: vfr_496956067dc5ad79
license: CC-BY-4.0
findings: 22
accepted core: 1
contested: 1
links: 0
sources: 22
evidence: 22
avg conf: 0.83

used by 1 · replayed by 1 producer · second seat open

e33/33 · finding.asserted · reviewer:will · 2026-06-03 · null→e123

Source record

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Behrend 1946

id: vs_50a4cd210cbedc58
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
type: paper

source boundary

frontier-owned

declared

finding bindings

record context

1 findings

evidence atoms

materialized

1 atoms

review context

inspectable

1 events

1 reviewable changes and 0 evaluations are attached through this source or its findings.

citation

locator

title:Behrend 1946

imported

2026-05-09T22:52:52.298918+00:00

extraction mode

manual_curation

authors

agent:research-bot-2026-05-09

caveats

No caveats recorded.

Bound findings

Behrend's construction yields subsets of {1,...,N} of size N * exp(-c * sqrt(log N)) containing no nontrivial 3-term arithmetic progression, the densest such known until 2020.
theoretical · vf_11e2e2a19e75887d

Evidence atoms

vea_92db9ae1d5af39f4theoretical · unknown
Behrend's construction yields subsets of {1,...,N} of size N * exp(-c * sqrt(log N)) containing no nontrivial 3-term arithmetic progression, the densest such known until 2020.

Review, event, and evaluation records

events

vev_49d1b9096fd11088finding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_e8f2d600cbebd03dfinding.add
Manual finding added to frontier state
applied · agent:research-bot-2026-05-09 · 2026-05-09

evaluations

No evaluation rows are attached.