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

Evidence atom

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Bourgain's Fourier-analytic increment argument lowers the density threshold for 3-AP existence in {1,...,N} to alpha > C * (log log N)^2 / sqrt(log N).

id: vea_b9ff3d8dd467bcc7
frontier: Additive combinatorics: Sidon sets and N(h,k) bounds
source: vs_4e47b67b4645ebc9
finding: vf_d7781ce5f2c7330a

evidence boundary

unknown

theoretical

finding binding

bound

theoretical

Bourgain's Fourier-analytic increment argument lowers the density threshold for 3-AP existence in {1,...,N} to alpha > C * (log log N)^2 / sqrt(log N).

source binding

source-bound

Bourgain 1999

vs_4e47b67b4645ebc9

review context

unverified

1 events

1 reviewable changes and 0 evaluation records target this atom or its bound objects.

statement

Bourgain's Fourier-analytic increment argument lowers the density threshold for 3-AP existence in {1,...,N} to alpha > C * (log log N)^2 / sqrt(log N).

extraction method

manual_curation

support relation

unknown

condition refs

vcnd_bdba1c64bd88b673

caveats

missing evidence locator

Review, event, and evaluation records

events

vev_fbadbe719c1840d5finding.asserted
Manual finding added to frontier state
agent:research-bot-2026-05-09 · 2026-05-09

reviewable changes

vpr_7092498559ec0e3ffinding.add
Manual finding added to frontier state
applied · agent:research-bot-2026-05-09 · 2026-05-09

evaluations

No evaluation rows are attached.

theoretical

theoretical

Bourgain 1999

1 events

Review, event, and evaluation records

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